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3 years ago

All corresponding sides are proportional (same ratio) in similar figures. True or False

Mathematics

2 answers:

gayaneshka [121]3 years ago

8 0

Answer:

true

Step-by-step explanation:

kipiarov [429]3 years ago

7 0

Answer:

True

Step-by-step explanation:

The corresponding sides are proportional if they have the same ratio. The statement is true.

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If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

2 years ago

Which ordered pair is shown on the graph?

Oliga [24]

Answer:

(2,4)

Step-by-step explanation:

look at the x axis and y axis and see where they meet

6 0

2 years ago

Read 2 more answers

In the expression a + 2b − 12c2, a, 2b, and −12c2 are examples of _____

Vaselesa [24]

Answer:
Terms

Explanation:
Any expression is formed of terms separated by addition or subtraction.
A term can be a number, a variable or the product of multiplying a number and a variable.
Now, the given expression is:
a + 2b + 12c^2
This expression has three terms all separated by addition. These terms are:
a : which is only a variable
2b : which is the product of a number and a variable
12c^2 : which is the product of a number and a variable

Hope this helps :)

8 0

3 years ago

What is 5\18 equal to

Evgesh-ka [11]

The answer is 3.3 hope this helps you .Skateboards

6 0

3 years ago

The candy jar has 251 pieces of candy. Sophia adds 31 pieces of candy to it. If the candy is divided equally between 6 campers,

NeTakaya

Answer:

Step-by-step explanation:

251+31= 282

282 divided by six = 47

4 0

3 years ago

Read 2 more answers