Fill in the blank. In the triangle below x = ______. Round your answer to two decimal places.
Answers
x=35tan42° units
x≈31.51 units (to nearest hundredth of a unit)
Answer:
[tex]x=31.51\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle
[tex]tan(42\°)=x/35[/tex]
isolate the variable x
[tex]x=35tan(42\°)=31.51\ units[/tex]
Related Questions
N a poisson probability problem, the rate of errors is one every two hours. what is the probability of at most three defects in four hours
Answers
The probability of having at most three defects in a four-hour period is approximately 0.8572.
The Poisson probability distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate at which the events occur. In this problem, the rate of errors is given as one error every two hours. We need to find the probability of having at most three defects in a four-hour period.
To solve this problem, we can use the Poisson probability formula, which is:
P(x; λ) = (e^(-λ) * λ^x) / x!
where P(x; λ) is the probability of having exactly x events occur in the given interval, λ is the average rate of events, e is the base of the natural logarithm, and x! is the factorial of x.
First, we need to calculate the average rate of events in a four-hour period. Since the rate is given as one error every two hours, we can calculate the rate for a four-hour period as follows:
Average rate = (4 hours) / (2 hours/error) = 2 errors
Now, we can plug this average rate (λ = 2) into the Poisson probability formula for x = 0, 1, 2, and 3 to find the probabilities of having at most three defects:
P(0; 2) = [tex](e^{(-2)} * 2^0)[/tex] / 0! ≈ 0.1353
P(1; 2) = ([tex]e^{(-2)} * 2^1[/tex]) / 1! ≈ 0.2707
P(2; 2) = [tex](e^{(-2)} * 2^2)[/tex] / 2! ≈ 0.2707
P(3; 2) = [tex](e^{(-2)} * 2^3)[/tex] / 3! ≈ 0.1805
To find the probability of at most three defects, we sum up these individual probabilities:
P(at most 3 defects) = P(0; 2) + P(1; 2) + P(2; 2) + P(3; 2) ≈ 0.8572
So, the probability of having at most three defects in a four-hour period is approximately 0.8572.
Two buses leave at the same time traveling in opposite directions. One bus travels at 63mph and the other at 62mph. How soon will they be 187.5
miles apart?
Answers
the buses are traveling in opposite directions, but both are taking off at the same time
let's say bus A is going at 63mph and bus B is going at 62mph, so, we know their "r" rate for each
ok, after they had travelled for "t" time, they're both 187.5 miles apart, at that instant, bus A has been travelling for "t" hours and bus B has been also travelling for "t" hours as well
now, if bus A covered say "d" miles in those "t" hours, then bus B covered the slack from 187.5 and "d", or 187.5 - d
thus
[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{bus A}&d&63&t\\ \textit{bus B}&187.5-d&62&t \end{array} \\\\\\ \begin{cases} \boxed{d}=63t\\ 187.5-d=62t\\ ----------\\ 187.5-\boxed{63t}=62t \end{cases}[/tex]
solve for "t".
what is 802 and 6 hundredths in expanded form
Answers
Hope this helps!
what is the axis of symmetry of y=3x^2+6x+5
Answers
----------------------------------------------
Explanation:
The equation y = 3x^2+6x+5 is in the form y = ax^2+bx+c
In this case, a = 3, b = 6, c = 5.
We will plug a = 3 and b = 6 into the formula below
x = -b/(2*a)
x = -6/(2*3)
x = -6/6
x = -1
Therefore, the axis of symmetry is x = -1
This is the vertical line that passes through the vertex. We can reflect the parabola over this line to have one half of the curve line up perfectly with the other half of the curve.
Ace Hardware sells boxes of wrenches ($ 100) and hammers ($300). Howard ordered 40 boxes of wrenches and hammers for $ 8,400. How many boxes of each are in the order.
Answers
h+w=40, h=40-w, using this h in the first equation gives you:
100w+300(40-w)=8400 perform the indicated multiplication on left side
100w+12000-300w=8400 combine like terms on the left side
-200w+12000=8400 subtract 12000 from both sides
-200w=-3600 divide both sides by -200
w=18, and since h=40-w
h=40-18=22
So Howard ordered 18 boxes of wrenches and 22 boxes of hammers.
Answer:
18 boxes of wrenches and 22 boxes of hammers.
Step-by-step explanation:
Solve the quadratic equation by completing the square. x^2-14x+42=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.
