Step-by-step explanation:
The formula the amusement parc use is 100y-39000=55(x-800)
The slope intercept form of a function is wriiten generally as:
y = mx+c
- m is a slope
- c is a constant and represents the y-intercept
- x is a variable
- y is the input of the function
Let's rewrite our equation in the precedent form
- 100y-39000 = 55(x-800)
- 100y -39000 = 55x-44000 add 39000 in both sides
- 100y-39000+39000 = 55x-44000+39000
- 100y = 55x-5000 divide both sides by 100
- y = 0.55x-50
The slope intercept form of this equation is:
y= 0.55x-50
Given Information:
Area of rectangle = 16 square feet
Required Information:
Least amount of material = ?
Answer:
x = 4 ft and y = 4 ft
Step-by-step explanation:
We know that a rectangle has area = xy and perimeter = 2x + 2y
We want to use least amount of material to design the sandbox which means we want to minimize the perimeter which can be done by taking the derivative of perimeter and then setting it equal to 0.
So we have
xy = 16
y = 16/x
p = 2x + 2y
put the value of y into the equation of perimeter
p = 2x + 2(16/x)
p = 2x + 32/x
Take derivative with respect to x
d/dt (2x + 32/x)
2 - 32/x²
set the derivative equal to zero to minimize the perimeter
2 - 32/x² = 0
32/x² = 2
x² = 32/2
x² = 16
x =
ft
put the value of x into equation xy = 16
(4)y = 16
y = 16/4
y = 4 ft
So the dimensions are x = 4 ft and y = 4 ft in order to use least amount of material.
Verification:
xy = 16
4*4 = 16
16 = 16 (satisfied)
Answer: xp=py
<xpa=<apy
4 right angles are formed
2(xp)=xy
<xpa and <apy are supplements.
Step-by-step explanation:
The cost to mail a 2-lb package is $7.
The cost to mail a 2-lb, 1 oz package is $7+$0.30(1).
That to mail a 2-lb, 2 oz package is $7+$0.30(2) = $7.60.
Following this pattern, the general formula is f(x) = $7 + $0.30x, where x represents the number of ounces OVER 2 lb.