1
Suppose f(x) = x2 - x - 12, g(x) = x + 3, and h(x) = 6x - 1. Which of the following function operations are
three that apply.
A (g x h)(x) = 6x2 + 17x-3
B (n + 1)(x) = x2 + 5x - 13
C (f = g)(x) = x - 4
D (f - h)(x) = x2 - 7x-13
E (g- h)(x) = 5x - 4
о
Answers
Related Questions
If a population has 500 individuals in it in 2010, and the per capita birth rate is 0.3 and the per capita death rate is 0.2, is the population growing or shrinking?
Answers
The population is growing as the births are more than deaths in an year.
What is Population Growth?Increases in a population's or a dispersed group's membership are referred to as population growth.
Given:
Total population = 500Per capita birth rate = 0.3Per capita death rate = 0.2To find: Is population growing or shrinking?
Finding:
Number of new-borns in an year = total population (per capita birth rate) = 500(0.3) = 150Number of deaths in an year = total population (per capita death rate) = 500(0.2) = 100Difference in the number of births and deaths = 150 - 100 = 50Hence the population is growing as the births are more than deaths in an year.
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The given curve is rotated about the y-axis. Set up, but do not evaluate, an integral for the area of the resulting surface by integrating (a) with respect to x and (b) with respect to y.
x = e5y, 0 ≤ y ≤ 2
Answers
We have that, given the curve x = e5y, 0 ≤ y ≤ 2, it rotates around the y axis, we are going to obtain the following integrals
Part A: State, but do not evaluate, an integral for the surface area resulted by integrating with respect to x. Integrating with respect to x, the formula for finding the surface area of a curve rotated about the y axis is:
\(S=2\pi \int abxf(y)\sqrt{[1+({f(x))^2}']}dx\)
Since the curve revolves around the y-axis, the equation will have the form x = f(y). Therefore, x = e5yTaking the derivative of the equation, we have:
\({f(y)}' = 5e5y\)
multiplying by
\(f(y)2\pi \intabxf(y)\sqrt{[1+(f′(x))^2]}dx=2\pi \int 02e^5y(2\pi(5e5y)\sqrt{[1+(5e^5y)^2]}dx\)
Integrating and substituting the limits are obtained;
\(2\pi \int 02e^5y( 2\pi(5e^5y)\sqrt{[1+(5e5y)^2}]dx = 2 \pi \int 02e^5y \sqrt{(1+ 25e10y)}dy\)
Part B: Establish, but do not evaluate, an integral for the surface area resulted by integrating with respect to y. Integrating with respect to y, the formula for finding the surface area of a curve rotated about the y-axis is:
\(S=2\pi \int abxf(y)\sqrt{[1+(f′(x))^2}] dx\)
Since the equation is given as \(x = e^5y\), we will convert it to \(y = f(x)\) by taking the natural logarithm of both sides.
\(ln x = ln(e)^5y5 = 5y\)
So, the formula is \(y = 1/5 ln(x)\) using this formula as f(x) in the surface area formula;
\(S = 2\pi \int ab1/ 5ln(x) \sqrt{[1+((1 /5x)\\2}]dx.\)
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A teacher was making identical activity packets using 92 crayons and 23 sheets of paper. What is the greatest number of packets the teacher can make with no items left over?
Answers
Answer:
the teacher can make 23 packets with 4 crayons in each packet
Step-by-step explanation:
the teacher can make 23 packets with 4 crayons in each packet wit no left over.
What is the scale factor of the dilation?
One-eighth
One-fourth
4
8
Answers
The image of the parallelogram which is larger than the preimage,
indicates that the scale factor is larger than 1.
Correct response:
The scale factor of the dilation is 4Which is the Method used for finding the scale factorThe scale factor is found by finding the ratio of the corresponding sides.
The possible given diagram in the question is a parallelogram FGHJ
dilated to form the similar parallelogram, F'G'H'J'.
The length of side FG = -2 - (-4) = 2
The length of side F'G' = 3 - (-5) = 8
\(The \ scale \ factor = \mathbf{ \dfrac{Length \ of \ F'G'}{Length \ of \ FG} }\)Which gives;
\(The \ scale \ factor = \dfrac{8}{2} = 4\)
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Answer:
C) 4
Step-by-step explanation:
PLEASE HELP HARD FOR ME BUT EASY FOR OTHERS
Answers
You add 31 and 39 first to get 70 degrees.
