MATHEMATICS HIGH SCHOOL

The number 3.14 is a rounded value of the mathematical quantity π. If you replace 3.14 with π, what is the exact formula for the circumference in terms of the diameter, d, and in terms of the radius, r?

Answers

Answer 1

Answer:

Answer:

Circumference of a circle is given by:

$C = 2\pi r$

where

C represents the circumference of a circle.

r represents the radius of a circle.

As per the statement:

Use $\pi = 3.14$ and diameter(d) = 2r units

Circumference in terms of diameter (d) is:

$C = 2 \pi r = \pi (2r) = \pi d$

Substitute the value of $\pi = 3.14$ we have;

$C = 3.14d$ units

Now:

find the circumference in terms of radius r.

$C = 2 \pi r$

$C = 2 \cdot 3.14 \cdot r = 6.28r$ units

Therefore, the exact formula for the circumference in terms of the diameter, d is, C = 3.14d and in terms of r is C= 6.28r.

Answer 2

Answer: exact formula of circumference in diameter in 3.14*d=3.14d
and in terms of radius= 3.14*2r=6.28r

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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

This answer uses NMF for which, if needed, the syntax can be found in my profile. Please ignore the LaTeX (the image), I cannot remove it/change it, and it is incorrect. The answer is: f(x)={π{{x}^{2}}/{4}+x(16-{πx}/{2}-x)}/{2}

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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PLEASEEE ITS EASY ALGEBRA 1 ):

Answers

Answer:

6, 7, and 8

Step-by-step explanation:

2x/3 + 7 > 11

Subtract 7 from both sides

2x/3 > 4

Multiply both sides by 3

2x > 12

Divide both sides by 2

x > 6

6, 7, and 8 are the ones that work

One positive number is 5 times another number. The difference between the two numbers is 200, find the numbers.

Answers

x = 5y, where x > 0 and y > 0;
x - y = 200 => 5y - y = 200 => 4y = 200 => y = 200/4 => y = 50 => x = 250.

The diagram shows two parallel lines a andb cut by transversal lines.
Part A
What is an equation that can be used to
solve for x?
Part B
What is the value of x?

Answers

Answer:

y = 180 - (36 + 65)

x = 69

Step-by-step explanation:

Final answer:

To solve for x in the given diagram of parallel lines cut by a transversal, use the concept of corresponding angles. The value of x is 60°.

Explanation:

Part A: To solve for x, we can use the corresponding angles formed by the transversal and the parallel lines. One of the corresponding angles is x + 60°. Since the other corresponding angle is 120°, we can set up the equation x + 60° = 120°. Solving for x, we find that x = 60°.

Part B: The value of x is 60°.

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Which symbol makes the sentence true? − 7 over 8 square − 14 over 16 A. < B. > C. =

Answers

If you have an iphone download gotitt and they will do it for you

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