An archer releases an arrow with an initial velocity of 20 feet per second at a height of 12 feet. The path the arrow takes can be modeled using the function f(x)=−16x^2+20x+12, where f(x) represents the height, in feet, of the arrow and x represents the time the arrow travels in seconds. What is the maximum height, in feet, reached by the arrow? Round your answer to the nearest hundredth if necessary. Do not include units in your answer.

Answers

Answer 1

Answer:

18.25 feet

Step-by-step explanation:

The given function is quadratic.

The maximum of the quadratic function is its vertex.

The x-coordinate is determined by x = - b/(2a)

x = - 20/(-16*2) = 5/8

Apply the x-value and find the value of f:

f(x) = - 16(5/8)² + 20(5/8) + 12 = 18.25 feet
Answer 2

Answer:

18.25

Step-by-step explanation:

we are given a quadratic function

[tex] f(x) = - 16 {x}^{2} + 20x + 12[/tex]

where:

f(x) represents the heightx represents the time

To find the maximum value of f(x) in other words, the maximum height, in feet, reached by the arrow.

Differentiate both sides:

[tex] f'(x) = \dfrac{d}{dx}( - 16 {x}^{2} + 20x + 12)[/tex]

with sum differentiation rule, we acquire:

[tex] \displaystyle f'(x) = \frac{d}{dx}( - 16 {x}^{2} )+ \frac{d}{dx} 20x + \frac{d}{dx} 12[/tex]

recall that,

differentiation of a constant is equal to 0[tex] \dfrac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]

utilizing the rules we acquire:

[tex] \displaystyle f'(x) = - 32 {x}^{} + 20 [/tex]

now equate f'(x) to 0:

[tex] \displaystyle - 32 {x}^{} + 20 = 0[/tex]

solving the equation for x yields:

[tex]x _{max}= \dfrac{5}{8} [/tex]

plug in the maximum value of x into the quadratic function:

[tex]f(x )_{max}= - 16 {( \frac{5}{8} )}^{2} + 20( \frac{5}{8} ) + 12[/tex]

simplify:

[tex]f(x )_{max} = 18.25[/tex]

hence,

The maximum height reached by the arrow is 18.25 feet


Related Questions

solve. solve this question if you are intelligent ​

Answers

Answer:

(a) 0 (b) 1^2

Step-by-step explanation:

photo number 1 is answer for question 2(a)

photo number 2 is answer for question 2(b)

Look at the equation below. Identify which equation has no solution

Answers

Answer:

C

Step-by-step explanation:

[tex]24a-22 = -4(1-6a)\\\\\implies 24a-22 = -4+24a\\\\\implies -22 = -4\\\\\text{Which is not true, so no solutions exist.}[/tex]

-
Angle A and B are vertical angles. If Angle A = (5x – 3)° and Angle B = (4x + 21)°,
then find the measure of Angle A.

Answers

Answer:

Angle A=87°

Step-by-step explanation:

(5x-3)°+(4x+21)°=180°

9x°+18°=180°

9x°+18°-18°=180°-18°

9x°=162°

9x°/9°=162°/9°

x=18°

Angle A=(5x18-3)°

(90-3)°

Angle A=87°

How do I do this this folks?

Answers

for the answer most likey it would be from the range of 88 to 66 that would make a little sence corecct me if im wrong

Step-by-step explanation:

Kerry cut an 8 foot long board in 3 pieces that are equal in length. How long was each board?​

Answers

Answer:

2 2/3 foot

Step-by-step explanation:

3x=8

x=8÷3

=2 2/3 foot

Write a qbasic progrsm to check pass or fail​

Answers

Step-by-step explanation:

CLS

INPUT " Enter total marks "; M

IF M > 40 THEN

PRINT "You are passed "

ELSE

PRINT " You are failed "

END IF

END..

The cone shaped roof has the height of 30ft and the radius of 15ft find it's lateral area and the surface area

Answers

Answer:

Lateral surface area of cone is 1580 feet²Surface area of cone is 2287 feet²

[tex]\\[/tex]

Step-by-step explanation:

Given that Height of cone shaped roof is 30 ft and radius is 15 ft.

