Assuming you know that max/min problems involve finding when f'(x)=0,
#1 If the base of the ladder is x feet from the fence, and the height up the wall is y, then the length z of the ladder is
z^2 = (x+7)^2 + y^2
and using similar triangles,
y/(x+8) = 8/x
Now you can substitute in y, and you have z as a function of x. Find x where z'=0.
#2. If the height of the rectangular part is y and the width is 2x, then the max light is admitted when the area a is max.
a = xy + π/2 x^2
x + 2y + πx = 23
#3 If the base's dimensions are x and 2x, and the height is z, then the cost c is
c = 14x(2x) + 11(2xz + 2(2x)z)
x(2x)z=14
eliminate z and find where c'(x)=0
1. A fence 8 ft tall runs parallel to a tall building at a distance of 7 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth.
a.21.20 ft
b. 22.20 ft
c. 21.19 ft
d. 20.10 ft
e. 21.40 ft
2. A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 23 ft, find the dimensions of the window so that the greatest possible amount of light is admitted. Round the result to the nearest hundredth.
a. 6.44 ft, 3.22 ft
b. 6.42 ft, 4.22 ft
c. 7.44 ft, 3.19 ft
d. 6.54 ft, 3.42 ft
e. 6.44 ft, 2.72 ft
3. A rectangular storage container with an open top is to have a volume of 14 m^3. The length of its base is twice the width. Material for the base costs $14 per square meter. Material for the sides costs $11 per square meter. Find the cost of materials for the cheapest such container.
a. $341.96
b. $342.98
c. $342.96
d. $341.46
e. $340.66
Please HELP!
1 answer
1 answer