Then add 38 degrees because the angle in the lower corner is the same as one the would be placed to the right of the top two angles. 70 plus 38 equals 108 degrees.
Next you subtract 108 from 180 to get the answer for x. That gives you 73 degrees.
Complete the sentence. Then, use the laws of exponents to write an equivalent expression for the given expression.
To divide powers that have the same base and different exponents, keep the ___ and ___ the exponents.
Answers
To divide powers that have the same base and different exponents, keep the base and subtract the exponents.
How to divide exponents with same baseWhen dividing two powers that have the same base but different exponents, you keep the base and subtract the exponents.
For example, if you want to divide a^m by a^n,
you can write it as a^m / a^n
= a^(m-n).
The new exponent is the result of subtracting the exponents of the two powers.
hence the division will result to a^(m-n).
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The formula for relating a man's shoe size S and the length of his foot L in inches is
S3L
26. Find the length of a man's foot if he wears a size 12 shoe.
Answers
Answer:
12 5/6 inches
Step-by-step explanation:
You want to find the value of L when S=12 1/2, using the formula S = 3L -26.
Foot lengthYou can substitute for S in the formula before or after you solve for L. Here, we'll solve for L first:
S +26 = 3L . . . . add 26 to both sides
(S +26)/3 = L . . . . divide both sides by 3
Substituting 12 1/2 for S, this becomes ...
L = (12 1/2 +26)/3 = (38 1/2)/3 = (77/2)/3 = 77/6 = 12 5/6
A man's foot is 12 5/6 inches long if he wears a size 12 1/2 shoe.
Answer:
the length of his foot in inches is 12
The water level (In feet) In Boston Harbor during a certain 24 hour period is approximated by the formula H = 4.8 sin[π/6 (t - 10)] + 7.6, 0 ≤ t ≤ 24 where t = 0 corresponds to 12 AM. What it the average water level in Boston Harbor over the 24 hour period on that day? At what times of the day did the water level in Boston Harbor equal the average water level? (use Mean value Theorem for integrates)
Answers
The average water level in Boston Harbor over the 24-hour period is 7.2 feet.
To find the average water level in Boston Harbor over the 24-hour period, we need to calculate the average value of the function H(t) over the interval [0, 24]. The Mean Value Theorem for Integrals states that if f(x) is continuous on the interval [a, b], then there exists a number c in the interval (a, b) such that the average value of f(x) over [a, b] is equal to f(c).
In our case, the function H(t) = 4.8 sin[(π/6)(t - 10)] + 7.6 is continuous over the interval [0, 24]. To find the average value, we integrate H(t) over the interval [0, 24] and divide by the length of the interval.
Let's calculate the integral first:
∫[0,24] H(t) dt = ∫[0,24] (4.8 sin[(π/6)(t - 10)] + 7.6) dt
Using the antiderivative of the sine function and evaluating the integral over the interval [0, 24], we get:
= [-9.6 cos[(π/6)(t - 10)] + 7.6t] evaluated from 0 to 24
= (-9.6 cos[4π] + 7.6 * 24) - (-9.6 cos[0] + 7.6 * 0)
= (-9.6 + 182.4) - (-9.6)
= 172.8
The length of the interval [0, 24] is 24 - 0 = 24.
Therefore, the average water level over the 24-hour period is:
Average = (1/(24 - 0)) * ∫[0,24] H(t) dt
= (1/24) * 172.8
= 7.2
To determine the times of the day when the water level equals the average, we need to find the values of t that satisfy H(t) = 7.2. We can solve this equation:
4.8 sin[(π/6)(t - 10)] + 7.6 = 7.2
Simplifying the equation, we have:
4.8 sin[(π/6)(t - 10)] = 7.2 - 7.6
4.8 sin[(π/6)(t - 10)] = -0.4
Dividing by 4.8, we get:
sin[(π/6)(t - 10)] = -0.4/4.8
sin[(π/6)(t - 10)] = -1/12
To find the values of t, we can take the arcsine (inverse sine) of both sides:
(π/6)(t - 10) = arcsin(-1/12)
Solving for (t - 10), we have:
(t - 10) = (6/π) * arcsin(-1/12)
Finally, solving for t:
t = (6/π) * arcsin(-1/12) + 10
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Solve for x, no links please!
