The rate change of the distance between the car and the person at that instant will be 15.69 meter.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
A person stands 30 meters east of an intersection and watches a car driving away from the intersection to the north at 17 meters per second.
At a certain instant, the car is 161616 meters from the intersection.
Now,
Let the distance of the car from the intersection and from the person be x and y at any time t respectively.
So, We can apply the Pythagoras theorem as;
y² = x² + 10²
y = √ x² + 10²
Differentiate with respect to t , we get;
[tex]\frac{dy}{dt} = \frac{1}{2\sqrt{x^2 + 100} } 2x \frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt} = \frac{1}{\sqrt{x^2 + 100} } x \frac{dx}{dt}[/tex]
Since, the person standing towards the intersection at 17 m/s.
dx/dt = 17
Hence, [tex]\frac{dy}{dt} = \frac{1}{\sqrt{x^2 + 100} } x *17[/tex]
At x = 16 meters
So, [tex]\frac{dy}{dt} = \frac{1}{\sqrt{24^2 + 100} } 24 *17[/tex]
[tex]\frac{dy}{dt} = 408 / \sqrt{676}[/tex]
[tex]\frac{dy}{dt} = 408 / 26[/tex]
[tex]\frac{dy}{dt} = 15.69[/tex]
Thus, The rate change of the distance between the car and the person at that instant will be 15.69 meter.
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Which temperature is warmest?
-12°
0°
-17°
-34°
Answer:
0
Step-by-step explanation:
It is 0 because that is not negative and it is the closest to positive as positive is usually warmer than negative temperatures
What is the product?
(6r-1)(-8r-3)
-4872-10r +3
- 48r2-10r-3
-48P?+ 3
-48r2-3
-48r^2−10r+3
Step-by-step explanation:
(6r-1)(-8r-3)
Apply the distributive property by multiplying each term of 6r−1 by each term of -8r−3
-48r^2−18r+8r+3
Combine -18r and 8r to get -10r.
-48r^2−10r+3
Therefore the product of this equation is -48r^2−10r+3
Hope this helps! If you have any more questions or you need further clarification on anything please comment down below. Good luck!
The value of the product of the expression is,
⇒ - 48r² - 10r + 3
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition
Given that;
The expression is,
⇒ (6r - 1) (- 8r - 3)
Now, We can multiply as;
⇒ (6r - 1) (- 8r - 3)
⇒ - 48r² - 18r + 8r + 3
⇒ - 48r² - 10r + 3
Thus, The value of the product of the expression is,
⇒ - 48r² - 10r + 3
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I ran 800m, 5km,1,000cm. How many meters did I run all together
Answer:
5810 meters
Step-by-step explanation:
800 meters
5km = 5,000 meters
1,000 cm = 10 meters
Add all together to get 5810 meters
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The measure of angle is 6. The measure of its reference angle is
9 and sin o is
Answer:
The measure of angle θ is 7π/6. The measure of its reference angle is 210°
and sin θ is -1/2.
Step-by-step explanation:
The correct question is:
The measure of angle θ is 7π/6. The measure of its reference angle is ___
and sin θ is ___
180° is equivalent to π radians. To transform 7π/6 radians to degrees, we have to use the following proportion:
180° / π radians = x° / (7π/6 radians)
x = (180/π) * (7π/6 radians)
x = 210°
And sin(210°) = -1/2
A cell phone company is offering a special deal. If you choose from payment plans A, B, and C and one of four different phones, you can choose a free gift of a case, a car charger, or a memory card. What is the probability that Rusty will choose plan A, phone 2, and the car charger? (Find the sample space) *
A) 1/9
B) 1/18
C) 3
D) 1/36
Answer:
B
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Find the volume of the oblique cylinder. Round your answer to the nearest tenth.
Answer:
The Volume of an Oblique Cylinder:
An oblique cylinder, on the other side, is a cylinder whose base and top are not perpendicular to the sides. Interestingly, the volume of an oblique cylinder is the same as the volume of a right cylinder, and it is calculated as V=πr2h V = π r 2 h .
Step-by-step explanation:
The letter represents where the amount of $158.29 should be written.
The letter represents where the amount of $250 should be written.
Answer:
The letter A represents where the amount of $158.29 should be written.
The letter D represents where the amount of $250 should be written.
Step-by-step explanation:
Ivan spent $158.29 on groceries so that would be debit -
For letter D he is transferring money
The letter 'a' represents where the amount of $158.29 should be written. And the letter d represents where the amount of $250 should be written.
