Answers
Step-by-step explanation:
For solving this, it's important to know basic trigonometric functions:
sin = opposite side / hypotenuse
cos = adjacent side / hypotenuse
tan = opposite side / adjacent side
It's also important to know that it is necessary to know their values for special right triangles and angles of 30°, 45° and 60°
1. We are given angle if 45° and its adjacent side of 13. We want to know the opposite side (x) and hypotenuse (y). So:
tan = opposite side / adjacent side
tan 45 = x / 13
1 = x / 13
x = 13
Remember that tangent of 45° angle is 1.
We found the opposite side to be also 13.
To find y we can use:
sin = opposite side / hypotenuse
sin 45 = 13 / y
(√2)/2 = 13 / y
y = 13√2
Important to remember, sin 45 and cos 45 are (√2)/2
2. We are given 45° angle and hypotenuse of 30. We need to find opposite side (x) and adjacent side (y).
sin = opposite side / hypotenuse
sin 45 = x / 30
(√2)/2 = x / 30
x = 15√2
Also:
cos = adjacent side / hypotenuse
cos 45 = y / 30
(√2)/2 = y / 30
y = 15√2
We can conclude that in the right triangle, when angle is 45°, opposite and adjacent sides are equal.
3. We are given angle of 60° and adjacent side of 3. We need to find opposite side (y) and hypotenuse (x).
cos = adjacent side / hypotenuse
cos 60° = 3 / x
1/2 = 3 / x
x = 6
Note that cos 60° equals 1/2.
sin = opposite side / hypotenuse
sin 60° = y / 6
(√3)/2 = y / 6
y = 3√3
Note that sin 60° equals (√3)/2.
4. We are given angle of 30° and hypotenuse of 34. We need to find opposite side (y) and adjacent side (x).
sin = opposite side / hypotenuse
sin 30° = y / 34
1/2 = y / 34
y = 17
Note that sin 30° equals to cos 60° equals 1/2.
cos = adjacent side / hypotenuse
cos 30° = x / 34
(√3)/2 = x / 34
x = 17√3
Remember that cos 30° equals to sin 60° which is (√3)/2.
5. We are given an angle of 45° and hypotenuse of 10√2. We need to find the opposite side (y) and adjacent side (x).
sin = opposite side / hypotenuse
sin 45° = y / 10√2
(√2)/2 = y / 10√2
y = 10
To save time, we already said that opposite and adjacent sides are equal in right triangle with 45° angle, so x = y = 10.
6. We are given angle of 60° and opposite side of 25√3. We need to find adjacent side (y) and hypotenuse (x).
sin = opposite side / hypotenuse
sin 60° = 25√3 / x
(√3)/2 = 25√3 / x
x = 50.
tan = opposite side / adjacent side
tan 60° = 25√3 / y
√3 = 25√3 / y
y = 25.
Remember that tangent of 60° angle is √3.
7. We are given angle of 45° and hypotenuse of 2√14. We need to find adjacent side (x) and opposite side (y).
cos = adjacent side / hypotenuse
cos 45° = x / 2√14
(√2)/2 = x / 2√14
x = √28
Again, adjacent and opposite sides are equal in 45° right triangle, so x = y = √28.
8. We are given an angle of 30° and an adjacent side of 24. We need to find the opposite side (y) and hypotenuse (x).
tan = opposite side / adjacent side
tan 30° = y / 24
(√3)/3 = y / 24
y = 8√3
sin = opposite side / hypotenuse
sin 30° = 8√3 / x
1/2 = 8√3 / x
x = 16√3
Note that tan = sin/cos, so tan 30° = sin 30° / cos 30°
tan 30° = 1/2 / (√3)/2 = (√3)/3
I'm showing you this, so you don't have to memorize tan for special angles, you can find it from sin and cos.
9. We are given an angle of 60° and hypotenuse of 22√3. We need to find the opposite side (y) and adjacent side (x).
sin = opposite side / hypotenuse
sin 60° = y / 22√3
(√3)/2 = y / 22√3
y = 33
cos = adjacent side / hypotenuse
cos 60° = x / 22√3
1/2 = x / 22√3
x = 11√3
10. We are given an angle of 30° and the opposite side of √6. We need to find the adjacent side (x) and hypotenuse (y).
sin = opposite side / hypotenuse
sin 30° = √6 / y
1/2 = √6 / y
y = 2√6
tan = opposite side / adjacent side
tan 30° = √6 / x
(√3)/3 = √6 / x
x = √18
11. We are given an angle of 45° and an adjacent side of √10. We need to find the opposite side (x) and hypotenuse (y).
In this triangle opposite and adjacent sides are equal (45° angle), so x = √10
sin = opposite side / hypotenuse
sin 45° = √10 / y
(√2)/2 = √10 / y
y = √20 = 2√5
12. We are given an angle of 60° and the opposite side of 4√21. We need to find the adjacent side (x) and hypotenuse (y).
sin = opposite side / hypotenuse
sin 60° = 4√21 / y
(√3)/2 = 4√21 / y
y = 8√7
tan = opposite side / adjacent side
tan 60° = 4√21 / x
√3 = 4√21 / x
x = 4√7
13. Now things get a little trickier. We are given an angle of 30° and the opposite side of 17. We need to find the adjacent side (x).
