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Viktor [21]
3 years ago
9

Given the following shape with parellel lines, explain why these two triangles are similar.

Mathematics
1 answer:
ohaa [14]3 years ago
3 0

Answer:

All 3 angles are the same, it is simply a dilation. the size is the only difference.

Step-by-step explanation:


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Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. width units height units
dmitriy555 [2]

This question is incomplete, the remaining part of the question is upload as an image alongside this answer.

Answer:

Width = 2x = 2( r/√2 ) =  √2 r units

Height = 2y = 2( r/√2 ) =  √2 r units

Step-by-step explanation:

From the Figure on the image; lets consider the circle of radius r, centered at the origin.  

let ABCD be the largest rectangle that can be inscribed inside the circle.  

Let the half width of the rectangle be x, then in right triangle ONB using Pythagorean theorem,  

half height of rectangle y = √(r² - x²)

Thus the width of the inscribed rectangle = 2x and height of the inscribed rectangle = 2√(r² - x²)

thus the area of the inscribed rectangle = length × width

⇒ A(x) = 2x(2√(r² - x²))

⇒ A(x) = 4x√(r² - x²)  

now in order to maximize the area, we find critical points.

so we find the derivative and set that zero, that is Ai(x) = 0.

so using product rule, we get

A'(x) = 4x × ( -2x / 2√(r² - x²) ) + ( 4 × √(r² - x²)  )

A'(x) = ( -4x² / √(r² - x²) ) + ( 4√(r² - x²)  )

Now for critical points, set A'(x) = 0

so

( -4x² / √(r² - x²) ) + ( 4√(r² - x²)  ) = 0

( 4x² / √(r² - x²) ) =  ( 4√(r² - x²)  )

x² = r² - x²

2x² = r²

x² = r²/2

x = ±√(r²/2)

Now since x represent the with, it cannot be negative, Thus

x = r/√2

hence

y = √(r² - x²) = √(r² -  r²/2) = √(r²/2) =  r/√2

Therefore, the dimensions of the rectangle of largest area will be;

Width = 2x = 2( r/√2 ) =  √2 r units

Height = 2y = 2( r/√2 ) =  √2 r units

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3 years ago
What numbers are 0.6 unit from 1.3 on a number line?
ruslelena [56]

Answer:

A

Step-by-step explanation:

HOEP IT HELPS I TRY MY BEST

6 0
3 years ago
The population of fish in a certain lake increased from 350 to 430 over the months of March and April. At what rate is the popul
Xelga [282]
40 fish a day increase(unit rate)
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Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.
Natali [406]
The answer to what the length of the leg would be is 15.

You would do this problem by first writing down your Pythagorean Theorem, which is a^2 + b^2 = c^2.

Since we have our hypotenuse which is c^2 in our equation, we would write or insert the number we have.

So our equation could be that a or b leg equals 20, it doesn’t matter which one.

So we could write, 20^2 + b^2 = 25^2. So we don’t know what b leg is.

First we should figure out what 20^2 is and what 25^2 is.

20^2 is 400 and 25^2 is 625.

Our equation now comes to 400 + b^2 = 625.

Now we take 400 and subtract it from
625 -> 400 + b^2 = 625
-400.

So 625 - 400 comes out to be 225.

Lastly instead of squaring or putting 225 to the second power, we do the opposite.

So instead of squaring 225 we must square root 225. √ 225 .

The square root of √ 225 comes out to be 15.

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What is the slope of the line that passes through the points (-2, 2), and (-4, -2)?
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C is the ryt answer ......
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