What is Debit?Debit is an entry in the accounting sheet where there forms an increase in the assets or decrease in the liabilities. Positive values for assets and liabilities are debited and the negative balances are credited on balance sheet.
Given that Ivan spent $158.29 on groceries.
He then transferred $250 to his savings account.
On the check register, there are two letters, letter a and letter d.
a is the amount debited for groceries. So the letter a represents where the amount of $158.29 should be written.
d is the amount debited for a transfer. So the letter d represents where the amount of $250 should be written.
Hence the letter 'a' represents where the amount of $158.29 should be written. And the letter d represents where the amount of $250 should be written.
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The full question is :
Look at ivan’s check register. ivan spent $158.29 on groceries. he then transferred $250 to his savings account. a check register. a is the amount debited for groceries. d is the amount debited for a transfer. the letter represents where the amount of $158.29 should be written. the letter represents where the amount of $250 should be written.
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
f(x) = −4(x − 8)2 + 3
Answer:
the symmetry for each function is -8 and -4
hoped that helped:P
The axis of symmetry for the function f(x) = -4(x - 8)^2 + 3 is x = 0.
Explanation:The axis of symmetry of a quadratic function can be found using the formula:
x = -b / (2a)
For the function f(x) = -4(x - 8)^2 + 3, the coefficient of the x^2 term is -4 (which is a) and the coefficient of the x term is 0 (which is b).
Therefore, the axis of symmetry can be found as:
x = -b / (2a) = -0 / (2*(-4)) = 0
So, the axis of symmetry for the function f(x) = -4(x - 8)^2 + 3 is x = 0.
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Find the slope of a line which goes through the points (2,5) and (−4,3)
Answer:
slope (m) = 0.75
Step-by-step explanation:
Slope (m) =
ΔY
ΔX
=
1
3
= 0.33333333333333
θ =
arctan( ΔY ) + 180°
ΔX
= 198.43494882292°
ΔX = -4 – 2 = -6
ΔY = 3 – 5 = -2
Distance (d) = √ΔX2 + ΔY2 = √40 = 6.3245553203368
Equation of the line:
y = 0.33333333333333x + 4.3333333333333
or
y =
1 x
3
+ 13
3
When x=0, y = 4.3333333333333
When y=0, x = -13
please mark brainliest
Are (-1,3) and (1,5) parallel
Answer:
no
Step-by-step explanation:
assuming these are slopes?? two points cant be parallel theyre just dots, no these are not parallel
Please mark as brainliest
Darla got a job at a jewelry store. She gets paid $20 for each ring she sells and $50 for each necklace she sells. How much will she earn if she sells 15 rings and 9 necklaces?
Answer:
$750
Step-by-step explanation:
Answer:
$750
Step-by-step explanation:
50 times 9 = 450
20 times 15 = 300
450+300=750
2. In an effort to improve emergency response times, the city manager made the following line graph. The graph represents the average
response times of the police department and the paramedics to traffic incidents where both departments responded to the same call.
Use the graph and predict at which of the following times that the paramedics will have a faster response time.
Answer:
2 PM
3 PM
4 PM
8 PM
Step-by-step explanation:
*Note the following:
I used the hours after midnight to calculate the time of day/night.
The lower the graph on the line, the lower (AKA faster) response time.
The paramedics had a faster average response time at the following times:
2 PM
3 PM
4 PM
8 PM
Therefore, we can predict that if this pattern continues, their response time will be faster during those hours.
What is the A ⋃ B for the venn diagram
Answer:
The elements contain in A U B is {11,12,13,14,15,16,17} .
There are 7 elements in A U B.
Jackie makes an $800 deposit into a bank account earning 4.5% interest.
a. If the interest is compounded quarterly how much money will Jackie have in 10 years?
b. If the interest is compounded continuously how much money will Jackie have in 10 years?
C. If Jackie's money is compounded continuously, how long will it take her money to double?
d. If Jackie's money is compounded monthly, how long will it take her money to triple?
For part a, Jackie will have approximately $1217.62 after 10 years with quarterly compounding interest. For part b, Jackie will have approximately $1226.96 after 10 years with continuous compounding interest. For part c, it will take approximately 15.43 years for Jackie's money to double with continuous compounding interest. For part d, it will take approximately 38.51 years for Jackie's money to triple with monthly compounding interest.
Explanation:For part a, to calculate the amount of money Jackie will have in 10 years with quarterly compounding interest, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years. Plugging in the values, we have A = 800(1 + 0.045/4)^(4*10), which gives us A ≈ $1217.62.
