Answer:
The answer is below
Step-by-step explanation:
Let x be the diameter of the semicircle. radius = x/2
The window is a combination of a rectangle and semicircle.
Width of window = diameter = x, let length of the window = y.
Perimeter of semicircle = πr = πx/2
Perimeter of window = x + y + y + πx/2
20 = x + 2y + πx/2
2y + x + πx/2 = 20
2y = 20 - x(1 - π/2)
y = 10 - x(1 - π/2)/2
Area of semicircle = (1/2)πr² = (1/2)π(x/2)²
Area of window = xy + (1/2)π(x/2)²
A = x(10 - x(1 - π/2)/2) + πx²/8
A = 10x - x² - πx²/4 + πx²/8
A = 10x - x² - πx²/8
The maximum area is at dA / dx = 0
dA / dx = 10 - 2x - 2πx/8
0 = 10 - 2x - πx / 4
2x + πx / 4 = 10
2.785x = 10
x = 3.59 feet
Maximum area = 10x - x² - πx²/8 = 10(3.59) - 3.59² - π(3.59²) / 8
Maximum area = 17.95 feet²
Well set it up first. You get: 8.2-(-3.5) so what you do is that you first subtract 8.2-3.5=4.7. Then you want to find out weather it is negative or positive. First point out which one is bigger in this case 8.2 is bigger and a positive so your answer would be positive. Answer: +8.2 or 8.2
Answer:
56deg
Step-by-step explanation:
A triangle has 180deg.
180 = 68 + 56 + x >> add 68 and 56
180 = 124 + x >> subtract 124 from both sides
56 = x
The missing side is 56deg
Answer:
Slope: 1
Step-by-step explanation:
In this question, we need to find the slope with the given points.
To find the slope, we would use the equation:
m = y2-y1/x2-x1
Plug in your coordinates and solve:
m = 0 - 7/-2 - 5
m = -7/-7
Two negatives cancel each other to make a positive, and 7/7 = 1
m = 1
This means that the slope would be 1.