To calculate the lateral surface area and Surface area of the cone we will use the formula given below:

[tex]\\[/tex]

[tex]\star \: { \underline { \boxed { \purple{ \pmb { \sf{Lateral \: surface \: Area _{(cone)} = \pi rl}}}}}}[/tex]

[tex]\\[/tex]

[tex]\star{\underline{ \boxed{ \purple{ \pmb { \sf{Surface \: area _{(cone)} = \pi rl + \pi {r}^{2} }}}}}}[/tex]

[tex]\\[/tex]

Finding the Slant height of the cone:

[tex]\dashrightarrow \: \:L = \sqrt{ {(r)}^{2} + {(h)}^{2} } \\ [/tex]

[tex] \dashrightarrow \: \: L = \sqrt{225 +900 } \\ [/tex]

[tex] \dashrightarrow \: \: L = \sqrt{1125 } \\ [/tex]

[tex]{ \dashrightarrow \: \: { \pink{ \boxed { \: L = 33.541 }}}}\\ [/tex]

Hence, Slant height of cone is 33.54 feet.

Substituting values in above formula:

[tex]\dashrightarrow \: \: LSA = \pi rl \\ [/tex]

[tex]\dashrightarrow \: \: LSA = \dfrac{22}{7} \times 15 \times 33.54 \\ [/tex]

[tex]\dashrightarrow \: \: LSA = \dfrac{22 \times 15 \times 33054}{7} \\ [/tex]

[tex]\dashrightarrow \: \: LSA = \dfrac{11068.2}{7} \\ [/tex]

[tex]\dashrightarrow \: \:{ \boxed { \pmb{ \sf {\pink{ LSA \: \approx1580 \: {ft}^{2}}}} }} \\ [/tex]

[tex]\\[/tex]

Hence, Lateral surface area of cone is 1580 feet²

Now, Calculating surface area:

[tex]\dashrightarrow \: \:SA = \pi rl + \pi {r}^{2} \\ [/tex]

[tex]\dashrightarrow \: \:SA = \pi (15)(33.54) + \pi {(15)}^{2} \\ [/tex]

[tex]\dashrightarrow \: \:SA = \pi(503.1) + 22 5 \pi \\ [/tex]

[tex]\dashrightarrow \: \: SA = 728.1 \pi \\ [/tex]

[tex]\dashrightarrow \: \:SA = 728.1 \times 3.14 \\ [/tex]

[tex]\dashrightarrow \: \:{ \boxed{ \pmb{ \pink{ \sf{SA \approx2287 \: {ft}^{2} }}}}} [/tex]

[tex]\\[/tex]

Hence, surface area of cone is 2287 feet²

What is the quotient if 2/4 of 40 is divided by 4/5 of 5/7?

Answers

Answer:

2/4 * 40 4/5 * 5/7 = 102/

7

= 14 4/

7

≅ 14.5714286

Step-by-step explanation:

To find a new numerator:

a) Multiply the whole number 40 by the denominator 5. Whole number 40 equally 40 * 5/

5

= 200/

5

b) Add the answer from previous step 200 to the numerator 4. New numerator is 200 + 4 = 204

c) Write a previous answer (new numerator 204) over the denominator 5.

Forty and four fifths is two hundred four fifths

Multiple: 2/

4

* 204/

5

= 2 · 204/

4 · 5

= 408/

20

= 102 · 4/

5 · 4

= 102/

5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(408, 20) = 4. In the following intermediate step, cancel by a common factor of 4 gives 102/

5

.

In other words - two quarters multiplied by two hundred four fifths = one hundred two fifths.

Multiple: the result of step No. 2 * 5/

7

= 102/

5

* 5/

7

= 102 · 5/

5 · 7

= 510/

35

= 102 · 5/

7 · 5

= 102/

7

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(510, 35) = 5. In the following intermediate step, cancel by a common factor of 5 gives 102/

7

.

