Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
Answer:
2
Step-by-step explanation:
2^2+4(2)=12
4+8=12
So, x=2
Hope this helps.
-Amelia
Answer:
Step-by-step explanation:
Given
Represent Babysitting with B
Represent Gas Station with G
Total workhours = At most 15
Earnings = At least $90
First, we need to represent the work hours as inequality
B + G = At most 15
At most 15 means less than or equal to 15.
So, we have:
Next, we represent the earnings as inequality.
6 hours of babysitting is: 6B
10 hours at gas station is: 10G
So:
6B + 10G is at least 90
At least 90 means greater than or equal to 90
So, we have:
Answer:
y intercepts= 0 x intercepts= none
nation:
The 2 funtions above the x axis do not intercept with the y-axis or the x-axis. They just hover above it, but never atcually touch it.
The function bellow the x-axis only intercepts the y-axis at 0,0
Answer:
Step-by-step explanation:
Mariam is making two types of paper lanterns. One type of flashlight needs 0.75 square feet of cardboard, while the other needs 1.15 square feet. If she made 5 of each type of flashlight, it means that
For the first type flashlight that she made, she used 0.75 × 5 = 3.75 square feet of cardboard.
For the second type of flashlight she made, she used 1.15 × 5 = 5.75 square feet of cardboard.
Total amount of cardboard used is
3.75 + 5.75 = 9.5 square feet
Mariam has 12.75 square feet of paper left over. Assuming the total square feet of cardboard that she used is x, then x = amount of cardboard used + the amount that is left over. It becomes
x = 9.5 + 12.75 = 22.25 square feet
She used 22.25 square feet
