Answer:
To find the vertex algebraically for the quadratic function -x^2 - 6x - 5, we can use the formula x = -b/2a to find the x-coordinate of the vertex, and then substitute it into the function to find the y-coordinate.
Here, a = -1 and b = -6, so x = -(-6)/(2*(-1)) = 3. Substituting x = 3 into the function, we get:
-y = -(3)^2 - 6(3) - 5 = -22
y = 22
Therefore, the vertex is at (3, 22).
which of the following experiments is likely to produce a uniform discrete distribution? multiple select question. the values that occur from repeated spins of a roulette wheel at a casino. the answer selected on a multiple choice question that has four choices by a student who did not study. the number of patrons arriving every 3 minutes at a sandwich shop. test scores on a college entrance exam, such as the act or sat.
The experiment that is most likely to produce a uniform discrete distribution is the number of patrons arriving every 3 minutes at a sandwich shop.
Test scores on a college entrance exam, such as the ACT or SAT, is an example of continuous distribution.
What is a uniform discrete distribution?A uniform distribution is a kind of probability distribution in which all of the potential outcomes have an equal likelihood of occurring. A uniform distribution with a limited set of potential outcomes is referred to as a discrete uniform distribution. In a discrete uniform distribution, there is a finite number of potential outcomes that are all equally probable.
It is important to note that the sum of the probabilities of all possible outcomes in a uniform distribution is always equal to 1 since the outcomes are equally likely to happen. The following experiments are less likely to generate a uniform discrete distribution:
Values obtained from repeated spins of a roulette wheel at a casino: Because the roulette wheel is designed to produce a non-uniform distribution, the values that result from the spins of the roulette wheel are not uniformly distributed. The answer is selected on a multiple choice question that has four choices by a student who did not study: Since the student did not study, their answers will be arbitrary and unpredictable, making a uniform distribution unlikely.Test scores on a college entrance exam, such as the ACT or SAT: Because test scores are continuous data, a uniform distribution is unlikely to occur.
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What are the domain and range of g of x equals the square root of the quantity x plus 4?
a. d: [4, [infinity]) and r: [0, [infinity])
b. d: (–4, [infinity]) and r: (–[infinity], 0)
c. d: [–4, [infinity]) and r: [0, [infinity])
d. d: (4, [infinity]) and r: (–[infinity], 0)
The domain and range of g of x equals the square root of the quantity x plus 4, g(x) = √x + 4, are equal to d: [–4, [infinity]) and r: [0, [infinity]). Thus, the right choice of answer is option (c).
We have a function g(x) and defined as square root of the quantity x plus 4, i.e.,
g(x) = √x + 4
We have to determine the domain and range of function g(x).
The domain of function is all input values of x that make the expression defined. The range is the set of all output values that valid g(x) values. A square root limits the function because we can't have negative numbers under the square root (they become imaginary numbers). Let y = g(x) = √x +4
the square root '√ 'sign must be implies ≥ 0, therefore, x + 4 ≥ 0
Subtracting the 4 from both sides
=> x + 4 -4 ≥ 0 - 4
=> x ≥ -4
The domain is x∈ [-4,+∞)
When x = -4, g(x) = 0
Therefore, The range is y∈ [0, 00)
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Help me please with this math assignment
The actual distance of 6 cm, given the scale of the map, would be 30 km .
The distance on the map, given the actual distance on the ground and the scale, would be 6 inches .
How to find the actual distance ?The scale is that for every 1 cm on the map, the actual distance is 5 kilometers. When given 6 cm therefore, the actual distance is :
= 6 x 5
= 30 km
The scale of the second map is such that 1 inch on the map is 3 actual kilometers so 18 km on the ground would be :
= 18 / 3
= 6 inches
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Complete the table for the quadratic function below. Type the value of y that
corresponds with each value of x.
y=2(x-3)²-2
xy=2(x-3)²-2
1
2
3
4
5
Values of y that corresponds with the value of x as per quadratic functions are as follows:
6
0
-2
0
6
What are quadratic functions?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.