In other words - one hundred two fifths multiplied by five sevenths = one hundred two sevenths.

I = PRT

C = 2r A = r2

Answers

Answer: Calculate Total Amount Accrued (Principal + Interest), solve for A. A = P(1 + rt)

Calculate Principal Amount, solve for P. P = A / (1 + rt)

Calculate rate of interest in decimal, solve for r. r = (1/t)(A/P - 1)

Calculate rate of interest in percent. ...

Calculate time, solve for t

Step-by-step explanation:

-7/3y-2/9=1/3 solve for y

Answers

Answer:

y = -12

Step-by-step explanation:

-7/3y - 2/9 = 1/3

cross multiple for 1/3:

-21/3y - 6/9 = 1

cross multiply for 3y and 9:

-21 - 6 = 3y + 9

3y + 9 = -27

3y = -36

y = -12

Find the area of the figure

Answers

Answer:

100 mm

Step-by-step explanation:

this right awnser

Answer:

Formula for area of circle (since two semi circles form a full circle);

a = π[tex]r^{2}[/tex]

First, figure out our radius,

D/2 = Radius

10/2 = 5 is our radius.

Plug in your values:

a = π[tex]r^{2}[/tex]

a = 3.14(5^5)

a = 3.14(25)

a = 78.5 is the area of the two semi circles.

Now the square;

A = L x W

A = 10(10)

A = 100.

Add your areas;

78.5 + 100

= 178.5 mm2

please help meeeeeeeee worth a bunch of points

Answers

Answer:

220

Step-by-step explanation:

first u gotta bla bla bla

Answer:

137°

Step-by-step explanation:

a straight line is 180°

x = 180 - (22 + 21)

x = 180 - 43

x = 137

PLSS ANSWER

Round each fraction to help you estimate the solution for the equation.

three sixths plus three sixths

A. 0
B. one half
C. 1
D. one and one half

Answers

[tex] \frac{3}{6} = three \: sixths[/tex]

[tex] \frac{3}{6} + \frac{3}{6} = \frac{3 + 3}{6} = \frac{6}{6} = 1[/tex]

Letter C

15+45+6+834+32453+853=

Answers

Answer: Your solution is 34206

Hope this helps you!!!!

!!20 POINTS!!
Find the value of X. Round to the nearest tenth

Answers

The answer. Is 40 because remember the formula

A coin is flipped 8 times. Find the probability of the event:
exactly 6 heads
A.0.4375
B.0.75
C.0.0039
D.0.109

Answers

b. 0.75 because if you flip it 8 times and get heads 6 times, the probability would be 6/8 and that would simplify to 3/4 (0.75).

Answer:

D. 0.109

Step-by-step explanation:

Just did the test, its not B

The zoo has 14 penguins. There are 6 more penguins than lions. How many lions are at the zoo?

Answers

Answer:

8 lions

Step-by-step explanation:

We need to subtract!!

14 - 6 = 8

Have an amazing day!!

Please rate and mark brainliest!!

Step-by-step explanation:

let the number of penguins be X and the number of lions be Y. then X=14 and since there are more penguins than lions the equation will be X=Y+6

Substitute 14 instead of X. 14=Y+6

and now shift 6 to the left 14-6=Y

then the answer should be 8lions

Find the equation that passes through the points (8,10) and (4,5). Give your results using function notation

Answers

Answer:

  f(x) = 5/4x

Step-by-step explanation:

The equation of the line can be found using the 2-point form of the equation of a line:

  y -y1 = (y2 -y1)/(x2 -x1)(x -x1)

This can be rearranged to the desired funtional form.

__

Using the given points (x1, y1) = (8, 10) and (x2, y2) = (4, 5), we have ...

  y -10 = (5 -10)/(4 -8)(x -8)

  y = (-5/-4)(x -8) +10 = (5/4)x . . . . . add 10 and simplify

The equation can be written ...

  f(x) = 5/4x

b) The following patterns are made using small squares.
Pattern 1
Pattern 2
Pattern 3
Write an expression for the number of small squares in pattern n.
Write your answer in the form (n + a)? + b or an? + bn + C where a, b and care integers.