Form: ______
Solution: _______
Answers
x^2 - 14x = -42
x^2 - 14x + 49 = 49 - 42
(x - 7)^2 = 7
x - 7 = (+-) sqrt 7
x = 7 (+-) sqrt 7
solutions are : x = 7 + sqrt 7 and x = 7 - sqrt 7
x^2-14x=-42 halve the linear coefficient, square it, add it to both sides, in this case: (14/2)^2=7^2=49, add 49 to both sides
x^2-14x+49=7 now the left side is a perfect square...
(x-7)^2=7 take the square root of both sides
x-7=±√7 add 7 to both sides
x=7±√7
The above is the two solutions, 7+√7 and 7-√7
I am not sure what they mean by the proper form other than perhaps the point when you have a complete square as in the point in the process where you have a perfect square...
(x-7)^2=7
The rarest form of dichromatism is _____.?
a. ?protanopia
b. ?deuteranopia
c. ?tritanopia
d. ?fruitopia
Answers
The rarest form of dichromatism is tritanopia. This condition affects the perception of blue and yellow colors and is less common than protanopia and deuteranopia which affect red and green perception respectively.
Explanation:The rarest form of dichromatism is tritanopia. The term dichromatism refers to an abnormality in color vision where an individual can only perceive two of the three primary colors. This question is related to the broader topic of color vision deficiencies, a study within biology. Among the options listed, protanopia and deuteranopia tend to be the most common color vision deficiencies, both affecting the perception of red and green respectively. Tritanopia is a condition that impacts the ability to perceive blue and yellow and is the least common form, while 'Fruitopia' is not related to this topic as it's a brand of fruit drinks.
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what is 2500g converted to kg
Answers
2500 g = 2,5 kg
A new surgery is successful 75% of the time. if the results of 10 such surgeries are randomly sampled, what is the probability that fewer than 9 of them are successful
Answers
This is a binomial probability problem where we calculate the probability of fewer than 9 successful surgeries out of 10, given a success rate of 75% for each surgery. The probabilities of 0 to 8 successful surgeries are calculated and summed up.
Explanation:The question asks for the probability that fewer than 9 out of 10 surgeries are successful, given that each surgery has a 75% chance of being successful. This is a binomial probability problem since each surgery can result in either success (75%) or failure (25%), and we are dealing with a fixed number of independent trials (10 surgeries).
To solve this, we first calculate the probability of exactly 8 successes, exactly 7 successes, and so on down to 0 successes, then sum these probabilities. The binomial probability formula is P(x) = (nCx) * (p^x) * ((1-p)^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and nCx is the combination of n items taken x at a time.
However, calculating each probability individually and summing them can be tedious, and tools or calculators designed for binomial distributions are often used to compute this more efficiently. For a result of fewer than 9 successes, we would add the probabilities of getting 8, 7, ..., down to 0 successful surgeries.
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 58:03 The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the standard form of the equation for this line?
Answers
The standard form of the equation for the line passing through (-5, -1) and (10, -7) is y = x - 17.
Explanation:The standard form of the equation for the line passing through the points (-5, -1) and (10, -7) can be found using the point-slope form given, which is y + 7 = (x - 10).
First, let's convert this equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Subtracting 7 from both sides of the equation, we get y = x - 17.
This is the standard form of the equation for the line passing through (-5, -1) and (10, -7).
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6nsquared - 5nsquared + 7nsquared simplify the expression
Answers
n^2+7n^2= 8n^2
Final answer: 8n^2
Remember that all of these terms are like terms so you can just add/subtract coefficients.
What is the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice?
Answers
The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The total number of probability is given as,
Total event = 6 x 6
Total event = 36
The samples are given as,
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Then the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be given as,
P = (4/36) + (11/36)
P = 15/36
P = 5/12
The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.
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The numbers 1 through 9 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random.
What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?
Answers
Write all the 4-digit numbers that can be formed using the digits from 1 to 9, without repetition, in pieces of paper, and put them in a bag. What is the probability of picking the 4-digit number 1234, among these numbers.
The connection of the 2 problems is as follows:
The 4-digit number, for example 5489, represents drawing first 5, then 4, then 8, then 9 , in the original question.
we did not allow repetition, because for example the number 8918 would represent drawing 8, then 9, then 1 then 8 (again!!), which is not possible, so we lose the connection between the problems.
So there are in total 9*8*7*6= 3024 4-digit numbers, with non-repeating digits.