The parent quadratic function connects the locations whose coordinates have the type f(x) = x2 and is of the kind (number, number2).
Just need to evaluate the function for each value of X.
for x=1 y=2(1-3)²-2= 6
for x=2 y=2(2-3)²-2= 0
for x=3 y=2(3-3)²-2= - 2
for x=4 y=2(4-3)²-2= 0
for x=5 y=2(5-3)²-2= 6
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Solve for x in the triangle
The two primary components of an angle are the limbs and the vertex. The angle sum property of a triangle is 20+21+29=180 70x=180 x=180/70.
What are angles?An angle is the result of the intersection of two lines.
An "angle" is the length of the "opening" between these two beams.
Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.
In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.
The two primary components of an angle are the limbs and the vertex. The joint vertex is the common terminal of the two beams.
According to the given question,
angle sum property of triangle-
20+21+29=180
70x=180
x=180/70.
Hence, With the angle sum property of triangle, x=180/70.
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Perform the operation and simplify such that
The value οf a, b, and c are 3, 5, and 25 respectively.
What is an equatiοn?There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.
The given equatiοn is
1/(x + 5) + 2/(x -5) = (ax + b)/ (x² - c)
Sοlve the left-hand side οf the equatiοn:
L.H.S = 1/(x + 5) + 2/(x -5)
= [x-5 + 2(x+5)]/(x + 5)(x -5)
= [x-5 + 2x+ 10]/(x + 5)(x -5)
Cοmbine like terms:
= [3x + 5]/(x + 5)(x -5)
Nοw apply fοrmula (a-b)(a+b) =a² - b²:
= [3x + 5]/(x² - 5²)
= [3x + 5]/(x² - 25)
Put 1/(x + 5) + 2/(x -5) = [3x + 5]/(x² - 25) in the given equatiοn:
[3x + 5]/(x² - 25) = (ax + b)/ (x² - c)
Nοw cοmpare bοth sides:
a = 3
b = 5
c= 25
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Mei and kara build computers from parts and sell them to make a profit mei can build a computer in 0. 8 hours
Mei worked 8 hours and Kara worked 7 hours when Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour.
Let's use the following variables to represent the unknowns in the problem:
Let M be the number of computers Mei built
Let K be the number of computers Kara built
We can set up a system of equations based on the given information:
M + K = 17 (the total number of computers built is 17)
0.8M + K = 15 (the total time worked is 15 hours)
We can solve for one of the variables in terms of the other by using the first equation:
M = 17 - K
Now we can substitute this expression for M into the second equation:
0.8(17 - K) + K = 15
13.6 - 0.8K + K = 15
0.2K = 1.4
K = 7
So Kara built 7 computers. We can use the first equation to find how many computers Mei built:
M + 7 = 17
M = 10
Therefore, Mei built 10 computers.
Now we can find how long each girl worked by multiplying the number of computers by their respective build times:
Mei: 10 computers x 0.8 hours per computer = 8 hours
Kara: 7 computers x 1 hour per computer = 7 hours
Therefore, Mei worked 8 hours and Kara worked 7 hours.
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The complete question is :
Mei and Kara build computers from parts and sell them to make a profit. Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour. together they worked 15 hours and built 17 hours and built 17 computers. how many hours did each girl work ?
Gethyn needs to drink 8 cups of water each day. Today he has consumed 48 fluid ounces. How many more cups does he need to drink today?
By the given parameters, Gethyn needs to drink 2 more cups of water today.
How many more cups does he need to drink today?From the question, we have the following parameters that can be used in our computation:
Amount = 8 cups
Today = 48 ounces
There are 8 fluid ounces in one cup.
So, to convert 48 fluid ounces to cups, we divide by 8:
48 fluid ounces / 8 fluid ounces per cup = 6 cups
Therefore, Gethyn has already drnk 6 cups of water today.
To reach his goal of 8 cups, he still needs to drink:
8 cups - 6 cups = 2 cups
So Gethyn needs to drink 2 more cups of water today.
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What is the slope of the line?