Answers
Answer:
Solution given:
\( \frac{5 + x}{2} = 4 \)
multiplying both side by 2
\( 5 + x = 4 \times 2 \)
subtracting both side by 5
we get
x = 8 -5
x = 3
x = 3is a required answer.
in Windsor area of New South Wales, flood flow needs to be drained from a small locality at a rate of 120 m³/s in uniform flow using an open channel (n=0.018) Given the bottom slope as 0.0013 calculate the dimensions of the best cross section if the shape of the channel is (a) circular of diameter D and (b) trapezoidal of bottom width b Write your solution on A4 page, scan the solution and upload the scanned pdf file in vUWS. Do not email the solution to the lecturer tutor
Answers
The bottom width and depth of the trapezoidal channel are 2.25 m and 1.67 m, respectively.
In Windsor area of New South Wales, flood flow needs to be drained from a small locality at a rate of 120 m³/s in uniform flow using an open channel (n=0.018) Given the bottom slope as 0.0013 calculate the dimensions of the best cross section if the shape of the channel is (a) circular of diameter D and (b) trapezoidal of bottom width b.
(a) Circular channel:
For a circular channel, the best hydraulic section can be achieved by using the formula,
Q = (1 / n) x (A / P)2 / 3 x S0.5
where Q is the discharge; A is the area of the flow section; P is the wetted perimeter, S is the slope of the channel; and n is the roughness coefficient of the channel.
Assuming that the channel is flowing at full capacity, the depth of flow can be calculated using the following formula,
Q = (1 / n) x (π / 4) x D2 / 2 x D1 / 2 x S0.5
where D is the diameter of the channel; S is the slope of the channel; and n is the roughness coefficient of the channel.
Solving for D,
D = (8Q / πnD12S0.5)
For the given values of Q, n, and S,
D = (8 × 120 / π × 0.018 × 0.00132 × 120.5)
D = 1.98 m
Therefore, the diameter of the circular channel is 1.98 m.
(b) Trapezoidal channel:
For a trapezoidal channel, the best hydraulic section can be achieved by using the formula,
Q = (1 / n) x (A / P)2 / 3 x S0.5
where Q is the discharge; A is the area of the flow section; P is the wetted perimeter, S is the slope of the channel; and n is the roughness coefficient of the channel.
Assuming that the channel is flowing at full capacity, the depth of flow can be calculated using the following formula,
Q = (1 / n) x ((b + y) / 2) y / ((b / 2)2 + y2)0.5 x ((b / 2)2 + y2)0.5 x S0.5
where b is the bottom width of the channel; y is the depth of flow in the channel; S is the slope of the channel; and n is the roughness coefficient of the channel.
Rewriting the equation,
120 = (1 / 0.018) x ((b + y) / 2) y / ((b / 2)2 + y2)0.5 x ((b / 2)2 + y2)0.5 x (0.0013)0.5
Simplifying the equation,
658.5366 = (b + y) y / ((b / 2)2 + y2)0.5 x ((b / 2)2 + y2)0.5
Squaring both sides,
433407.09 = (b + y)2 y2 / ((b / 2)2 + y2) x ((b / 2)2 + y2)
Multiplying both sides by ((b / 2)2 + y2),
433407.09 ((b / 2)2 + y2) = (b + y)2 y2 x ((b / 2)2 + y2)
Simplifying the equation,
216703.545 = b2 y3 / 4 + b y4 / 2 + y5 / 4
Solving the above equation by using trial and error, the bottom width and depth of the trapezoidal channel are 2.25 m and 1.67 m, respectively.
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A reaction occurs when solid X is placed into solution Y. As a result, the temperature of the new solution increases by 3°C. The
temperature rises another 2°C when more of solid X is added to the solution. What does this indicate about the effect of
adding more solid?
It increased the number of molecular collisions.
It decreased the number of molecular collisions,
It decreased the space between the molecules and lowered the reaction rate.
It increased the space between the molecules and increased the reaction rate.
Answers
Answer:
A. It increased the number of molecular collisions.
what do the symbols p with hat on top, x with bar on top, and s represent? variables of interest sample statistics defined variables population parameters
Answers
The symbols p,x, and s represent sample statistics.
- p (pronounced "p-hat") is the sample proportion. It is used to estimate the population proportion. It is computed as the number of successes in the sample divided by the sample size.
-x (pronounced "x-bar") is the sample mean. It is used to estimate the population mean. It is computed as the sum of all the values in the sample divided by the sample size.
- s is the sample standard deviation. It is used to estimate the population standard deviation. It measures how spread out the data is in the sample. It is computed as the square root of the sum of the squared deviations from the sample mean divided by the sample size minus one.