Answers

Answer:

(N+2)^2+6

Step-by-step explanation:

Which of the following is true of the numbers 4 and 10?

A. The greatest common factor is
B. The least common multiple is
C. The greatest common factor is 20.
D. The least common multiple is 40.​

Answers

Answer:

None

Step-by-step explanation:

Answer is isn't there

the gcf = 2

the LCM = 20

HELP!!
what is 23x+(4-5b)

Answers

Answer:

just remove the bracket and write normally so it's 23x+4-5b

Step-by-step explanation:

if you meant something else then let me know

PLEASE HELP I WILL GIVE BRAINLIEST

Answers

Answer:

Volume

Step-by-step explanation:

Length times width times height, is volume and the formula of finding what is inside something.

Volume :- it's the amount of the mass a body can hold

WILL GIVE EXTRA POINTS FOR ANSWER ⭐️⭐️!! PLEASE EXPLAIN IF POSSIBLE

Answers

Answer:

B. (-3, 10)

Step-by-step explanation:

     I am going to graph the given equation. I then will see which of the points given are within the required area.

-> See attached.

-> I have explained in the image more in-depth as well.

i will give you both my kidneys for this answer!!!! Select the correct answer.
Consider functions fand g.
f(x) = 3x+1.what is the value of (f(g(1))

Answers

Answer:

1

Step-by-step explanation:

when x is 1 g(1) is 0

so

(f(g(1)) is f(0)

f(0) is 3√0 + 1 which is

1

sorry it looks like its not one of the answer choices

https://brainly.com/question/19425686

The composition of functions f ( g ( 1 ) ) = 1

What is Composition of functions?

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 3√x + 1

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

g ( 1 ) = 0

g ( 2 ) = 1

g ( 3 ) = 4

g ( 4 ) = 9

Now , the composition of function is given by f ( g ( 1 )

The value of g ( 1 ) = 0

And , f ( x ) = 3√x + 1

when x = 0

So , the value of f ( 0 ) = 3√0 + 1

The function is f ( 0 ) = 1

Hence , the value of the function f ( g ( 1 ) = 1

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Solve: |x+2|=3

Can someone explain how to do this

Answers

Hey there!

ORIGINAL EQUATION:
|x + 2| = 3

TRANSLATE:

x + 2 = 3 or x + 2 = -3


SOLVING for: x + 2 = 3

SUBTRACT 2 to BOTH SIDES

x + 2 - 2 = 3 - 2

CANCEL out: 2 - 2 because it give you 1

KEEP: 3 - 2 because help solve for the current x-value

NEW EQUATION: x = 3 - 2

SIMPLIFY IT!
x = 1


Thus, your answer is: x = 2

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\


SOLVING for: x + 2 = -3

SUBTRACT 2 to BOTH SIDES

x + 2 - 2 = -3 - 2

CANCEL out: 2 - 2 because it give you 0

KEEP: -3 - 2 because it help solve for the current x-value

NEW EQUATION: x = -3 - 2

SIMPLIFY IT!
x = -5

Thus, your answer is: x = -5

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\


Therefore, your answer is: x = 1 or x = -5


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

A triangle has one side that is 6 units long and another side that is 3 units long.

Which of the following could be the length of the third side?

2 units
3 units
4 units
6 units
8 units
10 units

Answers

The possible value of the third length is an illustration of Triangle inequality theorem

The possible third lengths are 4 units and 6 units

How to determine the possible length of the third side?

To determine the third length, we make use of the following Triangle inequality theorem.

a + b > c

Let the third side be x.

So, we have:

x + 6 > 3

x + 3 > 6

3 + 6 > x

Solve the inequalities

x > -3

x > 3

x < 9

Remove the negative inequality value.

