Project #8994 - calc

1)Sylvia has an apple orchard. One season, her 100 trees yielded 140 apples per tree. She wants to increase her production by adding more trees to the orchard. However, she knows that for every 10 additional trees she plants, she will lose 2 apples per tree (i.e., the yield per tree will decrease by 2 apples). How many trees should she have in the orchard to maximize her production of apples?


2Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past experience, she knows that the number of people who will attend is a linear function of the price per ticket. If she charges 5 dollars, 1160 people will attend. If she charges 7 dollars, 930 people will attend. How much should she charge per ticket to make the most money? (Round your answer to the nearest cent.)


3)A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 16 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible? (Round your answers to two decimal places.)

width  ft
height      ft

4Jun has 360 meters of fencing to make a rectangular enclosure. She also wants to use some fencing to split the enclosure into two parts with a fence parallel to two of the sides. What dimensions should the enclosure have to have the maximum possible area? (Enter your answers as a comma-separated list.)

Answer in meters

5)You have $6000 with which to build a rectangular enclosure with fencing. The fencing material costs $30 per meter. You also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. The material for the partitions costs $25 per meter. What is the maximum area you can achieve for the enclosure? (Round your answer to the nearest whole number.)


6)Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 52 inches long and cuts it into two pieces. Steve takes the first piece of wire and bends it into the shape of a perfect circle. He then proceeds to bend the second piece of wire into the shape of a perfect square. What should the lengths of the wires be so that the total area of the circle and square combined is as small as possible? (Round your answers to two decimal places.)

length of wire for the circle  in
length of wire for the square      in

What is this combined minimal area? (Round your answer to two decimal places.)

7)Two particles are moving in the xy-plane. They move along straight lines at constant speed. At time t, particle A's position is given by

x = t + 4y = 
t − 7

and particle B's position is given by

x = 24 − 2ty = 8 − 
(a) Find the equation of the line along which particle A moves.
y =  

Sketch this line, and label A's starting point and direction of motion.

(b) Find the equation of the line along which particle B moves.
y =  

Sketch this line on the same axes, and label B's starting point and direction of motion.


(c) Find the time (i.e., the value of t) at which the distance between A and B is minimal. (Round your answer to two decimal places.)
t =  s

Find the locations of particles A and B at this time. (Round your answers to two decimal places.)
particle A (xy) = 
particle B     (xy) = 


Question Part
Submissions Used
After a vigorous soccer match, Tina and Michael decide to have a glass of their favorite refreshment. They each run in a straight line along the indicated paths at a speed of 10 ft/sec.
WebAssign Plot
Write parametric equations for the motion of Tina and Michael individually after t seconds. (Round all numerical values to three decimal places as needed.)
Tina x =
  y =
Michael     x =
  y =

Find when and where Tina and Michael are closest to one another. (Round your answers to one decimal place.)
  t =  
Tina (xy) =
Michael      (xy) =

Compute this minimum distance. (Round your answer to one decimal place.)
9)Sven starts walking due south at 6 feet per second from a point 130 feet north of an intersection. At the same time Rudyard starts walking due east at 4 feet per second from a point 150 feet west of the intersection.
(a) Write an expression for the distance d between Sven and Rudyard t seconds after they start walking.
d =  

(b) When are Sven and Rudyard closest? (Round your answer to two decimal places.)
t =  s

What is the minimum distance between them? (Round your answer to two decimal places.)
d =  ft
10)For each of the following equations, find the value(s) of the constant α so that the equation has exactly one solution, and determine the solution for each value.
αx2 + x + 1 = 0
α  =   Incorrect: Your answer is incorrect.
x  =   Incorrect: Your answer is incorrect.

x2 + αx + 9 = 0
α  =   (smaller value)
x  = 
α  =   (larger value)
x  = 

x2 + x + α = 0
α  = 
x  = 

x2 + αx + 3α + 1 = 0
α  =   (smaller value)
x  = 
α  =   (larger value)
x  = 

Subject Mathematics
Due By (Pacific Time) 07/12/2013 10:30 am
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