These sample statistics are used to make inferences about the corresponding population parameters, which are denoted by Greek letters such as μ (mu) for the population mean and σ (sigma) for the population standard deviation.
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(x+1)^2 -(x+1)
Worth 10 points
Answers
Answer:
x^2+x
Step-by-step explanation:
Answer:
x(x+1)
Step-by-step explanation:
What operation is being done to the variable in the equation -5m = -40?
It's being multiplied by -5.
It's being divided by -5.
It's being multiplied by -40.
It's being divided by -40.
Answers
Answer:
it's being divided by -5
Step-by-step explanation:
-5m= -40
m=8
The operation is being done to the variable in the equation -5m = -40 is multiplied by -5.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
The equation is given as; -5m = -40
-5m= -40
Solving, multiplied by -5.
m= - 40/-5
m = 8
Therefore, the operation is being done to the variable in the equation -5m = -40 is multiplied by -5.
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Use the quadratic formula to find the solutions for
y = -x2 - 5x + 12
Answers
Add the variables
Y=-7x+12
There^
words from a written text the person can remember after five minutes with the text.
Answers
The words from a written text that a person can remember after five minutes with the text are known as short-term memory.
Short-term memory refers to the storage of information for a brief period of time, usually a few seconds to a few minutes. It is a type of memory that is involved in the conscious processing of information and is responsible for holding information in mind for immediate use.
The capacity of short-term memory is limited and varies from person to person. Generally, it can hold about 7 pieces of information or less, and can only hold it for a short period of time. This is why it is important to transfer important information from short-term memory to long-term memory through a process called encoding.
To improve short-term memory, one can use techniques such as repetition, chunking, visualization, and association. By doing this, it is possible to hold more information in short-term memory for a longer period of time.
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if a decreases, then b will also decrease. the graph relating the two variables a and b is:
Answers
The graph relating the variables a and b would be a downward-sloping line or a negative correlation. When it is stated that "if a decreases, then b will also decrease," it indicates a negative relationship or correlation between the variables a and b.
In this case, as the value of a decreases, the value of b also decreases. This relationship can be visually represented by a downward-sloping line on a graph.
As you move from left to right along the x-axis (representing a), the corresponding values on the y-axis (representing b) decrease. This negative correlation suggests that there is an inverse relationship between the two variables, where changes in a are associated with corresponding changes in the opposite direction in b.
The extent and strength of the negative correlation can vary, ranging from a perfect negative correlation (a straight downward-sloping line) to a weaker negative correlation where the relationship is less pronounced.
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how much more probable is it that one will win 6/48 lottery than the 6/52lottery?
Answers
It is about 1.657 times more probable to win a 6/48 lottery than a 6/52 lottery.
To find out how much more probable it is to win a 6/48 lottery than a 6/52 lottery, we need to compare their respective probabilities of winning.
The probability of winning a 6/48 lottery is given by the formula:
P(6/48) = C(6, 48) = 1/12271512
where C(6, 48) is the number of ways to choose 6 numbers out of 48.
Similarly, the probability of winning a 6/52 lottery is given by the formula:
P(6/52) = C(6, 52) = 1/20358520
where C(6, 52) is the number of ways to choose 6 numbers out of 52.
To find out how much more probable it is to win the 6/48 lottery than the 6/52 lottery, we can calculate their relative probabilities:
P(6/48) / P(6/52) = (1/12271512) / (1/20358520) ≈ 1.657
Therefore, it is about 1.657 times more probable to win a 6/48 lottery than a 6/52 lottery.
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Here is the equation of four straight lines. Two of these lines are parallel. Which two
lines? (3)
Line A y = 2x+3
Line B 2y = 6- 3x
Line C 4x -2y =3
Line D y = 3-2x
Answers
Answer:
Line A and Line C are parallel.
Step-by-step explanation:
ANSWER FAST PLEASE!! ILL GIVE BRAINLEST
What is the solution to the system of equations below?
Answers
Answer:
the solution is (-2,-5)
Step-by-step explanation:
What is the sum of the roots of the equation -2x² + 7 = 13x ?
Answers
Answer: x=1/2
x= − 7
Step-by-step explanation:
Simplify the expression
Divide both sides by the same factor
Simplify the expression
Divide both sides by the same factor
Help please thank you
Answers
Answer:
I'm pretty sure this would be C.
