Ask question

Ask question

All categories

3 years ago

5

Find the measure of the central angle that you would draw to represent 67% in a circle graph. Round your answer to the nearest d

egree. A. 241 B. 24,120 C. 254 D. 229

1 answer:

klio [65]3 years ago

5 0

Okay so there are 360 degrees in a circle graph
So 67%*360 degrees =241 degrees

You might be interested in

use the change of base formula to evaluate log[3](58). then convert log[3](58) to a logarithm in base 4?

devlian [24]

Log[3](58)=3.69597450
log[3](58) to a logarithm in base 4= 167.957<span>
if you still need it.</span>

3 0

3 years ago

A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 25 fe

Varvara68 [4.7K]

Answer:

$Length =\frac{25}{4 + \pi}$ and $Width = \frac{50}{4+\pi}$

Step-by-step explanation:

This question is better understood with an attachment.

See attachment for illustration.

Given

<em>Represent Perimeter with P</em>

$P = 25ft$

Required

Determine the dimension of the rectangle that maximizes the area

First, we calculate the perimeter of the rectangular part of the window.

From the attachment, the rectangle is not closed at the top.

So, The perimeter would be the sum of the three closed sides

Where

$Width = 2x$

$Length = y$

So:

$P_{Rectangle} = y + y + 2x$

$P_{Rectangle} = 2y + 2x$

Next, we determine the circumference of the semi circle.

Circumference of a semicircle is calculated as:

$C = \frac{1}{2}\pi r$

From the attachment,

$Radius (r) = x$

So, we have:

$C = \frac{1}{2}2\pi * x$

$C = \pi x$

So, the perimeter of the window is:

$P = P_{Rectangle} + C$

$P =2y + 2x + \pi x$

Recall that: $P = 25$

So, we have:

$25 =2y + 2x +\pi x$

Make 2y the subject

$2y = 25 - 2x - \pi x$

Make y the subject:

$y = \frac{25}{2} - \frac{2x}{2} - \frac{\pi x}{2}$

$y = \frac{25}{2} - x - \frac{\pi x}{2}$

Next, we determine the area (A) of the window

A = Area of Rectangle + Area of Semicircle

$A = 2x * y + \frac{1}{2}\pi r^2$

$A = 2xy + \frac{1}{2}\pi r^2$

Recall that

$Radius (r) = x$

$A = 2xy + \frac{1}{2}\pi x^2$

Substitute $\frac{25}{2} - x - \frac{\pi x}{2}$ for y in $A = 2xy + \frac{1}{2}\pi x^2$

$A = 2x(\frac{25}{2} - x - \frac{\pi x}{2}) + \frac{1}{2}\pi x^2$

Open Bracket

$A = 2x * \frac{25}{2} - 2x * x - 2x * \frac{\pi x}{2} + \frac{1}{2}\pi x^2$

$A = 25x - 2x^2 - \pi x^2 + \frac{1}{2}\pi x^2$

$A = 25x - 2x^2 - \frac{1}{2}\pi x^2$

To maximize area, we have to determine differentiate both sides and set A' = 0

Differentiate

$A' = 25 - 4x - \pi x$

$A' = 0$

So, we have:

$0 = 25 - 4x - \pi x$

Factorize:

$0 = 25 -x(4 + \pi)$

$-25 =-x(4 + \pi)$

Solve for x

$x = \frac{-25}{-(4+\pi)}$

$x = \frac{25}{4+\pi}$

Recall that

$Width = 2x$

$Width = 2(\frac{25}{4+\pi})$

$Width = \frac{50}{4+\pi}$

Recall that:

$y = \frac{25}{2} - x - \frac{\pi x}{2}$

Substitute $\frac{25}{4+\pi}$ for x

$y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\pi (\frac{25}{4+\pi})}{2}$

$y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\frac{25\pi}{4+\pi}}{2}$

$y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{25\pi}{4+\pi} * \frac{1}{2}$

$y = \frac{25}{2} - \frac{25}{4+\pi} - \frac{25\pi}{2(4+\pi)}$

$y = \frac{25(4+\pi) - 25 * 2 - 25\pi}{2(4 + \pi)}$

$y = \frac{100+25\pi - 50 - 25\pi}{2(4 + \pi)}$

$y = \frac{100- 50+25\pi - 25\pi}{2(4 + \pi)}$

$y = \frac{50}{2(4 + \pi)}$

$y = \frac{25}{4 + \pi}$

Recall that:

$Length = y$

So:

$Length =\frac{25}{4 + \pi}$

Hence, the dimension of the rectangle is:

<em></em> $Length =\frac{25}{4 + \pi}$ <em> and </em> $Width = \frac{50}{4+\pi}$ <em></em>

3 0

3 years ago

The pyramid has a volume of 972 cubic inches what are the dimensions of the pyramid

Maurinko [17]

The volume alone is not sufficient to specify the dimensions.

It might be 18 in square and 9 in high.

6 0

4 years ago

Convert 2/3 to a decimal

Vitek1552 [10]

The answer is .66666666 however on a calculator it will show .66666667 as a way to round all you have to do is divide 2 and 3

7 0

3 years ago

Read 2 more answers

A bus travels 36 miles in 45 minutes. How many miles will it travel in 60 minutes at this rate?

____ [38]

Answer:

48 miles

Step-by-step explanation:

7 0

3 years ago