Consider the following problem: A rectangular lot whose perimeter is 1600 feet is fenced along three sides. An expensive fencing along the lot's length costs $20 per foot. An inexpensive fencing along the two side widths costs only $5 per foot. The total cost of the fencing along the three sides comes to $13,000. What are the lot's dimensions

The dimensions of rectangular lot is Length=500 feet and Width=300 feet

Step-by-step explanation:

The formula for perimeter of rectangle is given by,  

Where, L = length, W = width and P = Perimeter.  

According to given data, rectangular lot has a perimeter of 1600 feet. Therefore,  

 ….1

Now, cost of fencing along one length is given as $ 20 per feet. So total cost of one length is,  

Similarly, cost of fencing along two width is given as $ 5 per feet. So total cost of two width is,  

Total cost of fencing along three sides is given as $13000. Therefore,  

Total cost = Cost of fencing of one length + Cost of fencing of two width

Substituting the value,

 ….2

So, there is two equations and two unknown. Solve it by substitution method.

Solving equation 1 for W.

Dividing both sides of equation by 2,  

Subtracting L from both sides,  

 ….3

Substituting equation 3 into equation 1 and simplifying,  

So value of length is 500 feet. Substituting the value of L in equation 1 and simplifying,  

So value of width is 300 feet.  

4x and 6y

im not sure though

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.