For part b, to calculate the amount of money Jackie will have in 10 years with continuous compounding interest, we can use the formula: A = P * e^(rt), where e is Euler's number and approximately equal to 2.71828. Plugging in the values, we have A = 800 * e^(0.045 * 10), which gives us A ≈ $1226.96.
For part c, to find out how long it will take Jackie's money to double with continuous compounding interest, we can use the formula: t = ln(2) / r, where t is the time in years and r is the interest rate. Plugging in the values, we have t = ln(2) / 0.045, which gives us t ≈ 15.43 years.
For part d, to find out how long it will take Jackie's money to triple with monthly compounding interest, we can use the formula: t = ln(3) / (n * ln(1 + r/n)), where t is the time in years, n is the number of times compounded per year, and r is the interest rate. Plugging in the values, we have t = ln(3) / (12 * ln(1 + 0.045/12)), which gives us t ≈ 38.51 years.
a. If the interest is compounded quarterly, Jackie will have approximately $1,313.63 in 10 years.
b. If the interest is compounded continuously, Jackie will have approximately $1,256.39 in 10 years.
c. If Jackie's money is compounded continuously, it will take approximately 15.4 years for her money to double.
d. If Jackie's money is compounded monthly, it will take approximately 62.47 years for her money to triple.
Step 1
To solve this problem, we can use the compound interest formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- A is the amount of money accumulated after t years, including interest.
- P is the principal amount (the initial deposit).
- r is the annual interest rate (as a decimal).
- n is the number of times interest is compounded per year.
- t is the time the money is invested for, in years.
Given:
- [tex]\( P = \$800 \)[/tex]
-[tex]\( r = 0.045 \)[/tex] (4.5% as a decimal)
- n is either 4 for quarterly compounding or tends to infinity for continuous compounding.
Step 2
We'll calculate each part step by step:
a. Quarterly compounding:
- [tex]\( n = 4 \)[/tex]
- [tex]\( t = 10 \)[/tex]
Substituting into the formula:
[tex]\[ A = 800 \left(1 + \frac{0.045}{4}\right)^{4 \times 10} \]\[ A = 800 \left(1 + \frac{0.045}{4}\right)^{40} \]\[ A = 800 \left(1 + 0.01125\right)^{40} \]\[ A = 800 \times 1.01125^{40} \]\[ A = 800 \times 1.642032881 \]\[ A = \$1,313.63 \][/tex]
Step 3
b. Continuous compounding:
For continuous compounding, we use the formula:
[tex]\[ A = P e^{rt} \][/tex]
Where e is the base of the natural logarithm, approximately equal to 2.71828.
Substituting the values:
[tex]\[ A = 800 \times e^{0.045 \times 10} \]\[ A = 800 \times e^{0.45} \]\[ A = 800 \times 1.570482165 \]\[ A = \$1,256.39 \][/tex]
Step 4
c. To find out how long it takes for the money to double with continuous compounding, we use the formula:
[tex]\[ A = P e^{rt} \][/tex]
We need to solve for t when [tex]\( A = 2P \):[/tex]
[tex]\[ 2P = P e^{0.045t} \]\[ 2 = e^{0.045t} \]\[ \ln(2) = 0.045t \]\[ t = \frac{\ln(2)}{0.045} \][/tex]
Substituting the values:
[tex]\[ t = \frac{\ln(2)}{0.045} \]\[ t = \frac{0.693}{0.045} \]\[ t = 15.4 \text{ years} \][/tex]
So, it takes approximately 15.4 years for Jackie's money to double with continuous compounding.
Step 5
d. To find out how long it takes for the money to triple with monthly compounding, we use the compound interest formula again, but this time we set [tex]\( A = 3P \)[/tex]:
[tex]\[ 3P = P \left(1 + \frac{0.045}{12}\right)^{12t} \]\[ 3 = \left(1 + \frac{0.045}{12}\right)^{12t} \]\[ \ln(3) = 12t \ln\left(1 + \frac{0.045}{12}\right) \]\[ t = \frac{\ln(3)}{12 \ln\left(1 + \frac{0.045}{12}\right)} \][/tex]
Substituting the values:
[tex]\[ t = \frac{\ln(3)}{12 \ln\left(1 + \frac{0.045}{12}\right)} \]\[ t = \frac{1.099}{12 \times 0.0037} \]\[ t = 62.47 \text{ years} \][/tex]
So, it takes approximately 62.47 years for Jackie's money to triple with monthly compounding.
Invent a data set with five numbers that has a mean of 10 and a median of 12.