So, we have:

x > 3 or x < 9

Rewrite as:

3 < x or x < 9

Combine the inequality

3 < x < 9

This means that the possible value of the third length is between 3 and 9 (exclusive)

Hence, the possible third lengths are 4 units and 6 units

Read more about Triangle inequality theorem at:

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wait hihfedhsdkfsffsdf

Answers

Pain au chocolat dur main

An airplane flying with the wind takes 5 hours to travel a distance of 960 miles. The return trip takes 6 hours flying against the wind. What is the speed of the airplane in still air and how fast is the wind blowing? ​

Answers

let's recall that d = rt, distance = rate * time.

a = speed of the airplane in still air.

w = speed of the wind

the distance travelled with the wind is 960 miles, so the return trip is pretty much just that, 960 miles.

when the airplane is going with with wind, the airplane is really not going as fast as "a" mph, is really going faster due to the wind, so the speed of the plane is "a + w", because the wind is adding its speed to it.

when the airplane is going against the wind is not really going "a" mph fast either, is really going slower at "a - w" mph, because the wind is subtracting speed from it, so

[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{with the wind}&960&a+w&5\\ \textit{against the wind}&960&a-w&6 \end{array}~\hfill \begin{cases} 960=(a+w)(5)\\\\ 960=(a-w)(6) \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{960=(a+w)(5)}\implies \cfrac{960}{5}= a + w\implies 192=a+w\implies \boxed{192-w=a}[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{960=(\underline{192-w}~~ - ~~w)(6)}\implies \cfrac{960}{6}=192-w-w\implies 160=192-2w \\\\\\ 2w+160=192\implies 2w=32\implies w=\cfrac{32}{2}\implies \blacktriangleright w=16 \blacktriangleleft ~\hfill \blacktriangleright \stackrel{192 - 16}{176=a} \blacktriangleleft[/tex]

Complete the inequality.
(-9/8)/(-2 3/4) ? 3/22
>
<
=

Answers

Answer:

(-3/8)/(-2 3/4) = 3/22  

Step-by-step explanation:

Solve the following;

[tex]\frac{\left(-\frac{3}{8}\right)}{\left(-2\frac{3}{4}\right)}[/tex]

[tex]=\frac{\left(-\frac{3}{8}\right)}{\left(-\frac{11}{4}\right)}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}[/tex]

[tex]=\frac{\frac{3}{8}}{\frac{11}{4}}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]

[tex]=\frac{3\cdot \:4}{8\cdot \:11}[/tex]

[tex]\frac{3}{22}[/tex]

Thus, [tex]\frac{\left(-\frac{3}{8}\right)}{\left(-2\frac{3}{4}\right)}[/tex] = [tex]\frac{3}{22}[/tex]

~Learn with lenvy~

giving brainliest+50 points!!

What is the five-number summary of this data set?

{852, 687, 515, 986, 907, 784, 967, 685, 965}

Drag the numbers into the boxes to correctly complete the five-number summary.

Minimum
Q1
Q2
Q3
Maximum

Answers

Answer:

the 852 is the perfect fit q3

Step-by-step explanation:

The five-number summary of this data set are minimum is 515, maximum value is 986, Q₁ is 686, Q₂ is 852 and Q₃ is 966.

What is Median?

Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order. It is also called second quartile.

Given data set is,

{852, 687, 515, 986, 907, 784, 967, 685, 965}

Arrange this in ascending order first.

{515, 685, 687, 784, 852, 907, 965, 967, 986}

Minimum value = 515

Maximum value = 986

First we have to find the median or the second quartile.

Second quartile, Q₂ = Middle element of the set

Q₂ = 5th element = 852

First quartile = 1/4 (n + 1)th element = 1/4 (9 + 1) = 2.5 th element

Q₁ = (685 + 687) / 2 = 686

Third quartile = 3/4(n + 1)th element = 3/4 (9 + 1) = 7.5th element

Q₃ = (965 + 967) / 2 = 966

Hence the five-number summary of this data set are found.

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