Note that, at the moment, we are only dealing with this smaller triangle.
tan = opposite side / adjacent side
tan 30° = 17 / x
(√3)/3 = 17 / x
x = 17√3
Now, note that hypotenuse of the smaller triangle is the same length as the side z (adjacent and opposite side of 45° angle)
With Pythagorean theorem, we can find the hypotenuse of the smaller triangle, which equals to z.
z = √(17^2 + (17√3)^2)
z = 34
And now, finally to find y (hypotenuse of bigger triangle). We are given 45° angle and adjacent side z (34).
cos = adjacent side / hypotenuse
cos 45° = 34 / y
(√2)/2 = 34 / y
y = 34√2
14. Photo added
Correct responses;
x = 13, y = 13·√2x = 15·√2, y = 15·√2x = 6, y = 3·√3x = 17·√3, y = 17x = 10, y = 10x = 50, y = 25x = 2·√17, y = 2·√17x = 16·√3, y = 8·√3x = 33, y = 11·√3x = 3·√2, y = 2·√6x = √10, y = 2·√5x = 4·√7, y = 8·√7x = 17·√3, y = 34·√2, z = 34x = 18·√3, y = 18, z = 9Methods used for finding the above valuesSolutions:
1. An acute angle of the right triangle is 45°, therefore, the triangle is an isosceles triangle, and the leg lengths are equal.
Therefore;
x = 13The length of the hypotenuse side of an isosceles right triangle = A leg length × √2
Therefore;
The length of the hypotenuse side, y = 13·√22. An interior angle of the triangle = 45°
Therefore;
x = y
30 = x·√2
Which gives;
[tex]x = \dfrac{30}{\sqrt{2} } = \dfrac{30 \cdot \sqrt{2} }{2} = \mathbf{15 \cdot \sqrt{2}} = y[/tex]
x = y = 15·√23. The interior angle adjacent to the leg of length 3 = 60°
Therefore;
The hypotenuse side, x = 2 × adjacent leg length
Which gives;
x = 2 × 3 = 6In a right triangle having an interior angle of 60°, we have;
2 × Opposite leg length = √3 × The length of the hypotenuse
Therefore;
2 × y = √3 × x
Which gives;
2 × y = √3 × 6
y = 3·√34. The leg lengths are, x and y
An interior angle opposite to the leg length y is 30°
The hypotenuse side = 34
The length of the hypotenuse side = 2 × The leg length opposite the 30° angle
Therefore;
34 = 2 × y
[tex]y = \dfrac{34}{2} = \mathbf{17}[/tex]
y = 17The leg with length x is adjacent to the 30° angle, which gives;
2·x = √3 × 34
x = 17·√35. An acute interior angle is 45°
Therefore, the relationship are;
x = y
x·√2 = 10·√2
Which gives;
x = 10 = y6. An acute interior angle is 60°, which in relation to the position of the sides gives;
x·√3 = 2 × 25·√3
Therefore;
x = 2 × 25 = 50
x = 50
y = x ÷ 2
Therefore;
y = 50 ÷ 2 = 25
y = 257. An acute interior angle is 45°, which gives;
x·√2 = 2·√14
[tex]x = \dfrac{2 \cdot \sqrt{14} }{\sqrt{2} } = \sqrt{2} \times \sqrt{14} = \sqrt{28} = 2 \cdot \sqrt{7} [/tex]
x = 2·√7y = 2·√78. An interior angle is 30°
With regards to the location of the variables, we have;
2 × 24 = x·√3
Therefore;
x = 16·√32·y = x
Therefore;
[tex]y = \dfrac{x}{2} [/tex]
Which gives;
[tex]y = \dfrac{16 \cdot \sqrt{2} }{2} = \mathbf{8 \cdot \sqrt{2} }[/tex]
y = 8·√29. An interior angle is 60°, which gives;
[tex]y = \dfrac{22 \cdot \sqrt{3} }{2} = 11 \cdot \sqrt{3} [/tex]
y = 11·√3√3 × 22·√3 = 2 × x
x = 11·√3 × √3 = 33
x = 3310. An angle of the right triangle is 30°
With respect to the location of the variables, we have;
y = 2 × √6 = 2·√6
y = 2·√6y·√3 = 2 × x
Therefore;
2·√6 × √3 = 2 × x
x = √(18) = 3·√2
x = 3·√211. Right triangle with a 45° interior angle
x = [tex]\underline{\sqrt{10} }[/tex]y = √(10) × √2 = √(20) = 2·√5
y = 2·√512. Interior angle of the right triangle is 60°
y·√3 = 2 × 4·√(21) = 8 × √7 × √3
y = 8·√7[tex]x = \dfrac{y}{2} [/tex]
Therefore;
[tex]x = \dfrac{8 \cdot \sqrt{7} }{2} = \mathbf{ 4 \cdot \sqrt{7} }[/tex]
x = 4·√713. The ratio of the adjacent leg to the opposite leg to the 30° angle is √3, therefore;