Answer:
7,7,12,12,12
Step-by-step explanation:
7+7+12+12+12=50/5=10=Mean
Median=12
The data set could be as follow 7,7,12,12,12 which has a mean of 10 and a median of 12.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
we have given the information of the data set with five numbers that have a mean of 10 and a median of 12.
Mean = 10
Let's assume the given data set 7,7,12,12,12 so, this must satisfy the information
7+7+12+12+12=50/5
Mean =10
Also,
Median=12
Thus, the data set could be as follow 7,7,12,12,12 which has a mean of 10 and a median of 12.
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The school bus Evie rides is scheduled to arrive at her bus stop at 8:20 a.m. each day. The table below shows the actual arrival times that of the bus for several days that were randomly selected over the past few months. Based on these data, what is the probability that the bus will arrive at Evies stop before 8:20 a.m. tomorrow
Answer:
The probability of the bus getting there BEFORE 8:20 isn't likely
I took an average of all of the numbers and its shows that he bus will be there about 8:20.25
Check all of the ordered pairs that satisfy the equation below.
y = 7x
A. (6,42)
B. (42,6)
C. (42,7)
D. (12, 84)
E. (84, 12)
F. (84, 14)
Answer:
A, D
Step-by-step explanation:
Your first clue is that y > x. That is only the case for choices A and D.
Answer:
A and D
Step-by-step explanation:
What number will make the proportion true? 6/12 = ?/18
Answer:
9/18
Step-by-step explanation:
Answer:
9/18
Step-by-step explanation: 9/18 and 6/12 both equal 1/2
a 71.9%
b 18%
c 28.1%
39.1%
Consider the system of equations represented in the
graph.
y-x = 2
x + y = 4
Which is a solution to the system of equations?
1. (1.3)
2. (2.2)
3. (3, 1)
4. (4,2)
ONLY ONE ANSWER
Answer: 1. (1,3)
Step-by-step explanation:
Insert 1 for x and 3 for y. The equations will look like
3 - 1 = 2
1 + 3 = 4
Both equations are true when these numbers are inserted, therefore, the answer is (1,3).
» What is the area?
10 mm
10 mm
Answer:
100mm
Step-by-step explanation:
Multiply the length times the width
Answer: 100 mm or 20 mm
Step-by-step explanation: You ethier times it together or add it together
Hope this helps :)
What’s the answer?????????
A circle has a radius of 6. An arc in this circle has a central angle of 330º.
What is the length of the arc?
Either enter an exact answer in terms of or use 3.14 for it and enter your answer as a decimal.
Answer:
The length of the arc is approximately [tex]\( 17.27 \)[/tex] units.
Explanation:
To find the length of the arc, we use the formula:
[tex]\[ \text{Arc Length} = \frac{\text{Central Angle}}{360^\circ} \times 2\pi r \][/tex]
where:
- Central Angle is the measure of the angle formed by the arc and the center of the circle
- [tex]\( r \)[/tex] is the radius of the circle
Given:
- Radius ([tex]\( r \)[/tex]) = 6
- Central Angle = 330º
Plugging the values into the formula:
[tex]\[ \text{Arc Length} = \frac{330^\circ}{360^\circ} \times 2\pi \times 6 \][/tex]
[tex]\[ \text{Arc Length} = \frac{330}{360} \times 2\pi \times 6 \][/tex]
[tex]\[ \text{Arc Length} = \frac{11}{12} \times 2\pi \times 6 \][/tex]
[tex]\[ \text{Arc Length} = \frac{11}{2} \pi \][/tex]
Using [tex]\( \pi \approx 3.14 \)[/tex], we can approximate the value:
[tex]\[ \text{Arc Length} \approx \frac{11}{2} \times 3.14 \][/tex]
[tex]\[ \text{Arc Length} \approx 17.27 \][/tex]
So, the length of the arc is approximately [tex]\( 17.27 \)[/tex] units.
Which is the solution to the inequality? One-fourth + x less-than StartFraction 5 over 6 EndFraction x less-than StartFraction 7 over 12 EndFraction x greater-than StartFraction 7 over 12 EndFraction x less-than 1 and StartFraction 1 over 12 EndFraction x greater-than 1 and StartFraction 1 over 12 EndFraction
Answer:
A
Step-by-step explanation:
The required solution of the given inequality is given as x < 7/12. Option A is correct.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Given inequality,
One-fourth + x less-than StartFraction 5 over 6 EndFraction,
So, the Above expression is given as,
1/4 + x < 5/6
Subtract 1/4 from both sides,
1/4 + x - 1/4 < 5/6 - 1/4
x < [20 - 6] / 24
x < 14 / 21
x < 7 / 12
Thus, the required solution of the given inequality is given as x < 7/12. Option A is correct.
