Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h ( t ) = − 16 t 2 + 16 t + 480 h(t)=−16t 2 +16t+480, where t is the time in seconds and h is the height in feet. What is the maximum height that Jason reaches?

Answers

Answer 1

Answer:

484feet

Step-by-step explanation:

If the height as a function of time could be modeled by the function h(t)=−16t^2 +16t+480, where t is the time in seconds and h is the height in feet.

The maximum height of Jason occurs when dh/dt = 0 (velocity is zero)

dh/dt = -32t + 16

0 = -32t + 16

32t = 16

t = 16/32

t = 1/2

t = 0.5secs

Get the maximum height

Recall that h(t)=−16t^2 +16t+480

Substitute t = 0.5

h(0.5)=−16(0.5)^2 +16(0.5)+480

h(0.5) = -4 + 8 + 480

h(0.5) = 4 + 480

h(0.5) = 484

Hence the maximum height reached by Jason is 484feet

Answer 2

The maximum height that Jason reaches is h =  484 feet and it will be reached at t = 0.5 sec.

How to find the maximum of a polynomial function?

Let the function be denoted by [tex]y = f(x)[/tex]

If it is twice differentiable, then, firstly, we differentiate it with respect to x and equate with 0 to find the critical values.

Let the obtained critical values be [tex]x_1, x_2, ... x_n[/tex]

The second derivative of that function is then evaluated on those critical values.

The [tex]i^{th}[/tex] critical value has got the maximum if [tex]f''(x_i) < 0[/tex]

That means, if at  [tex]x = x_i[/tex] , we get

[tex]f'(x-i) = 0\\and\\f''(x_i) < 0[/tex]

Then that point is where function will have maximum.
If [tex]f''(x_i) > 0[/tex], then the point where the function will have minimum

If value of second rate at point [tex]x_i[/tex] is 0, then we go for third rate of function and check the same facts so on for upper rate(if they exist).

For the given case, we're given the height function as:

[tex]h(t) = - 16t^2 + 16t + 480[/tex]

The function is infinitely differentiable as its polynomial(by a theorem).

Its first and second rate with respect to 't', we get;

[tex]h(t) = - 16t^2 + 16t + 480\\h'(t) = -32t + 16\\h''(t) = -32 < 0[/tex]

Thus, all critical points will be maximum points.

The critical points are evaluated by [tex]h'(t) = 0[/tex]

They are calculated as:

[tex]h'(t) = 0\\-32t + 16 = 0\\t = 0.5 \: \rm sec[/tex]

The height at t = 0.5 s is evaluated as:

[tex]h(0.5) = - 16(0.5)^2 + 16(0.5) + 480 = 484 \: \rm feet[/tex]

Thus, at time 0.5, the height function will be at its maximum value(484 feet). That means, the height of Jason will be maximum when time will be 0.5 seconds from initial time.

Learn more about maximum and minimum values here:

https://brainly.com/question/13333267


Related Questions

A woman is rowing a boat across a 60 wide river from west to east. She can row at 2 mph in still water, but the river's current is 5 mph from north to south. To the nearest foot, how far downstream on the east bank will she land?

Answers

Answer:

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Step-by-step explanation:

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The woman will land on the east bank of the river at a downstream of 37.5 miles.

What is meant by relative velocity ?

Relative velocity of an object in motion is defined as the velocity of the object with respect to another object.

Here,

Width of the river, W = 60 miles

Velocity of the boat in still water, Vb = 2 mph

Velocity of river, Vr = 5 mph

Relative velocity of the boat with respect to river in downstream,

Vbr = Vb + Vr

Vbr = 8 mph

Drift of the boat, d = Vr W/Vbr

d = 5 x 60/8

d = 37.5 miles downstream

Hence,

The woman will land on the east bank of the river at a downstream of 37.5 miles.

To learn more about relative velocity, click:

https://brainly.com/question/19260269

#SPJ3

PLEASE HELP THANK YOU

Answers

Answer:

thanks you too for having us

Consider this right triangle with given measures.

What is the length of the missing leg?

Answers

Answer:

The answer is 6 feet.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the diagram shows a track composed of a rectangle with a semicircle on each end. the area of the rectangle is 4,000 square meters. what is the perimeter of the track?