x = 17·√3The hypotenuse side = 2 × 17 = 34
The hypotenuse side of the right triangle having a 30° angle is a leg in
the right triangle that has the 45° angle, therefore;
z = 34y = 34·√214. In the 60° right triangle, we have;
x·√3 = 2 × 27 = 54 = 18 × 3
x = 18·√3[tex]Length \ of \ the \ common \ side = \dfrac{x}{2} [/tex]
Which gives;
[tex]Length \ of \ the \ common \ side = \dfrac{18 \cdot \sqrt{3} }{2} = 9 \cdot \sqrt{3} [/tex]
Length of the common side = 9·√3
In the 30° right triangle, we have;
x·√3 = 9·√3
Therefore;
z = 9y = 2·x
Therefore;
y = 2 × 9 = 18Learn more about special right triangles here:
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Related Questions
This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 11 vans and 9 buses with 624 students. High School B rented and filled 5 vans and 1 bus with 126 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
Answers
Answer:
There were 15 students in van and 51 students in the bus.
Step-by-step explanation:
Let the number of students in each van be 'x'.
Let the number of students in each bus be 'y'.
Given:
For High School A
number of vans = 11
Number of buses =9
Number of students = 624
now we can say that;
Total Number of students is equal to sum of the number of vans multiplied by the number of students in each van and Number of buses multiplied by the number of students in each bus.
framing in equation form we get;
[tex]11x+9y = 624 \ \ \ \ equation\ 1[/tex]
For High School B
number of vans = 5
Number of buses = 1
Number of students = 126
now we can say that;
Total Number of students is equal to sum of the number of vans multiplied by the number of students in each van and Number of buses multiplied by the number of students in each bus.
framing in equation form we get;
[tex]5x+y = 126 \ \ \ \ equation\ 2[/tex]
On solving both equation we will get the number of students in vans and buses.
First we will multiply equation 2 by 9 we get;
[tex]9(5x+y)=126\times 9\\\\45x+9y = 1134 \ \ \ \ equation\ 3[/tex]
Now Subtracting equation 2 from equation 1 we get;
[tex]45x+9y-(11x+9y)=1134-624\\\\45x+9y-11x-9y = 510\\\\34x=510[/tex]
Now dividing both side by 34 we get;
[tex]\frac{34x}{34}=\frac{510}{34}\\\\x= 15[/tex]
Now we will substitute the value of 'x' in equation 2 we get;
[tex]5x+y=126\\\\5\times15+y=126\\\\75+y =126\\\\y=126-75 = 51[/tex]
Hence There were 15 students in van and 51 students in the bus.
Suppose the following are given to you: D ( q ) = − 0.00029 q 2 − 0.0716 q + 557 C ( q ) = 81 q + 18300 Find the profit function.
Answers
Profit function= 81q +18300+0.00029q2+0.0716q-557
Step-by-step explanation:A profit function shows the relationship between a company's total profit and output.
The profit function is equal to the company's total rebenue(TR) minus total cost of the company(TC).
Mahemathically,Profit = TR-TC.
Let D(q)= TC=-0.00039q2-0.0716q+557C(q)
Let TR= 81q +18300.
Profit=TR-TC
Profit =81q+18300-(-0.00029q2-0.0716q+557)
Profit=81q+18300+0.00029q2+0.0716q-557.
D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2 and less than 9} The number 4 is D ∩ (E ∩ F).
1. True
2. False
Answers
Answer: 1. True
Step-by-step explanation:
Given : D = {x|x is a whole number} = { 0, 1 , 2, 3, 4, 5, ..................}
E = {x|x is a perfect square between 1 and 9} = {4 }
F = {x|x is an even number greater than or equal to 2 and less than 9} ={4 , 6 , 8}
Since intersection of sets contains all the values they have common.
Then, E ∩ F= {4}
Now , D∩ (E ∩ F) = { 0, 1 , 2, 3, 4, 5, ..................} ∩ {4} = {4}
Hence , The number 4 is D ∩ (E ∩ F).
Thus , the given statement is 1 . true.