A and B aren't good fits at all since they don't follow the trend of the points well. D would be a good fit, as it follows the trend well, however, C is better.
Please help NEEDED ASAP!!!!
taxi cab tariffs in London, England, are as follows.
For the first 234.8 metres or 50.4 seconds (whichever is reached first)
there is a minimum charge of 2.60 GBP.
For each additional 117.4 metres or 25.2 seconds (whichever is reached first), if the distance travelled is less than 9656.1 metres there is a charge of 0.20 GBP.
Once the distance has reached 9656.1 metres then there is a charge of 0.20 GBP for each additional 86.9 metres or 18.7 seconds (whichever is reached first)
1. Develop a piecewise linear model for the cost, C, of a taxi ride based on the distance travelled, m, in metres.
2. Find the cost of 0.2 km, 5 km, and 15 km rides.
3. Develop a piecewise linear model for the cost, D, of a taxi ride based on the time taken, t, in seconds, ignoring distance.
4. Find the cost of 0.5 minute, 5 minute, and 15 minute rides.
5. Given that the actual taxi fare is always the greater of the two models, find:
(i) the cost of a ride that takes 10 minutes to go 4 km (if) the cost of a ride that takes 5 minutes to go 4 km
Answers
Answer:
1. A piecewise linear model for the cost, C, of a taxi ride based on the distance travelled, m, in meters can be represented as:
C = 2.60 (m<234.8)
C = 2.60 + 0.20(m-234.8) (234.8<=m<9656.1)
C = 2.60 + 0.20(9656.1-234.8) + 0.20(m-9656.1) (m>=9656.1)
2.To find the cost of 0.2 km, 5 km, and 15 km rides:
0.2 km = 200 m, the cost would be 2.60 GBP
5 km = 5000 m, the cost would be 2.60 + (0.20 * (5000-234.8)) GBP = 2.60 + 858 GBP = 1118 GBP
15 km = 15,000 m, the cost would be 2.60 + (0.20 * (9656.1-234.8)) + 0.20(15,000-9656.1) GBP = 2.60 + (0.20 * 9656.1-234.8) + 0.20(15,000-9656.1) = 2.60 + 1712.2 + 2040 = 3964.8 GBP
3. A piecewise linear model for the cost, D, of a taxi ride based on the time taken, t, in seconds, ignoring distance can be represented as:
D = 2.60 (t<50.4)
D = 2.60 + 0.20(t-50.4) (50.4<=t<1260)
D = 2.60 + 0.20(1260-50.4) + 0.20(t-1260) (t>=1260)
4. To find the cost of 0.5 minute, 5 minute, and 15 minute rides:
0.5 minute = 30 seconds, the cost would be 2.60 GBP
5 minutes = 300 seconds, the cost would be 2.60 + (0.20 * (300-50.4)) GBP = 2.60 + 44 GBP = 2.60+44 = 3.04 GBP
15 minutes = 900 seconds, the cost would be 2.60 + (0.20 * (1260-50.4)) + 0.20(900-1260) GBP = 2.60 + (0.20 * 1260-50.4) + 0.20(900-1260) = 2.60 + 252 + -12 GBP = 2.48 GBP
5. Given that the actual taxi fare is always the greater of the two models, find:
(i) the cost of a ride that takes 10 minutes to go 4 km is 1118 GBP (by distance model)
(ii) the cost of a ride that takes 5 minutes to go 4 km is 3.04 GBP (by time model)
It is important to
N architect is standing 370 feet from the base of a building and would like to know the height of the building. If he measures the angle of elevation to be 50°, what is the approximate height of the building?
Answers
Answer:
h = 440.94 feet
Step-by-step explanation:
It is given that,
An architect is standing 370 feet from the base of a building, x = 370 feet
The angle of elevation is 50°.
We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :
\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)
So, the approximate height of the building is 440.94 feet
Complete the tables x and y for linear equations 2x-3=y
Answers
The completed table in tabular form
X Y
0 -3
1 -1
2 1
3 3
How to complete the tableTo complete the table for the equation y = 2x - 3, we can substitute the given x values into the equation to find the corresponding y values.