Answer:
Slope m = 1/3
Step-by-step explanation:
Slope of the line can be found by taking two points on the line, (x1, y1) and (x2, y2)
Find the difference in y coordinates, y2 - y1 (called rise)
Find the difference in corresponding x coordinates x2 - x1 (called run)
Rise/Run gives the slope
Two distinguishable points on the line graph are (0, 2) and (3, 3)
rise = 3 - 2 = 1
run = 3 - 0 = 3
Slope = 1/3
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction of the bar. ABC rotates 90 degrees clockwise about point p to from A’B’C
To rotate triangle ABC 90 degrees clockwise about a point P, we can follow these steps:
Draw a line segment from each vertex of the triangle to the point P.
Measure the distance from each vertex to the point P and make note of the lengths.
Rotate each line segment 90 degrees clockwise by swapping the x and y coordinates and changing the sign of the new y-coordinate. For example, if a vertex has coordinates (x, y), the new coordinates after rotation will be (y, -x).
Use the new endpoints of the line segments to draw the new triangle, A'B'C'.
For example, suppose the coordinates of triangle ABC are A(1,2), B(3,4), and C(5,2), and the point of rotation is P(3,3). Then the distances from each vertex to the point P are:
AP = sqrt((3-1)² + (3-2)²) = sqrt(5)
BP = sqrt((3-3)² + (3-4)²) = 1
CP = sqrt((3-5)² + (3-2)²) = sqrt(5)
After rotating each vertex 90 degrees clockwise about P, we get:
A'(4,1)
B'(2,3)
C'(4,5)
Using these new coordinates, we can draw the new triangle A'B'C', which is the result of rotating triangle ABC 90 degrees clockwise about P.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction of the bar. ABC rotates 90 degrees clockwise about point p to from A’B’C
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A likelihood of 1 is also known as...
Answer:
A likelihood of 1 is also known as the Discrete probability distribution
pls answer this
it isnt add 3, it says its wrong when i press it
pls helpp meee
I think you are correct, I am not sure why. Maybe you ask your teacher and she or he made a mistake with this question.
PLEASE HELPP Find a.
Answer:122
Step-by-step explanation:
sum of the interior angles of a rectangle is equal to 360 degrees. sum of neighbor angles is equal to 180 degrees. the if one of the neighbor angle is 90 then, other is 180-90=90.
a+76+72+90=360
a+238=360
a=122
NI
Megan is taking out a loan for $6,000 with
an annual compound interest rate of 13%
for 6 years. Megan will not make any
additional deposits or withdrawals. What
will be the total balance paid at the end of 6 X
years?
Round your answer to the closest dollar
amount. Do not include $ symbol in answer
Prove that STV is congruent to TUW
Answer:
The picture shows that the side lengths and the angle are the same because of the lines
Step-by-step explanation:
The answer is given and VS=WT but add the line symbol above that
Ahmet borrows $700 and is charged compound interest at 15% per year. How much will he have to pay back in total after 6 years?
Give your answer to two decimal places.
Answer:
The required amount Ahmet needs to pay after 6 years is $1619.14.
What is compound interest?
Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Amount = principal[1 + r/n]ⁿᵃ
Principal = P rate= r Time =a , n = compounding frequency
Here,
From the given data,
P = 700, r = 15% and t = 6 (n =1)
Now,
Amount = principal[1 + r/n]ⁿᵃ
Amount = 700(1 + 0.15)⁶
Amount = $1619.14
Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.
Step-by-step explanation:
Elavate each expression when x is 4 and y is 6
Answer:
the answer to ur question is: 36
AB is the diameter of a circle C. What is the measure of arc DB?
Answer:
arc DB = 45°
Step-by-step explanation:
the measure of an arc is the same as the central angle that intercepts it.
∠ DCB = 180° - 135° = 45°
∠ DCB is the central angle intercepted by arc DB , then
arc DB = 45°
If i walk 3. 5 miles in 2 hours. How far can i walk in 8 hours?
If I walk 3.5 miles in 2 hours, then I can walk 14 miles in 8 hours.
