A rectangular garden of area 50 square feet is to be surrounded
on three sides by a fence costing $2 per running foot and on one
side by a brick wall costing $6 per running foot. Let x be the
length of the brick wall side. Which of the following represents
the total cost of the material?
A rectangular box with a square base is to be constructed from
material that costs $6/ft2 for the bottom, $14/ft2 for the top, and
$5/ft2 for the sides. Find the greatest volume of the box if it
costs $240.
A rectangular box with a square base has a volume of 4 cubic
feet. The material for the bottom of the box costs $3 per square
foot, the top costs $2 per square foot, and the four sides cost $5
per square foot.
(a) If x is the side length of the square base, and y is the
height of the box, find the total cost of the box as a function of
one variable.
(b) Find the critical number...
A rectangular box with a square base has a volume of 4 cubic
feet. The material for the bottom of the box costs $3 per square
foot, the top costs $2 per square foot, and the four sides cost $5
per square foot.
(a) If x is the side length of the square base, and y is the
height of the box, find the total cost of the box as a function of
one variable.
(b) Find the critical number...
Three charges at the corners of a square of sides s = 3.40 m.
Here, q1 = q2 = −q and q3 = −1.5q where q = 9.00 nC. q2 is at the
top left of the square, q3 at the bottom left and q1 at the bottom
right.
(a) What is the magnitude of the electric field at the center of
the square due to these three charges?
(b) You now replace q1 in the square with another point...
A rectangular box is to have a square base and a volume of 40
ft3. If the material for the base costs $0.35 per square
foot, the material for the sides costs $0.05 per square foot, and
the material for the top costs $0.15 per square foot, determine the
dimensions of the box that can be constructed at minimum cost.
= Length
Width
Height
how do i find length width and height
a
rectangular open tank is to have a square base, and its volume is
to be 125 cubic metrrs. the cost per square meter for the bottom is
$24 and for the sides is $12. find the dimensions of the tank for
which the cost of the material is to be the least. what is the
least cost?
A
600 ft.^2 rectangular patch is to be enclosed by a fence and
divided into two equal parts by another fence parallel to one of
the sides. what dimensions for the outer rectangle would will
require the smallest total length of fence?
Let S be the square centered at the origin with sides of length
2, and C be the unit circle centered at the origin.
(a) If you randomly throw a point on S, what is the probability
that it will lie in C?
Ans: 0.785
(b) Describe how you could use simulation to estimate the
probability in part (a).
(c) How can you use simulation to estimate a?
For part b and c, there maybe a need to generate random...
Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°). Describe all the symmetries of the rhombus. Write down the Cayley table for the group of symmetries,