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daser333 [38]
3 years ago
15

If 1/4 inch equals 50 miles, find the miles represented by 4 1/2 inches.

Mathematics
2 answers:
Lostsunrise [7]3 years ago
3 0

Answer:

900 miles

Step-by-step explanation:

Well, 200 miles is 1 inch. 100 miles is 1/2 an inch.

dem82 [27]3 years ago
3 0

Answer:

900

Step-by-step explanation:

Given: 1/4 in. = 50 miles

Find the amount of miles per inch. Multiply 4 to both sides of the equation.

(1/4 in.) x (4) = (50 miles) x (4)

4/4 in. = 200 miles

1 in. = 200 miles

Now, find the amount of miles for 4 1/2 in. Multiply 4 1/2 to both sides.

Note that 4 1/2 = 4.5

(1 in.)(4.5) = (200 miles) x (4.5)

4.5 = 200 x 4.5

4.5 = 900

900 miles is your answer.

~

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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
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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)

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⇒ 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

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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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/////////////////////////////////////////////////
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