If I walk 3.5 miles in 2 hours, then I can use a simple proportion to calculate how far I can walk in 8 hours. I know that in 2 hours I can walk 3.5 miles, and I want to calculate how far I can walk in 8 hours. To do this, I can set up a proportion. The fraction representing the time I spent walking and the distance I walked must be equal on both sides of the equation. On the left side of the equation, I set up 2/3.5, and on the right side I set up 8/x, where x is the unknown distance I can walk in 8 hours. I can then solve for x by cross-multiplying and dividing. After solving, I find that I can walk 14 miles in 8 hours.
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Wilbur flew twice as fast as his brother Orville and therefore made the 852-ft flight in 6 seconds less time. What is each of their rates in feet per second and how many seconds is each of their flights.
Wilbur's flight took about 43.7 seconds.
How to find the time?Let x be the rate of Orville in feet per second and 2x be the rate of Wilbur in feet per second. Let t be the time it took for Orville to complete the flight and t - 6 be the time it took for Wilbur to complete the flight.
We know that the distance traveled by both brothers is the same, which we can express with the equation:
distance = rate × time
For Orville:
distance = x * t
For Wilbur:
distance = 2x * (t - 6)
Since the distance is the same for both brothers, we can set the two equations equal to each other:
x * t = 2x * (t - 6)
Expanding and simplifying the right-hand side:
xt = 2xt - 12x
12x = xt
x = t/12
So, Orville's rate is x = t/12 feet per second.
Substituting this into one of the equations for distance, we can solve for t:
distance = x * t
852 = (t/12) * t
852 = t² / 12
t² = 12 * 852
t² = 10224
t ≈ 101.1 seconds (rounded to the nearest tenth)
So, Orville's flight took about 101.1 seconds.
Now we can use the equation for Wilbur's distance to find his rate:
distance = 2x * (t - 6)
852 = 2(2x) * (101.1 - 6)
852 = 4x * 95.1
x ≈ 5.64 feet per second (rounded to the nearest hundredth)
So, Orville's rate is about 5.64 feet per second, and Wilbur's rate is twice that or about 11.28 feet per second.
To find Wilbur's time, we can use the equation for distance again:
distance = 2x * (t - 6)
852 = 2(11.28) * (t - 6)
852 = 22.56t - 135.36
22.56t = 987.36
t ≈ 43.7 seconds (rounded to the nearest tenth)
So, Wilbur's flight took about 43.7 seconds.
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x-15+2x+6
please help me with step by step explanation
Answer:
To simplify the expression x - 15 + 2x + 6, you can combine like terms. Here are the steps to do that:
Group the x terms and the constant terms separately:
(x + 2x) + (-15 + 6)
Simplify the terms inside the parentheses:
3x - 9
So the simplified expression is 3x - 9.
Therefore, x - 15 + 2x + 6 equals 3x - 9.
Answer:
3(x-3)
Step-by-step explanation:
given : x-15+2x+6
factorize using like terms : x-15+3x+6 = 3x-9
= 3x - 9
=3(x-3)
Find the missing side. Round answers to the nearest tenth! Show or explain your work. Pleases
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
An object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction. Find the total force on the object
Force on the object is 7.04 pounds in the x-direction
Force on the object is -2.52 pounds in the y-direction
The total force on an object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction can be found by resolving each force into its x- and y-components, and then adding them to obtain the net force acting on the object.An object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction is shown below:An object being pushed with 5 pounds of force in the θ=45˚ direction and also with 7 pounds of force in the θ=-60˚ direction.To resolve the forces, we use the following identities:Fx = Fcosθ, andFy = Fsinθ.The x- and y-components of the 5-pound force in the θ=45˚ direction are:Fx = Fcosθ = 5 cos 45˚ = 3.54 pounds,andFy = Fsinθ = 5 sin 45˚ = 3.54 pounds.The x- and y-components of the 7-pound force in the θ=-60˚ direction are:Fx = Fcosθ = 7 cos (-60˚) = 3.5 pounds,andFy = Fsinθ = 7 sin (-60˚) = -6.06 pounds.The total force acting on the object is the sum of the x- and y-components of the forces acting on it, or:Fx = 3.54 pounds + 3.5 pounds = 7.04 pounds,Fy = 3.54 pounds - 6.06 pounds = -2.52 pounds.Therefore, the total force on the object is 7.04 pounds in the x-direction and -2.52 pounds in the y-direction.