Answers

Answer:14400

160

=

90

Step-by-step explanation: 90

π

=

90

π

 If you are using an approximation such as 3.14 for  

π

, multiply that by 90

Add  

160

2

to the circumference since the lengths of the rectangle are also part of the perimeter.

160

2

=

320

90

π

+

320

Ryan's take-home pay is $2,500 each month. The amount for gas is $125. Calculate the percentage Ryan uses on gas from his take-home pay. please help!! O^O

Answers

Answer: 5%

Step-by-step explanation:

Since Ryan's take-home pay is $2,500 each month and the amount for gas is $125.

The percentage that Ryan uses on gas from his take-home pay will be:

= Amount used on gas / Take home pay × 100

= 125/2500 × 100

= 1/20 × 100

= 5%

He used 5% on gas.

Can someone please help me with this math problem please:):)

Answers

Answer:

y = 126° + 29° = 155°

Step-by-step explanation:

I think this may be a solution:

126°+29°=155°

So, y=155°

Find the measure of AC

Answers

Answer:

7 inch

Step-by-step explanation:

AC= BC+AB

= (BD-CD) + radius of B

= (radius of B-radius of D) + 4.5

=(4.5-2) +4.5

=2.5+ 4.5

=7 inch

I hope this is correct.

The measure of ABD is (0.18x + 67) degrees and the measure of CBD is (0.07 + 48) degrees. Find the value of X

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]ABD = 0.18x +67[/tex]

[tex]CBD = 0.07x + 48[/tex]

Required

Find x

The question is incomplete as the relationship between ABD and CBD is not stated.

Assume ABD = CBD

The solution is:

[tex]0.18x + 67 = 0.07x + 48[/tex]

Collect like terms

[tex]0.18x - 0.07x= - 67 + 48[/tex]

[tex]0.11x= -19[/tex]

Solve for x

[tex]x = -\frac{19}{0.11}[/tex]

[tex]x = -172.72[/tex]

Assume ABD and CBD are supplementary

The solution is:

[tex]ABD + CBD=180[/tex]

[tex]0.18x + 67 + 0.07x + 48 = 180[/tex]

Collect like terms

[tex]0.18x + 0.07x = - 48 - 67 + 180[/tex]

[tex]0.25x = 65[/tex]

Solve for x

[tex]x = \frac{65}{0.25}[/tex]

[tex]x = 260[/tex]

Assume ABD and CBD are complementary

The solution is:

[tex]ABD + CBD=90[/tex]

[tex]0.18x + 67 + 0.07x + 48 = 90[/tex]

Collect like terms

[tex]0.18x + 0.07x = - 48 - 67 + 90[/tex]

[tex]0.25x = -25[/tex]

Solve for x

[tex]x = \frac{-25}{0.25}[/tex]

[tex]x = -100[/tex]

A marine biologist measured one fish that was 9/10 of a foot long and a second fish that was 7/10 of a foot long. How much longer was the first fish?

Write your answer as a fraction or as a whole or mixed number.

Answers

Answer:

2/10 of a foot long.

Step-by-step explanation:

Answer:

The first fish was 1/3 of a foot longer.

mark me brainlest

Step-by-step explanation:

1/2=3/6

3/6>1/6

3/6-1/6=2/6

2/6 / 2/2

1/3

Observa las siguientes imágenes formadas por círculos:

Figura 1 (un circulo) Figura 2 (5 círculos)

-¿Cuántos círculos tendrá la Imagen 10?
-¿Cuántos círculos más tendrá la imagen 12 respecto de la imagen 7? ¿Puedes saberlo sin necesidad de encontrar la cantidad de círculos de cada imagen? ¿Cómo?

Answers

1.En 10 figuras habrá 37 puntos si te fijas en las imágenes lo único que hace es agregar 4 puntos a cada uno como la tercera imagen tiene 9 puntos hize 9 + 7x 4= 37
2.la imagen 12 tendrá 45 puntos y la 7 tendrá 25 puntos
La diferencia de puntos entre la figura 7 y 12 serán seran 20 puntos
-si lo pude saber sin la necesidad de encontrar la cantidad de los círculos de las imágenes porque cada ves vamos agregando 4 puntos

Veremos que en la imagen 10 hay 37 circulos, y la diferencia entre las imagenes 12 y 7 es de 20 circulos.