Consider the numbers 0, 10, 20, 30, and 40. Multiply each by 4 and compare the result to 60 to determine into which of the following intervals? What number can you multiply by 4 and then add 8 to the product to get?
a. 0 to 10.b. 10 to 20.c. 20 to 30.d. 30 to 40.
Answers
Answer:
Option (b) 10 to 20
Step-by-step explanation:
Let the number obtained between the interval be 'x'
Therefore,
according to the question:
multiplying the number with 4 and then adding 8 to it to get 60
thus,
mathematically, we get
4x + 8 = 60
or
4x = 60 - 8
or
4x = 52
or
x = 13
Hence,
The 13 lies between the interval 10 to 20
Option (b) 10 to 20
Help please! 10 pts
Find the missing side length in the right triangle below. Show your work.
Answers
Answer:
i think it is 18 or something
Step-by-step explanation:
Answer:
Side length B is 17.
Step-by-step explanation:
Use the Pythagorean Theorem a^2 + b^2 = c^2. if one of the legs is 8, and another is 15, the hypotenuse will be 17.
What is the difference? StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction StartFraction 2 (x + 6) Over (x + 4) (x minus 4) EndFraction StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction StartFraction x minus 3 Over (x + 5) (x minus 4) EndFraction StartFraction negative 2 (x minus 6) Over (x + 4) (x minus 4) EndFraction
Answers
Answer:
D
Step-by-step explanation:
[-2(x-6)] / [(x+4)(x-4)]
To simplify the given expression, we can break it down into fractions and multiply them together step by step.
Explanation:The given expression is quite complex, but we can simplify it step by step. Let's break it down:
Simplify the first fraction: StartFraction \frac{x}{x^2 - 16} \EndFractionSimplify the second fraction: StartFraction \frac{3}{x - 4} \EndFractionMultiply the two fractions together: StartFraction \frac{2(x + 6)}{(x + 4)(x - 4)} \EndFractionMultiply the result by the third fraction: StartFraction \frac{-2(x + 6)}{(x + 4)(x - 4)} \EndFractionMultiply the result by the fourth fraction: StartFraction \frac{x - 3}{(x + 5)(x - 4)} \EndFractionMultiply the result by the fifth fraction: StartFraction \frac{-2(x - 6)}{(x + 4)(x - 4)} \EndFractionBy following these steps, we have simplified the given expression.
Learn more about Simplifying fractions here:https://brainly.com/question/14693420
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Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on one day a week for a given year on one day a week for a given year, and the average (mean) value is 144.3 volts. Choose the correct answer below. A. The given value is a parameter parameter for the year year because the data collected represent a population population. B. The given value is a parameter parameter for the year year because the data collected represent a sample sample. C. The given value is a statistic statistic for the year year because the data collected represent a sample sample. D. The given value is a statistic statistic for the year year because the data collected represent a population population.
Answers
Answer:
C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.
Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
Step-by-step explanation:
The sample mean obtained was :
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}= 144.3[/tex]
A. The given value is a parameter parameter for the year year because the data collected represent a population population.
False. The data colected represent a sample of the population of interest, so for this case is not a parameter because we don't have the information about all the population of interest.
B. The given value is a parameter parameter for the year year because the data collected represent a sample sample.
False. First the sample average is not a parameter, and second the population mean is not equal to the sample mean most of the times.
C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.
Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
D. The given value is a statistic statistic for the year year because the data collected represent a population.
False. If is an statistic can't represent the population, since the parameter represent the population not the statistic.
In this exercise we have to use the knowledge of statistics to be able to identify the correct statement, so I can say that it is:
The letter C
So knowing the statistics topics we can recognize the true alternative:
A. False. The information in visible form colected show a sample of the inhabitants of a place of interest, so for this case exist not a limit cause we forbiddance bear the facts about all the inhabitants of a place of interest.
B. False. First the sample average exist not a limit, and second the inhabitants of a place mean happen inadequate the average value most of the opportunity.
C. Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
D. False. If exist an detail of action can't represent the inhabitants of a place, because the limit represent the inhabitants of a place not the detail of action.
See more about statistics at brainly.com/question/10951564
Assigned Media Question Help What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below.
A. The mean and standard deviation have the values of 0 and 1
B. The mean and standard deviation have the values of 0 and g 0.
C. The mean and standard deviation have the values of p = 1 and 0.
D. The mean and standard deviation have the values of - 1 and 0 -1.
Answers
Answer:
A
Step-by-step explanation:
The normal probability has two parameters mean and standard deviation. Every normal probability distribution can become a standard normal probability distribution when mean is zero and standard deviation is 1. This means that standard normal probability distribution centers at 0 and the spread about the mean is 1.