One of these numbers is 1234 (representing drawing 1, then 2, then 3, then 4)
among these 3024 numbers, the probability of picking 1234 is
[tex] \frac{1}{3024}= 0.00033[/tex]
We could have solved this problem also as :
P(drawing 1, 2, 3, 4 in order)= [tex] \frac{1}{9} * \frac{1}{8} * \frac{1}{7} * \frac{1}{6} = \frac{1}{3024} [/tex]
Answer:[tex] \frac{1}{3024}= 0.00033[/tex]
The probability of drawing the slips '1', '2', '3', and '4' in that order is 1/126 or approximately 0.0079.
Explanation:The probability that the drawn slips are '1', '2', '3', and '4', in that order, can be calculated by considering the number of favorable outcomes and the total number of possible outcomes.
There are 9 slips in the box, so the total number of possible outcomes is 9 choose 4, which is denoted as C(9,4) or 9!/(4!(9-4)!), which simplifies to 126.
Since we want the slips to be drawn in a specific order, the number of favorable outcomes is 1, because there is only 1 way to arrange the slips in the order '1', '2', '3', and '4'.
Therefore, the probability is 1/126, which simplifies to approximately 0.0079 or 0.79%.
The net of a pyramid is shown below. The net of a square based pyramid, with base edges labeled 4 inches and the height of the triangle labeled 8 inches. The surface area of the solid is ____ square inches.
Answers
Hydraulicists often express rainfall in acre-feet. this is the amount of water required to cover an area of one acre to a depth of one foot. there are 640.0 acres in a square mile, and 5280 feet in one mile. how many cubic feet are there in one acre-foot?
Answers
= (5280 ft)^2
=27878400 ft^2
Since 1 sq. mile contains 640 acres, therefore
1 acre
=27878400 ft^2 / (640 acres / sq. mile)
=43560 ft^2/acre
This means the volume of 1 acre-foot
= 43560 ft^2 * 1 ft
= 43560 ft^3
Answer:
1 acre foot = 43560 ft³
Step-by-step explanation:
1 square mile = 640 acres.
5280 feet = 1 mile
5280 x 5280 ft² = 640 acres.
1 acre = 43560 ft².
1 acre foot = 43560 x 1 ft³ = 43560 ft³
1 acre foot = 43560 ft³
42 out of 96 support a candidate in an office election what percent of the vote is that
Answers
divide
42/96 = 0.4375
0.4375*100 = 43.75 percent
round the answer as needed.
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager?
Answers
Answer:
3181 yards.
Step-by-step explanation:
All the given information can be used to draw a simple diagram. The diagram shows a triangle which is formed by the ships. There are two angles given and one side is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:
sin V / v = sin G / g.
It can be observed that the angle V is unknown, however, it can be calculated very easily. Simply use the law of triangle in which all the 3 angles sum up to 180 degrees. So V = 180 degrees - 44 degrees - 36 degrees = 100 degrees. So plugging in v = 4510 yards, V = 100 degrees, G = 44 degrees, and g = x yards into the sine rule gives:
sin 100 / 4510 = sin 44 / x.
Cross multiplying gives:
x*sin 100 = 4510*sin 44
Making x the subject gives:
x = (4510*sin 44)/sin 100.
x = 3181 yards (to the nearest yard).
Therefore, Norman and Voyager are 3181 yards apart from each other!!!
The required distance between the Norman and the Voyager is 3181 yards.
Given that,
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager is to be determined.
These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Here,
The measure of the angle between Gladstone and the norman,
= 180 - 44 + 36
= 100°
sin(100) / 4510 = sin(44) / x.
x = 3181.12
x ≈ 3181 yards
Thus, the required distance between the Norman and the Voyager is 3181 yards.
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It takes Sam 3 hours to do all of the yard work, but it takes his brother Carl only 2 hours. How long, in hours, would take them to do the yard work if they work together?
A.
5/6
B.
2/3
C.
6/5
D.
3/2
Answers
S=1/3, C=1/2
So for them working together:
t/3+t/2=1 making a common denominator of 6
2t/6+3t/6=1
5t/6=1
5t=6
t=6/5
Given that 3^x = 4^y = 12^z, show that z = (xy)/(x+y).
