1. Careena likes throwing rocks at the ocean. When she throws the rock upward from 160 ft above the ocean, h(t) = - 16t2 + 48t + 160 models the height, h, of the rock above the ocean as a function of time, t, in seconds. How long will it take the rock to reach the ocean (h = 0)?

Direction: Answer the following questions through factoring each given polynomial
functions.

Kindly answer all the questions please. With solution. Thank you in advance. 

1. Careena likes throwing rocks at the ocean. When she throws the rock upward
from 160 ft above the ocean, h(t) = - 16t2 + 48t + 160 models the height, h, of
the rock above the ocean as a function of time, t, in seconds. How long will it
take the rock to reach the ocean (h = 0)?

2. An object moves along the horizontal in a straight line according to the function
d = 4t – 2t2
, where d is the distance (in meters) and t is the time in seconds.
How long will it take the object to travel 70 meters?

3. The weight, w (in kilograms), of a certain fish can be modeled by w = x2 – 7x –
3 where x is the length of the fish in decimeters. What is the length of the fish
which weighs 15 kilograms?

4. A certain company can produce a minimum of 10 bicycles up to a maximum of
40 bicycles per week. The profit (in pesos) generated by producing and selling
n bicycles per week is given by the formula P(n) = - 5n2 + 400n – 600. How
many bicycles must be produced and sold to earn a profit of 5400 pesos in a
week?

5. Suppose that the safe stopping distance (in feet) of a car is given by d(s)= 1/20s²+s
, where s represents the speed of the car in kilometers per
hour. Determine the safe speed of the car if it is expected to stop in 40 feet?

6. A banker models the expected value of a company (in millions) by the
polynomial function V(n) = n3 – 3n2
, where n is the number of years in
business. If a production company has an expected value of Php 50 million,
how long was the company in business?

7. In colder climates, the cost, C (in dollars), of natural gas to heat homes can
vary from one day to the next. This can be represented by the function C(d) =
2d3 – 3d2 – 32d – 3, where d is the number of days that natural gas was used
to heat homes. How many days the natural gas was used to heat a certain
home which cost them 10 dollars?

8. A box is to be mailed. The volume (in cubic inches) of the box can be
expressed as the product of its three dimensions which can be represented by the function V(w) = w3 – w2 – 33w – 5, where w is the measure of its width in
inches. What is the width of the box if the volume of the box is 58 in3?

9. A production company has determined its daily revenue, R, by the polynomial
function R(n) = 6n3 + 150n2 – 1200n, where n represents the number of
products sold. If the company earns a revenue of 9 thousand pesos on a
certain day, how many products was sold?

10. It has been a while since Christine started working as a part time babysitter
and saved her earnings at the bank. The polynomial function E(y) = 100y3 +
400y2 – 1100y represents her savings, with interest, where y is the number of
years her savings stayed at the bank. How many years does it need for her
savings to reach 3000 dollars with interest?