Find an equation of the line that
a. has the same y-intercept as the line y+7x+3=0 and
b. Is parallel to the line -11x-12y=-7
Write your answer in the form y=mx+b
Answers
Answer:
y = (-11/12)x - 3
Step-by-step explanation:
Recall that for a linear equation in the form y = mx + b,
m = slope and b = y-intercept.
hence to satisfy parts (a) and (b) of the questions, we need to extract the y-intercept from the equation in part (a) and the slope from part (b)
For part (a)
given: y+7x+3=0 (rearrange this to get slope-intercept form)
y+7x+3=0 (subtract 3 from both sides)
y + 7x = -3 (subtract 7x from both sides)
y = -7x - 3
we can see that the y-intercept is -3.
For part (b)
given: -11x -12y=-7 (rearrange this to get slope-intercept form)
-11x -12y=-7 (add 11x toboth sides)
-12y = 11x - 7 (divide both sides by -12)
y = (-11/12) - (7/12)
we can see that the slope is (-11/12).
combining the y-intercept from part (a) and the slope from part (b) into the general equation given in the first line above,
y = (-11/12)x - 3 (answer)
Find the area of the sector of a circle with radius 4 inches formed by a central angle of [tex]\frac{5\pi}{4}[/tex] radians. Give your answer correct to 3 decimal places.
Answers
Answer:
10in²
Step-by-step explanation:
5π/4 is 62.5% of a circle if you look at the unit circle.
So just find the area of a circle and take 62.5% of it.
A = πr²
A = π(4)²
A = 16π
16π(.625) = 10
Traviling upstream on the Mississippi River, a barge travels 56 mi in 7 h. Downstream, it travels the same distance in 4 h. Find the rate of the barge in still water and the rate of the current
Answers
Answer:the speed of the barge in still water is 11 mph
the speed of the current is 3 mph
Step-by-step explanation:
Let x represent the speed of the barge in still water.
Let y represent the speed of the current.
Traveling upstream on the Mississippi River, the barge travels 56 mi in 7 h. This is against the water current. It means that the total speed of the barge would be
x - y mph
Distance = speed × time
Therefore,
56 = 7(x - y)
8 = x - y - - - - - - - - - - - -1
Downstream, it travels the same distance in 4 h. This is in the same direction with the water current. It means that the total speed of the barge would be
x + y mph
Therefore,
56 = 4(x + y)
14 = x + y - - - - - - - - - - - -2
Adding equation 1 and equation 2, it becomes
22 = 2x
x = 22/2 = 11
Substituting x = 11 into equation 2, it becomes
14 = 11 + y
y = 14 - 11 = 3
Select the graph of the solution set that would represent the following expression. 2 ( x + 1 ) > 3 x − 2
Answers
Answer:
B
Step-by-step explanation:
x>4
Answer:
None of the options are right. The correct answer is x < 4
Step-by-step explanation:
2(x + 1) > 3x - 2
2x + 2 > 3x - 2
2 > x - 2
4 > x
x < 4
A bike shop rents mountain bikes for a $4.004.00 insurance charge plus $2.502.50 for each hour. For how many hours can a person rent a bike with $17.75?
Answers
Answer: the person can rent the bike for 5.5 hours.
Step-by-step explanation:
Let x represent the number of hours that a person rents the bike.
Let y represent the total cost of renting the bike for x hours.
A bike shop rents mountain bikes for a $4.00 insurance charge plus $2.50 for each hour. This means that the expression for the total cost of renting the bike for x hours would be
y = 2.5x + 4
Therefore, if a person has $17.75, the number of hours for which he can rent the bike would be
17.75 = 2.5x + 4
2.5x + 4 = 17.75
2.5x = 17.75 - 4
2.5x = 13.75
x = 13.75/2.5
x = 5.5 hours
In Canada, $1 and $2 bills have been replaced by coins. When Marissa returned home to San Fran from a trip to Canada, she found that she had acquired 37 of these coins, with a total value of 51 canadian dollars. How many coins of each denomination did she have?
Answers
Answer:
$1 coin is 23
$2 coin is 14
Step-by-step explanation:
We need to form mathematical equations that we can solve from this Long citation.
Firstly, let the numbers of $1 coins be a and that of $2 be b.
We know that there are 37 coins. Hence
a + b = 37
Now, total is 51 Canadian dollars.
a + 2b = 51
Let’s now solve this simultaneously
From 2 , a + b + b = 51
Let’s say this is 3. Now substitute 1 into 3.
37 + b = 51, b = 51 - 37 = 14
Since a + b = 37
a = 37 - 14 = 23
I = prt
I = simple interest, p = principal, r = rate, t = time.
You want to study at the Hogwarts School of Witchcraft and Wizardry after five years. You need 800 pieces of muggle-money to study there. You decide to deposit some pieces in the bank at an annual interest rate of %12.
Answers
Answer:
The amount we need to invest is 500 muggle money.