Answers
[tex]3^{x} = 4^{y} = (4 \cdot 3)^{z}[/tex]
[tex]3^{x} = 4^{y} = 4^{z} \cdot 3^{z}[/tex]
[tex]\text{Let a } = 3^{x} = 4^{y} = 4^{z} \cdot 3^{z}[/tex]
[tex]log_3a = x[/tex]
[tex]log_4a = y[/tex]
[tex]log_{(4 \cdot 3)}a = z[/tex]
Using change of base:
[tex]x = \frac{lna}{ln3}[/tex]
[tex]y = \frac{lna}{ln4}[/tex]
[tex]z = \frac{lna}{ln(4 \cdot 3)}[/tex]
[tex]ln3 = \frac{lna}{x}[/tex]
[tex]ln4 = \frac{lna}{y}[/tex]
[tex]ln(4 \cdot 3) = \frac{lna}{z}[/tex]
Now, ln(4 · 3) = ln(4) + ln(3)
[tex]\frac{lna}{z} = \frac{lna}{x} + \frac{lna}{y}[/tex]
[tex]\frac{1}{z} = \frac{1}{x} + \frac{1}{y}[/tex]
[tex]\frac{1}{z} = \frac{x + y}{xy}[/tex]
[tex]\therefore z = \frac{xy}{x + y}[/tex]
Final answer:
To show that z = (xy)/(x+y) given that 3^x = 4^y = 12^z, logarithms and the properties of exponents are used to simplify and solve for z.
Explanation:
The problem given is to show that if 3^x = 4^y = 12^z, then z = (xy)/(x+y). To solve this, we can use logarithms or equate the expressions to a common variable. Since 12 = 3 × 4, it means that 12^z = (3^z)(4^z).
Remember that the original equations given were 3^x = 12^z and 4^y = 12^z.
Substituting z into these equations we have 3^x = 3^z × 4^z and 4^y = 3^z × 4^z.
Taking logarithms, we find
[tex]log(3^x) = log(3^z) + log(4^z) and log(4^y) = log(3^z) + log(4^z).[/tex]
Applying the power rule of logarithms, the equations simplify to
[tex]x log(3) = z log(3) + z log(4)[/tex]and [tex]y log(4) = z log(3) + z log(4).[/tex]
Dividing these equations by log(3) and log(4) respectively gives
[tex]x = z + z(log(4)/log(3))[/tex] and [tex]y = z + z(log(3)/log(4)).[/tex]
Adding these equations, we get
[tex]x + y = 2z + z[(log(4)/log(3)) + (log(3)/log(4))],[/tex]
which simplifies to x + y = 2z because [tex](log(4)/log(3)) + (log(3)/log(4)) = 1.[/tex]Finally, solving for z gives z = (xy)/(x+y) as desired.
A business has $11,080 to spend on new laptops and tablet computers for its salespeople. The laptops cost $515 each. The tablets cost $285 each. The business wants each salesperson to have either a laptop or a tablet. There are 30 salespeople. How many of each type of computer should the business buy?
Answers
T = number of tablets bought
ok.. so, we know there are 30 salespeople.... so... the business is getting 30 of devices.. .so, whatever L is and T is, we know L + T = 30
each laptop is 515 bucks, so if they buy L amount, they'd end up paying 515*L or 515L bucks
each tablet is 285, so if they buy T tablets they'd end up paying 285*T or 285T bucks for them.
whatever those may be, we know all they have is 11,080. so 515L + 285T = 11080
[tex]\bf \begin{cases} L+T=30\implies \boxed{T}=30-L\\ 515L+285T=11080\\ ----------\\ 515L + 285\left( \boxed{30-L} \right)=11080 \end{cases}[/tex]
solve for L, to see how many laptops they'd get.
what about the tablets? well, T = 30 - L.
515x + 285y = 11,080
x + y = 30
Use the slope formula to find the missing coordinate. m =3/5 , P(3, 2) and Q(8,_)
Answers
3/5 = (Z - 2)/(8-3)
3/5 = (Z-2)/5
3 = Z-2 and Z =5, So Q(8,5)
Answer:
The missing coordinate is 5
Step-by-step explanation:
Consider the equation y=2x+5 . Create a table of five ordered pairs that satify the equation. What is the y-intercept of the equation? What is the x-intercept of the equation?
