Mathematics, 21.09.2019 16:30 preservations

Genevieve is going to throw a rock from the top of a trail overlooking the ocean. when she throws the rock upward from 160 feet above the ocean, the function h(t)=−16t2+48t+160 models the height, h, of the rock above the ocean as a function of time, t. find a. the zeros of this function that tell us when the rock will hit the ocean. b. when the rock will be 160 feet above the ocean. c. the height of the rock at t=1.5 seconds.

Answers: 1

Show answers

Answers

Answer from: ooEVAoo

The rock will hit the ocean at t = 5 seconds, the rock will be 160 feet above the ocean at t = 0 and t = 3 seconds, and the height of the rock at t=1.5 seconds is 196 feet and this can be determined by using the given data.

Given :

Genevieve is going to throw a rock from the top of a trail overlooking the ocean.When she throws the rock upward from 160 feet above the ocean, the function h(t) =−16 $\rm t^2$ +48t+160 models the height, h, of the rock above the ocean as a function of time, t.

A) To evaluate the zeros of the given function equate h(t) equal to zero.

$\rm -16t^2+48t+160 = 0$

$\rm 16t^2 - 48t-160=0$

$\rm 16(t^2+3t+10)=0$

$\rm 16(t^2-5t+2t-10)=0$

16(t - 5)(t + 2) = 0

t = -2, 5

Time 't' is never negative. So, the rock will hit the ocean at t = 5 seconds.

B) Now, equate h(t) to 160.

$\rm 160 = -16t^2 + 48t +160$

$\rm 16t^2-48t=0$

16t(t - 3) = 0

t = 0 , 3

The rock will be 160 feet above the ocean at t = 0 and t = 3 seconds.

C) Put (t = 1.5) in the given function h(t).

$\rm h(1.5) = -16(1.5^2)+48(1.5)+160$

h(1.5) = -36 + 72 + 160

h(1.5) = 196 feet

So, the height of the rock at t=1.5 seconds is 196 feet.

For more information, refer to the link given below:

link

Answer from: perez120

see explanation

Step-by-step explanation:

Given

h(t) = - 16t² + 48t + 160

(a)

To find the zeros equate h(t) to zero, that is

- 16t² + 48t + 160 = 0 ( divide through by - 16 )

t² - 3t - 10 = 0 ← in standard form

(t - 5)(t + 2) = 0 ← in factored form

Equate each factor to zero and solve for t

t - 5 = 0 ⇒ t = 5

t + 2 = 0 ⇒ t = - 2

However t > 0 ⇒ t = 5 is when the rock hits the ocean

(b)

Equate h(t) to 160

- 16t² + 48t + 160 = 160 ( subtract 160 from both sides )

- 16t² + 48t = 0 ( divide through by - 16 )

t² - 3t = 0 ← factor out t from each term

t(t - 3) = 0

t = 0 ← time when rock was thrown from the top of the trail

t - 3 = 0 ⇒ t = 3

The rock is 160 ft above the ocean at 0 seconds and 3 seconds

(c)

Substitute t = 1.5 into h(t)

h(1.5) = - 16(1.5)² + 48(1.5) + 160 = - 36 + 72 + 160 = 196

The rock is 196 ft above the ocean at 1.5 seconds

Answer from: Quest

a. 12.5 kg

step-by-step explanation:

f = ma

m = f/a = (2500 n)/(200 m/s²) = 12.5 kg

1 n = 1 kg·m/s²

Answer from: Quest

B) greg: 30 points , tremaine 38 points

Another question on Mathematics

Mathematics, 21.06.2019 14:00

The revenue generated by a bakery over x months, in thousands of dollars, is given by the function f(x) = 2(1.2)* the cost of running the bakery forx months, in thousands of dollars, is given by the function g(x) = 2x + 1.4determine the equation for h if h(x) = f(x) - g(x).oa. m(x) = (1-2)*-x-07b.(x) = 2(1 2 - 2x -0.7)h(x) = -2((1.2) + x + 0.7)d.h(x) = 2((12) - x-0.7)

Answers: 1

Answer

Mathematics, 21.06.2019 16:10

The number of hours per week that the television is turned on is determined for each family in a sample. the mean of the data is 37 hours and the median is 33.2 hours. twenty-four of the families in the sample turned on the television for 22 hours or less for the week. the 13th percentile of the data is 22 hours. approximately how many families are in the sample? round your answer to the nearest integer.

Answers: 1

Answer

Mathematics, 21.06.2019 16:20

An equation representing lyle’s hedge-trimming business is a = 12n - 300 where a is the amount of profit or loss in dollars and n is the number of hedges trimmed. how would the graph of lyle’s business change if the equation a = 10n - 300 represented his business? the graph would be flatter. the graph would be steeper. the graph would start closer to the origin. the graph would start lower on the y-axis.

Answers: 2

Answer

Mathematics, 21.06.2019 18:30

Which of the statements about the graph of the function y = 2x are true? check all of the boxes that apply. the domain is all real numbers x because the exponent of 2 can be any real number when the x-values increases by 1 unit, the y-value multiplies by 2. the y-intercept is (0, 1). the graph never goes below the x-axis because powers of 2 are never negative. the range is all real numbers.

Answers: 1

Answer

You know the right answer?

Genevieve is going to throw a rock from the top of a trail overlooking the ocean. when she throws th...

Questions

Mathematics, 02.08.2019 19:10

Two suppliers manufacture a plastic gear used in a laser printer. the impact strength of these gears measured in foot-pounds is an important character...

Mathematics, 02.08.2019 19:10

Arectangle is constructed with its base on the x-axis and two of its vertices on the parabola yequals=196196minus−xsquared2. what are the dimensions o...