Step-by-step explanation:
Amount needle to study at Hogwarts = A = 800 muggle money
Principle amount that we need to invest = P
Duration of investment = T = 5 years
Rate if simple interest = R = 12%
Simple interest = S.I
A = S.I + P
[tex]800=\frac{P\times 12\times 5}{100}+P[/tex]
[tex]800=0.6P+P[/tex]
[tex]800=1.6P[/tex]
P = [tex]\frac{800}{1.6}=500[/tex]
The amount we need to invest is 500 muggle money.
Calculate the following derivatives. Assume y is a function of t . Use Y for the derivative of y . (a) d dt y7= Incorrect: Your answer is incorrect. (b) d dt y3e4t= Incorrect: Your answer is incorrect. (c) d dt t7 cos(y6)=
Answers
Answer:
(a) d dt y7=7Y^6
(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}
(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5
Step-by-step explanation:
We calculate the following derivatives. Since these are complex derivatives, we also calculate the formula for complex derivatives. We use Y for the derivative of y . Therefore, we calculate and we get
(a) d dt y7=7Y^6
(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}
(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5
The Cookie Monster stole 4 cookies before getting caught by grandma Cookie Monster.He continues stealing cookies when he gets caught. If he steals no less than 10 cookie how many more cookies does he need to steal?
Answers
Answer:
Cookie monster needs to steal at least 6 cookies more.
Step-by-step explanation:
Given:
Number of cookies already stole = 4
Total number of cookies he wants to steal [tex]\geq 10[/tex]
We need to find how many cookie he needs to steal more.
Solution:
Let number of cookies he needs to steal more be 'x'.
Now we can say that;
Number of cookies already stole plus number of cookies he needs to steal more should be greater than or equal to Total number of cookies he wants to steal
framing in equation form we get;
[tex]4+x\geq 10[/tex]
Now using Subtraction property of Inequality we will subtract both side by 4 we get;
[tex]4+x-4\geq 10-4\\\\x\geq 6[/tex]
Hence Cookie monster needs to steal at least 6 cookies more.
The Cookie Monster needs to steal at least 6 more cookies after getting caught.
Explanation:The Cookie Monster stole 4 cookies initially before getting caught. If he steals no less than 10 cookies each time, we need to determine how many more cookies he needs to steal. Let's represent the number of cookies he needs to steal as x. The equation to represent this situation is: x >= 10 - 4.
Simplifying the equation, we have x >= 6. Therefore, the Cookie Monster needs to steal at least 6 more cookies after getting caught.
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The distance between Quebec City and New York City is 520 miles. If Kate leaves Quebec and will leaves New York at 9 am and the drive towards each other at 55 mph and 75 mph respectively at what time will they meet
Answers
Answer:they would meet at 1 pm
Step-by-step explanation:
The distance between Quebec City and New York City is 520 miles.
At the point where Kate and Will meet, they would have travelled 520 miles.
Let t represent the time it takes Kate to travel a certain distance before they met.
Distance = speed × time
If Kate drives at 55mph, the distance covered would be
55 × t = 55t.will drives at 75 mph
Since Will left same that that Kate left, distance travelled by Will in t hours would be
75 × t = 75t
Since the total distance covered is 520 miles, it means that
55t +75t = 520
130t = 520
t = 520/130 = 4
9 am + 4 hours = 1 pm
Answer:
1 pm
Step-by-step explanation:
Their combined speed is 55 + 75 = 130 miles per hour. That is the rate at which the distance between them is decreasing. The time it takes for the distance between them to become zero is found from the relation ...
time = distance/speed
time = (520 mi)/(130 mi/h) = 4 h
4 hours after 9 am, Kate and Will will meet. That time is 1 pm.
40 points!! What is the limit of the infinite series?
Answers
As n goes onto infinity, the expression [tex]\frac{3n^5}{4n^5+1}[/tex] will approach [tex]\frac{3}{4}[/tex]. Note the 3 and 4 come from the leading coefficients of the numerator and denominator respectively. This only works because the degrees for the numerator and denominator are both the same (both are 5).
Since [tex]\frac{3n^5}{4n^5+1}[/tex] is not approaching 0 when n gets really large, adding on successive terms of these values will have the infinite sum diverge. After some very large n, we are effectively adding on 3/4 each time and that just makes the overall sum keep growing forever.
Answer: The sum divergesFinal answer:
The limit of an infinite series depends on whether it converges or diverges. If it converges, the limit is the value the series approaches as the number of terms approaches infinity. If it diverges, it does not have a finite limit.
Explanation:
The limit of the infinite series depends on the specific series being referred to. To find the limit of an infinite series, you need to determine if it converges or diverges. If the series converges, then the limit is the value that the series approaches as the number of terms goes to infinity. If the series diverges, then it does not have a finite limit.