Answers
The y-intercept is 5 (technically the point (0,5))
The x-intercept occurs when y=0 so:
2x+5=0
2x=5
x=2.5
So the x-intercept is the point (2.5, 0)
Answer:
five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)
y intercept is (0,5)
x intercept is (-2.5, 0)
Step-by-step explanation:
y=2x+5
To get 5 ordered pairs , plug in some random number for x and find out y
x y= 2x+5
-2 2(-2) + 5= 1
-1 2(-1) + 5= 3
0 2(0) + 5= 5
1 2(1) + 5= 7
2 2(2) + 5= 9
five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)
When x=0 , the value of y = 5
So y intercept is (0,5)
To find x intercept we plug in 0 for y
y=2x+5
0 = 2x +5
subtract 5 from both sides
-5 = 2x
divide by 2 on both sides
x= -5/2
so x intercept is (-2.5, 0)
On a cross-country trip, a couple drives 500 mi (miles) in 10h on the first day, and 400 mi in 8h on a second day. the average speed for the whole trip is:
Answers
The average speed = [500+400] ÷ [10+8]
The average speed = 900 ÷ 18 = 50 miles/hour
is 5 a solution to the equation 2x^2 + 10 = 60 yes or no
Answers
2(25)+10
50+10
60
Yes
yes : 2(5)² +10 = 60
50+10=60... ( right )
Ray and lilli are designing their own shoes. They have 4 color options for the base and 6 color options for the accent. They can also pick 2 fonts for the embroidery. What is the probability that ray and lilli design identical shoes?
Answers
To solve this problem, let us first calculate the probability of designing one shoe out of all the combinations.
Probability of designing one shoe = (probability of choosing 1 color for the base) * (probability of choosing 1 color for the accent) * (probability of choosing 1 font for the embroidery)
We know that probability is:
Probability = number of chosen event / number of total events
Therefore:
Probability of designing one shoe = (1 / 4) * (1 / 6) * (1 / 2)
Probability of designing one shoe = 1 / 48
This means that either Ray or Lilli has this probability of designing a specific shoe. Since we are asked for the probability that they will both design this specific shoe, so we multiply:
Probability they will design the same shoe = (1 / 48) * (1 / 48)
Probability they will design the same shoe = 1 / 2304 = 4.34 * 10^-4
The probability is around 0.043% that they will design the same shoe.
Lisa is asked to draw a triangle with the following specifications:
two angles are complementary
the side between the two complementary angles has a length of 10 centimeters
Which of the following statements about this triangle is true?
A.
More than one triangle exists with the given conditions, and all instances must be right triangles.
B.
More than one triangle exists with the given conditions, and all instances must be isosceles triangles.
C.
Exactly one triangle exists with the given conditions, and it must be a right triangle.
D.
Exactly one triangle exists with the given conditions, and it must be an isosceles triangle.
Answers
α+β are complementary means, their sum is 90°. So the measure of the remaining 3rd angle is 180°-90°=90°.
This means the triangle is a right triangle, with the length of the hypotenuse equal to 10 cm.
let the length of the sides be a and b.
So lisa can draw any right triangle, with sides a and b, such that
[tex] a^{2} + b^{2} = 10^{2}=100[/tex]
which means, infinitely many triangles.
Answer:
A.More than one triangle exists with the given conditions, and all instances must be right triangles.
The half life of cobalt -60 (used in radiation therapy) is 5.26 years ( actual data ).how much of a 200 g sample of cobalt-60 will remain after 26.3 years
Answers
For every half-life, one half of an isotope decays.
26.3 / 5.26 = 5
26.3 years is exactly 5 half-lives.
After EACH half-life we have one half of what we previously had.
So after one half-life we have 50%
2 half-lives 25%
3 half-lives 12.5%
4 half-lives 6.25%
5 half-lives 3.125%
So, how much is left of the 200 gram sample?
200 * .03125 = 6.25 grams
The amount of cobalt-60 will decrease with each half-life, which is 5.26 years. After 5 half-lives (26.3 years), the 200g sample will reduce to 6.25g.
Explanation:The subject of the question is the half-life of a radioactive substance, in this case, cobalt-60. Half-life is the time required for half the atoms in a sample to decay. Given that the half-life of cobalt-60 is 5.26 years, and we are interested in a period of 26.3 years, we first classify this period into 'half-life' units, which equals 26.3 / 5.26 = 5 half-lives.
With each half-life, the quantity of cobalt-60 is cut in half. We start with a 200g sample and after 5 half-lives, the amount of cobalt-60 would decrease as follows:
After the 1st half-life = 200/2 = 100g After the 2nd half-life = 100/2 = 50gAfter the 3rd half-life = 50/2 = 25gAfter the 4th half-life = 25/2 = 12.5gAfter the 5th half-life = 12.5/2 = 6.25gTherefore, after 26.3 years, only 6.25g of the original 200g sample of cobalt-60 will remain.
