Answer:
-2/3c + 8
Step-by-step explanation:
-2/3 (c-12) distribute (multiply) the -2/3 to everything in the parentheses.
-2/3 * c = -2/3c
-2/3 * -12 = 24/3 which simplifies to 8 (negative times a negative = positive)
-2/3c + 8 is your answer
Answer:
12 yards
Step-by-step explanation:
h = (3×198)/(½×11×9)
= 594/(49.5)
= 12 yds
Factorising quadratic expressions
Multiply these brackets to remind yourself how to factorise.
<span><span>( x + 2 ) ( x + 5 ) = x2 + 7x + 10</span><span>( x + 2 ) ( x + 3 ) = x2 + 5x + 6</span><span>( x - 3 ) ( x - 5 ) = x 2 - 8x + 15</span><span>( x + 6 ) ( x - 5 ) = x2 + x - 30</span><span>( x - 6 ) ( x + 5 ) = x2 - x - 30</span></span>
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