For example, consider the series 1/2 + 1/4 + 1/8 + ... This is a geometric series with a common ratio of 1/2. It converges to the value of 1, so the limit of this series is 1.
Some various tests and properties can be used to determine if a series converges or diverges. Some common ones include the ratio test, the root test, and the comparison test.
Find the value of x. Round to the nearest degree.
Answers
Answer:
The answer to your question is 32.64°
Step-by-step explanation:
Data
hypotenuse = 19
adjacent side = 16
x = ?
Process
1.- To solve this problem use trigonometric functions.
The function that relates the adjacent side and the hypotenuse is cosine.
cos x = [tex]\frac{adjacent side}{hypotenuse}[/tex]
2.- Substitution
cos x = [tex]\frac{16}{19}[/tex]
3.- cos x = 0.842
4.- cos ⁻¹x = x = 32.64°
I need help with this!!!!
Options are,
A: 1/3
B: 3/1
C: 1/4
D: 2/4
Answers
Answer:
D: 2/4
Step-by-step explanation:
Usually when we talk about a point partitioning a segment, we are interested in the ratio of the first segment to the second:
BC : CD = 2 : 2 = 1 : 1
Since this is not an answer choice, we need to "reverse engineer" the answer list to see if we can find an answer that corresponds to a reasonable interpretation of the question.
__
None of the segments is 3 units long, so neither of answer choices A or B makes any sense.
While segment BD is 4 units long, there is no segment that is 1 unit long, so answer choice C makes no sense, either.
There are segments that are 2 units long and a segment that is 4 units long, so if we interpret the question to be "what is the ratio of BC to BD?" then answer choice D is appropriate.
The population of Hawaii is growing by about 5% per year. If that rate were to continue, how long would it take for the population of Hawaii to double?
Answers
Answer:
14.2 years
Step-by-step explanation:
The multiplier of the population each year is 1 +5% = 1.05, so after n years the population has been multiplied by 1.05^n. You want to find the value of n that makes this expression equal to 2:
2 = 1.05^n
log(2) = n·log(1.05) . . . . . take logarithms
log(2)/log(1.05) = n ≈ 14.2
Growing at a rate of 5% per year, it will take about 14.2 years for the population to double.
Classify each number below as a rational number or an irrational number. −17.6 , 81 , 15π , (square root −29), 13/14
Answers
Answer:
Rational Numbers
−17.6 (-176/10)
81
13/14
Rational Numbers
15π
square root −29
Step-by-step explanation:
Rational Numbers are those numbers which can be written as Ratio of two numbers.
Irrationational Numbers are those which cannot be written as ratio of two numbers. such as recurring numbers.
e.g 0.26262626.........
Which expressions are equivalent to 8 (negative 10 x + 3.5 y minus 7)? Select two options. Negative 80 x + 24.5 y minus 56 Negative 80 x + 28 y minus 56 80 x + 28 y + 56 4 (negative 20 x + 7 y minus 14) Negative 4 (negative 20 x + 7 y minus 14)
Answers
Answer:
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
This is equivalent to -80x + 28y - 56
Step-by-step explanation:
Let's find out the options that are equivalent to:
8 (negative 10 x + 3.5 y minus 7)
8 ( - 10x + 3.5y - 7) =
-80x + 28y - 56
Options:
A. Negative 80 x + 24.5 y minus 56
This is not equivalent.
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
-80x + 28y - 56
This is equivalent to -80x + 28y - 56
D. Negative 4 (negative 20 x + 7 y minus 14)
80x - 28y + 56
This is not equivalent.
Answer:
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
Step-by-step explanation:
The volleyball team and the wrestling team at Weston High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $9 from past fundraisers. The wrestling team has raised $101 in the past, and they are making $3 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. How many cars will that take? What will that total be?
Answers
The volleyball and wrestling teams need to wash 23 cars each for their total funds raised to be equal. After washing this number of cars, each team will have raised a total of $92.
Explanation:In this scenario, the money each team has already raised and the amount they make per car equals the total they will have raised. We can express this as two equations and solve for the number of cars (let's call this 'x').
For the volleyball team:$4x + $9
For the wrestling team:$3x + $101
Setting these two equations equal to each other because they will have raised the same total gives us:
$4x + $9 = $3x + $101
The solution of this equation is x=23 cars. From this equation, we can also find the total raised by each team, which is $4*23 + $9 = $92 for each team.
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While performing intravenous drug injections, it is necessary to decrease the angle of the needle once a flashback is seen in the intravenous catheter to?
Answers
Answer: avoid passing through the vein.
Step-by-step explanation:
Each person in a group of twenty people at a hotel orders one meal chosen from oatmeal, eggs, or pancakes and one hot beverage chosen from coffee or tea. One person will be selected at random from the twenty people. What is the sample space for the meal and beverage for the person selected?