¿Como encontrar el patrón?

Primero, debemos contar la cantidad de circulos que tenemos en las imagenes mostradas.

En la primera, tenemos 1 circulo.En la segunda, hay 5 circulos.En la tercera, hay 9 circulos.En la cuarta, hay 13 circulos.

Entonces podemos ver que en cada imagen se agregan 4 circulos, es decir tenemos una secuencia aritmetica, de tal forma que la imagen número N tendremos:

[tex]C_N = 1 + (N - 1)*4[/tex]

Entonces, cuantos circulos hay en la imagen 10? para ver eso reemplazamos N por 10.

[tex]C_{10} = 1 + (10 - 1)*4 = 37[/tex]

¿Cuántos círculos más tendrá la imagen 12 respecto de la imagen 7?

Para ver esto calculamos:

[tex]C_12 - C_7 = (1 + (12 - 1)*4) - (1 + (7 - 1)*4) = 11*4 - 6*4 = 20[/tex]

Es decir, la image 12 tiene 20 circulos más que la imagen 7.

Sí quieres aprender más sobre secuencias, puedes leer:

https://brainly.com/question/7882626

How many more brooms must each earn in order to have enough credit to get a month off with pay?

Answers

Answer:

5

Step-by-step explanation:

There are 5 people at a party. They decide to share 3 ice cream sandwiches equally.
Which model shows how much of the ice cream sandwiches each person will get?
C.
D

Answers

Answer:

your answer will be D. I think :)

Answer: d

i have the test

louise decided to purchase a new mountain bike when he saw the sporting good store was offering 20% off their bike. what is the total cost of the mountain bike if the originally price at $249 and louise must pay 7.5% sales tax

Answers

$215.13




First off $249 x 20% = $49.8 so, $249- 49.8 = 199.2 ( the price after deducting the discount), 199.2 x 8% = 15.93 (this is the price of the tax), and 199.2 + 15.93 = $215.13 ( this is the price after the discount and with taxes) :D

based on the table, what is the slope,m, and y-intercept , b , on the line that models this relationship?

Answers

Answer: slope: 180  y intercept: -360

I hope this helps!

Can somebody help me with one of these i literally don’t get it.

Answers

Answer:

basically multiply the height and the base (area), using the two numbers shown. Just add for perimeter. Just use a calculator, no one really cares about doing it them selves

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the diameter is 26 inches, what is the radius

Answers

Answer:

13 inches

Step-by-step explanation:

In any circle, the radius is always half of the diameter.

So, the diameter can be found by multiplying the radius by 2, and the radius can be found by dividing the diameter by 2.

Since the diameter is 26 inches, we can divide this by 2 to get the radius

26/2

= 13

The radius is 13 inches

Answer:

[tex] \bf \huge13[/tex]

Step-by-step explanation:

Given that :

the diameter is 26 inches.

to find :

what is radius .

formulas used :

radius = diameter / 2

explanation :

we know that,

finding the radius

diameter = 26 inches

⟼ radius = diameter / 2

⟼ radius = 26 / 2 inches

⟼ radius = 13 / 1 inches

⟼ radius = 13 inches.

radius is 13 inches .

Eric carved this solid out of wood.

Find the volume of the solid

Answers

Answer:

3,456

Step-by-step explanation:

Just did the question and got it correct.

Hope this helps ;)

HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
3. Use the information about the m<2 and m determine the missing information.
m22 = 97°
m26 = 83°
m
2
5
m2 3 =
m2 5 =
3
4
7
8
m210 =
m2 7 =
9
10
13
14
m2 9 =
m216 =
$
11
12
15/16

Answers

Answer:

m<3 = 97

m<10 = 97

m<9 = 83

m<5 = 97

m<7 = 83

m<16 = 97

Step-by-step explanation:

m<3 = m<2 because of vertical angles

m<10 = m<2 because of corresponding angles

m<9 + 97 = 180

m<9 = 83

m<5 + 83 = 180

m<5 = 97

m<7 = m<6 because of vertical angles

m<16 = m<5 because of alternate exterior angles.

log(x+4)=logX + log4

Answers

Answer:

log

(

x

+

4

)

=

log

(

x

)

+

log

(

4

)

=

log

(

4

x

)

, so  

x

+

4

=

4

x

, hence  

x

=

4

3

Step-by-step explanation:

Layna can paint a 350-square foot room in 4 hours. It takes Bebe 7 hours to paint the same room. Which equation can be used to find the time in hours, t, it takes Layna and Bebe to paint the room together?