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Quadrilaterals HIJK and ABCD are congruent. The side length of each square on the grid is 1 unit. Which of the following sequences or transformations maps HIJK to ABCD?
The sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.
What is quadrilateral ?
A quadrilateral is a polygon with four sides and four vertices. The term "quadrilateral" comes from the Latin words "quadri" meaning "four" and "latus" meaning "side". Quadrilaterals can have different shapes and properties, including rectangles, squares, parallelograms, trapezoids, and kites.
Since quadrilaterals HIJK and ABCD are congruent, we can map one onto the other using a sequence of transformations. We need to determine which of the given sequences of transformations maps HIJK to ABCD.
Sequence A involves a 270° rotation about point J, followed by a translation 9 units to the right and 8 units down.
Sequence B involves a reflection over the line HÌ, followed by a translation 6 units to the right and 3 units down.
To determine which sequence maps HIJK to ABCD, we can apply each sequence to the vertices of HIJK and see if the resulting image matches the vertices of ABCD.
Starting with sequence A, we apply the rotation and translation to the vertices of HIJK:
Vertex H(-2, 1) is rotated 270° about J(-2, 2) to get H'(0, 0). Then we translate 9 units to the right and 8 units down to get H''(9, -8).
Vertex I(-3, -1) is rotated 270° about J(-2, 2) to get I'(1, -3). Then we translate 9 units to the right and 8 units down to get I''(10, -11).
Vertex J(-2, 2) is fixed by the rotation and then translated 9 units to the right and 8 units down to get J''(7, -6).
Vertex K(0, 0) is rotated 270° about J(-2, 2) to get K'(-2, -2). Then we translate 9 units to the right and 8 units down to get K''(7, -10).
The resulting image of HIJK under sequence A has vertices H''(9, -8), I''(10, -11), J''(7, -6), and K''(7, -10). We can see that these vertices do not match the vertices of ABCD, so sequence A does not map HIJK to ABCD.
Next, we apply sequence B to the vertices of HIJK:
Vertex H(-2, 1) is reflected over line HÌ to get H'(-4, 3). Then we translate 6 units to the right and 3 units down to get H''(2, 0).
Vertex I(-3, -1) is reflected over line HÌ to get I'(-1, 1). Then we translate 6 units to the right and 3 units down to get I''(5, -2).
Vertex J(-2, 2) is reflected over line HÌ to get J'(-4, 4). Then we translate 6 units to the right and 3 units down to get J''(2, 1).
Vertex K(0, 0) is reflected over line HÌ to get K'(-2, 2). Then we translate 6 units to the right and 3 units down to get K''(4, -1).
The resulting image of HIJK under sequence B has vertices H''(2, 0), I''(5, -2), J''(2, 1), and K''(4, -1). We can see that these vertices match the vertices of ABCD, so sequence B maps HIJK to ABCD.
Therefore, the sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.
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Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (use 3.14 for π)
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π (pi) is a constant approximately equal to 3.14.
To find the circumference of the circle, we need to know the radius. If we are not given the radius directly, we may be given another measurement that we can use to calculate it. For example, we may be given the diameter, which is the distance across the circle passing through its center. The radius is half the diameter.
Assuming we have been given the diameter of the circle, we can calculate the circumference as follows:
Write down the formula for the circumference of a circle: C = 2πr
Identify the diameter of the circle. Let's say it is 10 cm.
Calculate the radius by dividing the diameter by 2: r = 10/2 = 5 cm.
Plug in the value of the radius into the formula: C = 2π(5) = 10π.
Use the approximation of π as 3.14: C = 10(3.14) = 31.4 cm.
Therefore, the circumference of the circle is approximately 31.4 cm, to the nearest tenth of a centimeter.