1. {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)}2. {(oatmeal, pancakes), (oatmeal, eggs), (eggs, pancakes), (coffee, tea)}3. {(coffee, tea, oatmeal), (coffee, tea, eggs), (coffee, tea, pancakes)}4. {oatmeal, coffee, pancakes, eggs, tea}5. {(oatmeal, eggs, pancakes), (coffee, tea)}
Answers
Answer:
{(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)
Step-by-step explanation:
Sample space is the set of all possible outcomes of an experiment.
Here a person should choose one meal and a hot drink. Hence, each element in the set includes one meal and one beverage, which eliminates 2,because it indicates person choses oatmeal and pancakes which has no beverage. Sets should have elements in pairs so ,We should eliminate 3 ,4,5.
As a result person can choose
oatmeal as meal and coffee as drink
oatmeal as meal and tea for drink
eggs for meal tea for drink
eggs for meal coffee for drink
pancakes for meal tea for drink finally
pancakes for meal and coffee for drink
The sample space of a distribution is the list of possible options.
The sample space for the meal and the beverage is (a) {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)
From the question, the meals are:
Meals: Oatmeal, Eggs, Pancakes
And the beverages are:
Beverages: Coffee, Tea
This means that, the available selections are:
Oatmeal and CoffeeOatmeal and TeaEggs and CoffeeEggs and TeaPancakes and CoffeePancakes and TeaHence, the sample space is (a)
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Solve the equation by factoring x^2+6x-27=0
a. {-3,9}
b. {-9,3}
c. {3,9}
d. {-3,-9}
Answers
Answer:
b. {-9, 3}.
Step-by-step explanation:
x^2 + 6x - 27 = 0
We need 2 numbers whose product is -27 and whose sum is + 6.
These are + 9 and - 3. So the factors are:
(x - 3)(x + 9) = 0
(x - 3) = 0 or (x + 9) = 0
x = 3 or -9.
Answer: option b is the correct answer.
Step-by-step explanation:
The given quadratic equation is expressed as
x^2+6x-27=0
In order to solve the equation by factorization, the first step is to find two numbers such that their sum or difference is 6x and their product is
- 27x^2. The two numbers are 9x and - 3x. Therefore,
x^2 + 9x - 3x - 27 = 0
x(x + 9) - 3(x + 9) = 0
x - 3 = 0 or x + 9 = 0
x = 3 or x = - 9
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the equation or formula for the indicated variable. T= 2 r π h + 2 π r ^2; for h
Answers
For this case we have the following equation:
[tex]T = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
We must solve the equation for the variable "h":
We subtract [tex]2 \pi * r ^ 2[/tex] from both sides of the equation:
[tex]T-2 \pi * r ^ 2 = 2 \pi * r * h[/tex]
We divide by [tex]2 \pi * r[/tex] on both sides of the equation:
[tex]\frac {T-2 \pi * r ^ 2} {2 \pi * r} = h\\h = \frac {T} {2 \pi * r} - \frac {2 \pi * r ^ 2} {2 \pi * r}\\h = \frac {T} {2 \pi * r} -r[/tex]
Answer:
[tex]h = \frac {T} {2 \pi * r} -r[/tex]
Assume that the following statements are true.
A. If Trisha is drinking water, then it is dinnertime.
B. If it is lunchtime, then Rob is drinking milk and nothing else.
C. If it is dinnertime, then Anna is drinking iced tea and nothing else.
D. If it is breakfast time, then Sarah is drinking milk and nothing else.
E. Trisha is drinking water.
Using only the information given above, determine if "Anna is drinking iced tea" must be true, may be true, or is not true. Explain your reasoning. Assume that the following statements are true.
A. If Trisha is drinking water, then it is dinnertime.
B. If it is lunchtime, then Rob is drinking milk and nothing else.
C. If it is dinnertime, then Anna is drinking iced tea and nothing else.
D. If it is breakfast time, then Sarah is drinking milk and nothing else.
E. Trisha is drinking water.
Answers
Based on the provided conditional statements, if Trisha is drinking water, then it's dinnertime. Additionally, if it's dinnertime, then Anna is drinking iced tea. Given that Trisha is drinking water, we can conclude that Anna is drinking iced tea.
Explanation:The question here is dealing with conditional statements in logic. It's important to understand that if a conditional statement is true, and the first part (the condition) is true, then the second part must be true as well. In this case, Statement A states that if Trisha is drinking water, then it is dinnertime. So, if Trisha is drinking water (which is confirmed by Statement E), then it is dinnertime.
Statement C further adds to our understanding by stating that if it is dinnertime, then Anna is drinking iced tea and nothing else. Since based on Statements A and E, we know it is dinnertime, then following the logic from Statement C, we can conclude that Anna is drinking iced tea.
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