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A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)= 96t-16t^2 . After how long will it reach its maximum height? Do not round your answer.Time: ___ seconds
Answers
The time taken to reach the maximum height = 3 s
Further explanationQuadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
f (x) = ax² + bx + cwhere a, b, and c are real numbers and a ≠ 0.
The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value
So the maximum is if a <0 and the minimum if a> 0.
After t seconds, a ball height h (in feet) is given by the function h (t) = 96t-16t²
The maximum value of the function is obtained if the first derivative of the function h (t) = 0
96-32t = 0
96 = 32t
t = 3 s
Learn more
The maximum height
https://brainly.com/question/12298041
the fencing
https://brainly.com/question/7190180
domain of the function
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Final answer:
The ball reaches its maximum height after 3 seconds. This is determined by finding when the derivative of the height function h(t) = 96t - 16t² equals zero and solving for t.
Explanation:
To determine the time at which the ball reaches its maximum height, we need to analyze the function h(t) = 96t - 16t². Here, h(t) represents the height of the ball after t seconds. The ball achieves its maximum height when the derivative of the height function with respect to time is zero (i.e., when its upward velocity is zero).
To find this, we can take the derivative of h(t) and set it equal to zero to find the critical points:
h'(t) = d/dt (96t - 16t²) = 96 - 32t.
Setting the derivative equal to zero:
96 - 32t = 0
32t = 96
t = 96/32 = 3 seconds.
Therefore, the ball reaches its maximum height after 3 seconds.
At the swim club, what is the ratio of men to all members?
A
1:3
B
3:4
C
1:2
D
4:1
Answers
300 women
400 men
100 children
a. 1:3
b. 3:4
c. 1:2
d. 4:1
Add all the people present in the club--->100+400+300=800
Ratio of men means divide number of men by total members which is
400: 800
Simplify that and you get 1 : 2
Due to the lack of numerical details, a precise ratio of men to all members at the swim club cannot be determined. The ratio would be based on the exact number of men verses total members. Ratios offer a method to compare quantities.
Explanation:Unfortunately, without more information, it's impossible to definitively say what the precise ratio of men to all members at the swim club is. To determine the correct ratio, we would need to know the total number of members at the club, and the number of those members who are men. A ratio is a way to compare quantities or numbers, and in this case, the quantity of men compared to the quantity of all members.
For example, if there were 20 members total in the club, and 10 of those members were men, the ratio would be 1:2 (choice C), because for every one man, there are two total members. However, if there were 4 members and 3 of them were men, then the ratio would be 3:4 (choice B). Without the specific numbers, we cannot determine the correct answer from choices A, B, C, or D.
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Precalc: Vector word problem:
A channel flows from north to south at a rate of 15 mph.
A sailboat heads at an angle of 30 degrees upstream at 40 mph.
A strong wind blows towards northwest at 30 mph.
a. Write each vector in component form.
Answers
I can make this much from that, check the picture below.
A vector can be defined as an element of a vector space, which represents an object that has both magnitude and direction.
Assuming that; [tex]\left \{ {{x=rcos \theta} \atop {y=rsin \theta}} \right.[/tex]
For the channel:
Rate, r = 15 mph.The vector representing the flow from North to South is given by:
[tex]15 cos (\frac{3\pi}{2} ), \; 15 sin (\frac{3\pi}{2} )\\\\15(0),\; 15(-1)[/tex]
Vector = 0, -15
For the sailboat:
Rate, r = 40 mph.Angle = 30 degrees upstream.The vector representing the sailboat is given by:
[tex]40 cos (30 ), \; 40 sin (30)\\\\30(\frac{\sqrt{3} }{2} ),\; 30(\frac{1 }{2} )\\\\15\sqrt{3} ,\;15[/tex]
Vector = [tex]15\sqrt{3} ,\;15[/tex]
For the strong wind:
Rate, r = 30 mph.The vector representing the strong wind blowing towards northwest is given by:
[tex]30 cos (\frac{3\pi}{4} ), \; 30 sin (\frac{3\pi}{4} )\\\\30(\frac{-\sqrt{2} }{2} ),\; 30(\frac{\sqrt{2} }{2} )\\\\-15\sqrt{2},\;15\sqrt{2}[/tex]
Vector = [tex]-15\sqrt{2},\;15\sqrt{2}[/tex]
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