Answer:
.5 < x < 16.5
Step-by-step explanation:
The smallest x can be is greater than the difference of the other two sides
8.5 -8 = .5
The largest x can be the less than the sum of the two sides
8.5+8 = 16.5
.5 < x < 16.5
Answer:
20
Step-by-step explanation:
To calculate the sum of the residuals, subtract the predicted sales from the actual sales in the table below.
Actual sales 55 150 325 510 780 990
Predicted sales 40 150 300 500 800 1,000
This will show the change between them. Add each residual to find the sum.
55 - 40 = 15
150 - 150 = 0
325 - 300 = 25
510 - 500 = 10
780 - 800 = -20
990 - 1000 = -10
These add up to be 15 + 25+ 10 +-20 +-10 = 20
The correct answer is A: -1.8 + 5.4. Adding a negative is the same as subtracting.
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