Answers

1/4+1/7=t
I am 99% sure this is correct. Good luck

Answer:

A. 1/4t+1/7t=1

Step-by-step explanation:

can someone please help me with this?

Answers

Y=mx+b
Y=250+10c

The 250 is the b and the 10c is the mx

(HALP ILL GIVE BRAINLY AND IS A MULTIPLE CHOICE) no links or I will report

Answers

Answer: the correct answer is answer (4) (2,4)

Step-by-step explanation:

I hope you get it right :)

ASAP!!! and no links please 25 points!!!!!
The radius of a can of soda is 0.75 inches. Find the area of the top of the can. Round to the nearest hundredth.

(Values only! No units!)

Answers

Answer:

2.36

Step-by-step explanation:

Multiply the radius (0.75) with the value of pi (3.14.....)

0.75 x pi = area

area = 2.35619449019

ROUNDED TO HUNDREDTHS = 2.36

hope this helps :)

PLEASE HELP ME I WANT TO PASS THIS CLASS AND GRADUATE WILL GIVE BRAINLIEST

A recent study of high school students shows the percentage of females and males who have at LEAST one notation in their school record for inappropriate behavior. A simple random sample of high school students was interviewed. The students were asked whether they had a notation for inappropriate behavior in their school record. Of the 100 females, 21 answered yes, as did 145 of the 400 males.

Part A: Construct and interpret a 99% confidence interval for the difference in population proportions of females and males who have at LEAST one notation for inappropriate behavior. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)

Answers

lol the handwriting hurts

Answer:

other person!

Step-by-step explanation:

give the other person brainliest; hope you pass the class!

Which expression shows 3 decreased by the sum of 11 and a number? A. 3-(11+x) B. (11+x)-3 C. 3-11+x D. 3+11x

Answers

Answer:A

Step-by-step explanation:

Answer:

The correct answer Its A. 3-(11+x)

The lenght of a turtles shell z, in millimeters, is related to the turtles age in years a , as described by the equation below.
s=55a+37
Which statements about the turtle are true?
Select 3

Answers

Answer:

B, C , F

Step-by-step explanation:

The age multiplied 55, so the shell grows at rate of 55mm per year

in fact if the age is 2 we have (55 x 2) = 55 + 55

if 3 = (55 x 3) = 55 + 55 + 55

and so on

When the turtle is hatched the shell is 37 mm in lenght.

In fact, if we substitute 0 to a, we have

s = (55 x 0) + 37

s = 37

when the turtle is 1 year old, the shell is 92 mm in length.

in fact if we substitu a with 1, we have

s = (55 x 1) + 37

s = 55 + 37

s = 92

Question 5 (1 point)
Which statement about segregation in Arkansas following Reconstruction is true?
The United States Supreme Court supported segregation.
O Governor Clayton put a stop to segregation.
Only public transportation was segregated
The federal government resisted efforts to segregate.

Answers

Answer:

Step-by-step explanation:

The answer is the United states Supreme Court suported segreation

Find the equation parallel to y = -x - 5 and passing through (-3, -3)

Answers

Answer:

y = -x - 6

Step-by-step explanation:

If it's parallel, then it means that the slope will remain the same. The slope is

-1.

To find the y-intercept, you need to plug the coordinates into the equation,

y = -1x + b

-3 = -1(-3) + b

-3 = 3 +b

-6 = b

The equation is y = -x - 6

2/5 of the flowers in Veronica's garden are marigolds. If there are 55 flower plants in her garden, how many marigold plants does she have?

Answers

Answer:Veronica has 22 marigold plants

Step-by-step explanation:

Total Number of flower plants in her garden=55

fraction of flower plants which are marigolds=2/5

Number of flower plants which are marigolds=2/5 x Total Number of flower plants in her garden

=2/5 x 55

=22

Arthur went to dinner. The meal cost $157 and
he wants to leave an 18% tip. How much money
should he leave for the tip?

Answers

Arthur should leave a $28.26 tip

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