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Alex787 [66]
3 years ago
14

Polygon Y is a scaled copy of Polygon X using a scale factor of 1/3. Polygon Y’s area isn’t what fraction of Polygon X’s area?

Mathematics
1 answer:
loris [4]3 years ago
5 0

Answer:

1/9th.

Step-by-step explanation:

Because the area is measured in units squared, then you have to square 1/3 which is 19th.

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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

6 0
3 years ago
What are the missing angles?​
Romashka-Z-Leto [24]

Answer:

Adding the 2 known angles: 60° + 100° = 160° We subtract this from 180°. 180° – 160° = 20°. Our missing angle is 20°. To find a missing angle in a triangle we subtract the two known angles from 180°.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Can you help givie full info thanks
liubo4ka [24]

Answer:

13

Step-by-step explanation:

Using long division, you can multiply each given value by 100 to eliminate the decimals:

2.08x100=208

0.16x100=16

OR (calculator method)

2.08÷0.16=13

You must divide the amount of food per cat by the total amount of food available to determine how many cats can be fed.  This division can be done using a calculator.

OR

5 0
2 years ago
Read 2 more answers
e.Water has a density of about 0.0361 pounds/cubic inch. You might know that wood floats on water. What can you conclude about t
irina1246 [14]

Answer:

Step-by-step explanation:

the objects which have less density than water will float

and the objects which have more density than the density of liquid will sink in liquid or will not float.

8 0
2 years ago
Write the following equation in slope-intercept form 3x=-2y+4
Lorico [155]
The form is y=mx+b

3x=-2y+4 (add 2y)

3x+2y=4 (subtract 3x)

2y=-3x+4 (divide by 2)

y= -2/3x+2
5 0
3 years ago
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