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The mean absolute deviation for each pizzeria is approximately 10. Approximately how many times the mean absolute deviation is the difference between the means of the data sets?
Answer:31
Step-by-step explanation:
The difference between the means would be twice the MAD (mean absolute deviation) in this case, as 20 is two times 10.
The student's question is about determining how many times larger the difference between the means of the two data sets is compared to the mean absolute deviation (MAD) of each pizzeria, which is given as approximately 10. To answer this, we need to know the means of both data sets in order to calculate the difference between them. Without this information, it's not possible to provide a specific number.
However, if the means of the two data sets were known, for example, if the mean of the first set was 20 and the mean of the second set was 40, then the difference would be 40 - 20 = 20. The difference between the means would be twice the MAD in this case, as 20 is two times 10.
Find the value of x in the following diagram.
Answer:
x = 3.5
Step-by-step explanation:
diameter = radius × radius
d= ( 3x + 1 ) + ( x + 8 )
3x + 1 = x + 8
subtract 1 and x
2x = 7
divide by 2
x = 3.5
Segment KL is a diameter of circle Q. Circle Q is represented by the equation (x − 11)2 + (y + 15)2 = 7. What is KL?
A. 98
B. 14
C. 2 radical 7
D. radical 14
We have been given that segment KL is a diameter of circle Q. Circle Q is represented by the equation [tex]\left(x-11\right)^2+\left(y+15\right)^2=7[/tex]. We are asked to find the length of KL.
We know that standard equation of a circle is in form [tex]\left(x-h\right)^2+\left(y-k\right)^2=r^2[/tex], where point (h,k) represents center of circle and r represents radius of circle.
Upon comparing our given equation with standard equation of circle, we can see that the center of the circle is at point [tex](11,-15)[/tex] and [tex]r^2=7[/tex].
Let us solve for r by taking positive square root.
[tex]\sqrt{r^2}=\sqrt{7}[/tex]
[tex]r=\sqrt{7}[/tex]
We know that diameter is two times radius, so value of diameter KL would be 2 times r.
[tex]KL=2\cdot \sqrt{7}[/tex]
Therefore, the volume of KL is [tex]2\sqrt{7}[/tex] and option C is the correct choice.
You are at a sandwich shop. You can choose from white or rye bread, turkey or ham, and Swiss or American
cheese to make your sandwich. All eight possible sandwich combinations are listed below.
If we take sandwiches 3, 4, 5, and 6 as a subset of the sample space, which of the statements below describe
this subset?
Answer: The correct is answer is: The subset consists of all the sandwiches with either white bread and ham or rye bread and turkey.
Step-by-step explanation: I got this question correct.
The statement of the subset is given below. Then the correct options are A, C, and D.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
You are at a sandwich shop.
You can choose from white or rye bread, turkey or ham, and Swiss or American cheese to make your sandwich.
Then the number of the sample will be
Total sample = 2 x 2 x 2 = 8
The set will be {(WTS), (WTA), (WHS), (WHA), (RTS), (RTA), (RHS), (RHA)}.
All eight possible sandwich combinations are listed below.
If we take sandwiches 3, 4, 5, and 6 as a subset of the sample space.
Then the statements below describe this subset will be {(WHS), (WHA), (RTS)(RTA)}
The subset consists of all the sandwiches with either white bread and Swiss cheese or rye bread and American cheese.
The subset consists of all the sandwiches with white bread and ham.
The subset consists of all the sandwiches with rye bread and turkey.
Then the correct options are A, C, and D.
The complete question is attached below.
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What is the value of x in the equation 1,331 x ^3 − 216 = 0?
A. -6/11
B. 11/6
C. 1/6
D. 6/11 (correct)
Answer:
choice D . x = 6/11
Step-by-step explanation:
1,331 x ^3 − 216 = 0?
11^3 = 1331
6^3 = 216
(11x)^3 - 6^3 = 0
We have (11x - 6) * ( (11x)^2 + 6*(11x ) + 36) = 0
Solve 11x - 6 = 0
x = 6/11
IM USING THE REST OF MY POINTS FOR THIS!!!!!! CLICK ON IMAGE TO SEE IT
Answer:
The Graph has a x- intercept at (3,0)
Step-by-step explanation:
-3 +3 =0
so x=-3