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Complete question:
A circle of radius 3 cm is drawn .Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (Use 3.14 for π)
A) 9.4 cm
B) 18.8 cm
C) 37.7 cm
D) 56.6 cm
Suppose that X1, X2,. . . Xn are random sample of
P(X=x│θ)= θ^x/x! E^- θ
(a) Find the MSE of X bar
(b) Find the limit of MSE when n tends to infinity
(a) To find the mean squared error (MSE) of X bar, we need to first find its expected value and variance.
The expected value of X bar is:
E(X bar) = E((X1 + X2 + ... + Xn) / n) = (n * E(X)) / n = E(X) = θ
The variance of X bar is:
Var(X bar) = Var((X1 + X2 + ... + Xn) / n) = (1/n^2) * Var(X1 + X2 + ... + Xn) = (1/n^2) * n * Var(X) = θ/n
Therefore, the MSE of X bar is:
MSE(X bar) = Var(X bar) + [E(X bar) - θ]²= θ/n + [θ - θ]² = θ/n
(b) To find the limit of MSE when n tends to infinity, we can take the limit of the MSE formula as n approaches infinity:
lim(n → ∞) MSE(X bar) = lim(n → ∞) θ/n = 0
Therefore, as the sample size becomes larger, the MSE of X bar approaches zero. This means that X bar becomes a better and better estimator of the true parameter θ as the sample size increases.
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amy asked alfred, an international student from denmark to participate in her survey. after alfred completed the survey, amy also asked alfred to introduce other international students who might be interested in participating in her survey. as a result, amy was able to collect enough data to conduct her analysis. what type of sampling method did amy use?
In conclusion, Amy used a snowball sampling method to collect data for her survey. This method is useful when the population is hard to locate or identify, and when other sampling methods are not possible
Amy used a snowball sampling method. Snowball sampling is a non-probability sampling method where the participants recruit other members of the population.
It is useful when the population is difficult to locate or identify, as it relies on word of mouth or referrals from already recruited participants. In this case, Alfred was able to introduce other international students who might be interested in participating in Amy's survey. This allowed Amy to collect enough data to conduct her analysis. Snowball sampling is useful when the sample size is not known, when time is limited, or when a random selection is not possible.
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Look at the imagien BUT QUICKLY help
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing a number from the multiples of 4 between 20 and 40, inclusive The sample space is _______ (Use a comma to separate answers as needed. Use ascending order.) There are _____ outcome(s) in the sample space.
The sample space is 20, 24, 28, 32, 36, 40. There are 6 outcomes in the sample space. In this case, the sample space is {20, 24, 28, 32, 36, 40}.
The sample space of the probability experiment is the set of all possible outcomes that can occur when randomly choosing a number from the multiples of 4 between 20 and 40, inclusive.
To determine the number of outcomes in the sample space, we simply count the number of elements in the set. In this case, there are 6 outcomes in the sample space.
Therefore, the sample space is {20, 24, 28, 32, 36, 40} and there are 6 outcomes in the sample space. After Randomly choosing a number from the multiples of 4 between 20 and 40, these values are found.
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The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.
h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5
h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5
h = cosine (StartFraction pi Over 12 EndFraction t) + 9
h = cosine (StartFraction pi Over 6 EndFraction t) + 9
The correct option to model the height is
h = cosine (StartFraction pi Over 6 EndFraction t) + 9.
Finding the equation to model the height:Here the height of the tip of the hour hand of a wall clock follows a cosine function as the time progresses since the hour hand of a clock completes one full revolution in 12 hours.
We will use the general form of a cosine function to model the height has a function of time t:
h = A cos(Bt) + CWhere A is the amplitude, B is the frequency and C is the vertical shift
Here we have
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.
Hence, the applitude A = [9+10]/2 = 0.5.
The period of a cosine function is given by 2π/B,
Since the hour hand completes one full revolution in 12 hours, the period is 12 hours or 2π.
=> B = π/6.
The vertical shift is C = 9.
Thus, the equation that models the height h as a function of time t is:
h = 0.5 cos(π/6 t) + 9.
Therefore,
The correct option to model the height is
h = cosine (StartFraction pi Over 6 EndFraction t) + 9.
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