X value. 0. 1. 2. 3
by substituting x = 0 into the equation y = 2x - 3, we get:
y = 2(0) - 3
y = -3
by substituting x = 1 into the equation y = 2x - 3, we get:
y = 2(1) - 3
y = -1
by substituting x = 2 into the equation y = 2x - 3, we get:
y = 2(2) - 3
y = 1
by substituting x = 3 into the equation y = 2x - 3, we get:
y = 2(3) - 3
y = 3
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complete question
Complete the table for the equation y = 2x - 3
X value. 0. 1. 2. 3
Y value.
y - 2x =3 Solve for Y
Answers
Answer:Add x to both sides of the equation.y=3+2x
Step-by-step explanation:
could y be 9 im lost
One positive number is 6 times another number. The difference between the two numbers is 205. Find the numbers. (Enter your answers as a comma-separated list.)
Answers
Answer:
Hence the positive numbers are 246, and 41
(246, 41)
Step-by-step explanation:
From the question,
One positive number is 6 times another numberLet the first positve number be \(x\)
and the other number be \(y\)
Hence,
\(x = 6y\) ....... (1)
Also,
The difference between the two numbers is 205That is,
\(x - y =205\) ........(2).
To solve for the two unknowns, substitute the value of \(x\) in equation (1) into equation (2).
Since,
\(x = 6y\)
Then
\(x - y =205\) becomes
\((6y) - y =205\\\)
Then,
\(6y - y = 205\\5y = 205\\\)
Divide both sides by 5
\(\frac{5y}{5} = \frac{205}{5} \\ y = 41\\\)
∴ the value of \(y\) is 41
Now, substitute the value of y into equation (1) to find \(x\)
Then,
\(x = 6y\) becomes
\(x = 6(41)\\x = 246\\\)
∴ the value of \(x\) is 246
Hence the positive numbers are 246, and 41
(246, 41)
If £1 = US$1.11316 and A$1 = US$0.8558, how many British pounds will you get for one Australian dollar?
=£
Round to two decimal places
Answers
The correct answer is you will get approximately £1.30 for one Australian dollar.
To find out how many British pounds you will get for one Australian dollar, we need to determine the exchange rate between the British pound and the Australian dollar.
Given that £1 = US$1.11316 and A$1 = US$0.8558, we can calculate the exchange rate between the British pound and the Australian dollar as follows:
£1 / (US$1.11316) = A$1 / (US$0.8558)
To find the value of £1 in Australian dollars, we can rearrange the equation:
£1 = (A$1 / (US$0.8558)) * (US$1.11316)
Calculating this expression, we get:
£1 ≈ (1 / 0.8558) * 1.11316 ≈ 1.2992
Therefore, you will get approximately £1.30 for one Australian dollar.
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1/2 minus (1/8+1/8) I need help can somebody give me advice on this
Answers
Answer: 38
Step-by-step explanation:
Subtract 1/8 from 1/2
12 - 18 is 38.
Steps for subtracting fractions
Find the least common denominator or LCM of the two denominators:
LCM of 2 and 8 is 8
Next, find the equivalent fraction of both fractional numbers with denominator 8
For the 1st fraction, since 2 × 4 = 8,
12 = 1 × 42 × 4 = 48
Likewise, for the 2nd fraction, since 8 × 1 = 8,
18 = 1 × 18 × 1 = 18
Subtract the two like fractions:
48 - 18 = 4 - 18 = 38
Cancel CF which is 2
Now you will be with
1/2 - 1/4
Calculate
Solution
1/4
The function $y=-\frac{1}{40}\left(x-25\right)^2+15$ models the path of a football kicked by a player, where $x$ is the horizontal distance (in yards) and $y$ is the height (in yards). the player kicks the ball a second time so that it travels the same horizontal distance but reaches a maximum height that is 5 yards less than the maximum height of the first kick. write a function that models the path of the second kick.
Answers
The quadratic function that models the path of the second kick is given by:
y = -2/125(x - 25)² + 10.
What is the equation of a parabola of vertex (h,k)?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which the coefficients are explained as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.For the first kick, the equation is:
y = -1/40(x - 25)² + 15.
Meaning that the ball reached a maximum height of yards after an horizontal distance of 25 yards.
For the second kick, the horizontal distance is the same, but the maximum height if 5 yards less, that is, of 10 yards, hence the vertex is:
(h,k) = (25, 10).
Hence the equation is:
y = a(x - 25)² + 10.
After 50 yards, the ball hits the ground, hence the leading coefficient a is found as follows:
0 = a(50 - 25)² + 10
625a = -10
a = -10/625
a = -2/125
Hence:
y = -2/125(x - 25)² + 10.
More can be learned about quadratic functions at https://brainly.com/question/24808124
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