A particle is moving along the x-axis with position function
x(t)=2t^3-14t^2+22t-5, find the acceleration function.
What is a(t)=12t-28
100
You decide to construct a rectangle of perimeter 400 mm and maximum area. Find the length and the width of the rectangle.
What is 100x100 mm
100
Find two numbers whose sum is 20 and whose product is as large as possible.
What is 10 and 10
100
The production costs per week for producing "x" widgets is given by C(x)=500+350x-0.09x^2, find the marginal cost for producing 300 widgets
What is $296 per widget
100
The growth of a bacterial population is represented by the function p(t) = 5,000 + 1,000t², where t is the time measured in hours. Determine the average growth rate from 1 to 3 hours.
What is 4000 bacteria per hour
200
If s(t)=t^2-20, find the average velocity from t = 3 to t = 5.
What is average velocity equal to 8
200
We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field and so won’t need any fencing. Determine the dimensions of the field that will enclose the largest area.
What is 250 x 125 ft
200
Determine two real numbers with difference 20 and minimum possible product.
What is -10 and 10
200
A production facility is capable of producing 60,000 widgets in a day and the total daily cost of producing "x" widgets in a day is given by C(x)=250000+0.08x+(200,000,000/x)
How many widgets per day should they produce in order to minimize production costs?
What is 50,000 widgets
200
The growth of a bacterial population is represented by the function P(t) = 5,000 + 1,000t², where t is the time measured in hours. Determine the instantaneous rate of growth.
What is P'(t)=2000t
300
Find the acceleration at t=2 seconds if position function is s(t)=2t^3+ 5t-7, where "s" is given in meters
What is 24m/s^2
300
A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 800 m of wire at your disposal, what is the largest area you can enclose?
What is 80,000 m^2
300
An open-top box is to be made by cutting small congruent squares from the corners of a 12 by 12 in sheet of tin and bending up the sides. How large should the squares cut from the corners be to make the box hold as much as possible?
What is 2 x 2 in
300
An apartment complex has 250 apartments to rent. If they rent "x" apartments then their monthly profit, in dollars, is given by P(x)=-8x^2+3200x-80000
How many apartments should they rent in order to maximize their profit?
What is 200 apartments
300
The growth of a bacterial population is represented by the function P(t) = 5,000 + 1,000t², where "t" is the time measured in hours. Determine the instantaneous rate of growth after 3 hours.
What is 6,000 bacteria per hour
400
A body moves in a straight line according to this equation of motion:
s(t) = 10t^2−4t+8,
where "t" is measured in seconds and "s" in meters.
What is its position at the end of 5 sec?
What is 238m
400
What is the smallest perimeter possible for a rectangle whose area is 16 in^2
What is 16 in
400
We have a piece of cardboard that is 14 inches by 10 inches and we’re going to cut out the corners as shown below and fold up the sides to form a box, also shown below. Determine the height of the box that will give a maximum volume.
What is 1.91 in
400
Suppose that R(x)=9x and C(x)=x^3-6x^2+15x, where "x" represents millions of MP3 players produced. Is there a production level that maximizes profit? If so, what is it?
(Hint: Remember that Profit P(x)=R(x)-C(x))
What is 3.41 million of MP3 players
400
Suppose the population of a city is initially 100,000 and is growing at a rate of 5% per year then the population as a function of time is P(t)= 100 ( 1.05)^t where "t" is in years and the population is in thousands . Calculate the average rate of change between t = 0 and t = 5 .
What is 5.5 thousand people per year
500
A particle moves along a path with its position p=t^2−6t+8 given in meters. When does the velocity equal 30 meters per second?
What is 18 seconds
500
A three side fence is to be built next to a straight section of river, which forms the forth side of a rectangular region. The enclosed area is to equal 1800 ft^2. Find the minimum perimeter of the corresponding enclosure.
What is 120 ft
500
You are planning to make an open rectangular box from an 8 by 15 in piece of cardboard by cutting congruent squares from the corners and folding up the sides. What is the largest volume you can get?
What is 90.74 in^3
500
Suppose C(x)=x^3-6x^2+15x, where "x" represents thousands of units. Is there a production
level that minimizes cost? If so, what is it?
What is 3 thousand of units
500
The population of a certain species is given by P(t)=1000+800t+96t^2+12t^3-t^4, where "t" is given in weeks. Determine the population after 2 weeks.