A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 16 ft, express the area A of the window as a function of the width x of the window.
Answers
Final answer:
The area A of a Norman window in terms of its width x can be expressed as the function A(x) = 8x - x²/2 - πx²/8, deriving this equation involves isolating variables from the given perimeter equation.
Explanation:
A Norman window has the shape of a rectangle topped with a semicircle. If we take x as the width of the window and y as the height of the rectangle, then the perimeter of the window is given by P = 2y + x + πx/2 = 16 (since the perimeter is the sum of the rectangle's two sides, the width, and half the circumference of a circle with diameter x).
From this equation, we can express y as a function of x: y = 8 - x/2 - πx/4.
Then, the area A of the window is the sum of the area of the rectangle and the area of the semicircle, which equals A = xy + πx²/8 = x(8 - x/2 - πx/4) + πx²/8 = 8x - x²/2 - πx²/4 + πx²/8.
Therefore, the area A of the window as a function of the width x of the window is A(x) = 8x - x²/2 - πx²/8.
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x= -2 and x = -16
x = 2 and x = V-10
x = 4 and x = -10
x = 40 and x = -58
Answers
Answer:
The answer is x=4 or x=−10
Solutions:
(x + 3)² = 49
(x+3)(x+3)=49
x²+6x+9=49
x²+6x+9-49=0
(x-4)(x+10)
x-4=0 x+10=0
x=4 x=-10
Please and thanks
Answers
Answer:
Step-by-step explanation:
Use cross products,
Distribute,
Inverse operations,
432 ft3
Answers
= 1/3 * 24 * 18
= 144 ft^3
Answers
Answer:
124
Step-by-step explanation: Hope it helps
Final answer:
No matter how much the angle is rotated around the center, the size of the angle remains the same. Therefore, even after the rotation, the size of the angle is still 124 degrees.
Explanation:
When an angle is rotated around a center, the size of the angle doesn't change.
It's an important characteristic of angle rotation. So, if an angle of 124 degrees is rotated d degrees around a center, the size of the rotated angle will still remain 124 degrees. It is just in its new position after rotation. Regardless of the rotation of the angle, its size or measure remains the same as the rotation does not affect the measure of the angle.
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Answers
Answer:
25.12/100
Step-by-step explanation:
Percent means per hundred, so 25.12 percent means 25.12 per hundred. Thus, you can make 25.12 the numerator and 100 the denominator, and make 25.12 percent a fraction like this:
25.12/100
B. x - c is a factor of f(x).
C. c is a 0 for f(x).
D. All three statements are true.
Answers
For this case suppose we have a function of the form:
y = f (x)
Where,
x: independent variable
y: dependent variable
We have then that the value of the function for x = c is:
f (c) = 0
Therefore, we have that:
The point (c, 0) belongs to f (x)
x-c is a common factor of f (x) because the function evaluated at x = c is equal to zero.
x = c is a root of f (x) so c is a zero of the function f (x)
Answer:
D. All three statements are true.
Thank you.