Mathematics, 18.03.2020 17:22 aurora32

The equation h(t) = -16t² + 80t + 64 represented the height, in feet, of a potato t seconds after it has been launched.
a. Write an equation that can be solved to find when the potato hits the ground. Then solve the equation.
b. Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

Answers: 2

Show answers

Answers

Answer from: gomez36495983

The potato will hit the ground after 5.6 secsThe potato will be 40 feet above the ground after 10.3 secs

Given the equation that models the height of the potato given as h(t) = -16t² + 80t + 64, the potato hits the ground at when h(t) = 0

The equation becomes -16t² + 80t + 64 = 0

Factorizing there result:

16t² - 80t - 64 = 0

t² - 5t - 4 = 0

On factorizing the value of t

t = 5±√25-4(-4)/2

t =5±√25+16/2

t=5±√41/2

t = 5+6.4/2 and 5 - 6.4/2

t = 5.7secs

Hence the potato will hit the ground after 5.6 secs

b) If the potato is 40 feet off the ground, the equation becomes

-16t² + 80t + 64 = 40

Factorizing there result:

16t² - 80t - 24 = 0

2t² - 10t - 3 = 0

On factorizing the value of t

t = 10±√100-4(-3)/2

t =10±√100+12/2

t=10±√112/2

t = 10+10.6/2 and 10 - 10.6/2

t = 10.3 secs

The potato will be 40 feet above the ground after 10.3 secs

Learn more on factorization here: link

Answer from: Jasten

Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

h(t)=-16t^2+80t+64

where

h(t) is the height of a potato in feet

t is the time in seconds

Part A) Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

When the potato hit the ground, the value of h(t) must be equal to zero

For h(t)=0

-16t^2+80t+64=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

-16t^2+80t+64=0

$a=-16\\b=80\\c=64$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{10,496}} {-32}$

$t=\frac{-80+\sqrt{10,496}} {-32}=-0.70$

$t=\frac{-80-\sqrt{10,496}} {-32}=5.70$

therefore

The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

For h(t)=40 ft

substitute in the quadratic equation

-16t^2+80t+64=40

-16t^2+80t+24=0

Solve the quadratic equation

we have

$a=-16\\b=80\\c=24$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{7,936}} {-32}$

$t=\frac{-80+\sqrt{7,936}} {-32}=-0.28$

$t=\frac{-80-\sqrt{7,936}} {-32}=5.28$

therefore

The potato is 40 feet off the ground at the time t=5.28 seconds

Answer from: Quest

You have to find the angle i don’t know if i i try
Abcd is a parallelogram. find m ∠d. enter the answer as a number. abcd is a parallelogram. find the

Answer from: Quest

news channels,news papers,and the internet

Questions in other subjects:

Health, 04.02.2020 01:51

Scenario three: one of your friends thinks she is pregnant. write a short letter to her and inform her about the dangers of using tobacco, alcohol and drugs before, during and aft...

English, 04.02.2020 01:51

What are the most effective techniques to present text in a multimedia presentation? select three options....

Mathematics, 04.02.2020 01:51

What was the distance of the ship from its starting point

Chemistry, 04.02.2020 01:51

What type of energy is affected by temperature, sample size, and composition?...

Mathematics, 04.02.2020 01:51

What is the slope of a line that runs parallel to y = -x + 7?...

Health, 04.02.2020 01:51

For those who are less flexible, modified stretching can be done with the assistance of a towel or band. true or false...

Health, 04.02.2020 01:51

Explain how hiv/aids is commonly spread in the context of unequal power relations leading to social injustices among married couples...

English, 04.02.2020 01:51

Learning how to read to an audience directly the reader to: a .feel a sense of personal worth b. use deductive reasoning c. increase self-confidence d. find joy in sharing e. de...

French, 04.02.2020 01:51

substitute the underlined word with a direct object pronoun: est-ce que tu aimes regarder la télévision? est-ce que tu l'aimes regarder? est-...

English, 04.02.2020 01:51

How does marlow describe england when the romans first came ?...

More questions: Mathematics Another questions

Answers

Other questions on the subject: Mathematics

Questions in other subjects: