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Mathematics

1 answer:

Natali5045456 [20]2 years ago

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The circumference of the outer circle is greater than that of the inner circle by 18.86 feet.

<h3>What is Circle?</h3>

A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'.

The circumference of the inner circle is 88 ft.

Circumference of a Circle = 2πr

2πr = 88

2 X 22/7 X r = 88

r = 88 X 7 / 44

r = 14 ft.

Radius of the inner circle = 14 feet

If the distance between the inner circle and the outer circle is 3 ft, the radius of the outer circle = 14+3 = 17 feet.

circumference of the outer Circle = 2πr

= 2 X 22/7 X 17

= 106.86 ft.

Difference in Circumference = 106.86 - 88 = 18.86 feet

Thus, the circumference of the outer circle is greater than that of the inner circle by 18.86 feet.

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Find the distance from point A to the given line:<br> A(-1, 7), y=3x<br><br> How do I solve this?

kipiarov [429]

he formula of a distance between a point (a, b)

and a line Ax + By + C = 0:

$d=\dfrac{|Aa+Bb+C|}{\sqrt{A^2+B^2}}$

We have the point A(-1, 7) → a = -1, b = 7

and the line y = 3x → 3x - y = 0 → A = 3, B = -1, C = 0.

Substitute:

$d=\dfrac{|(3)(-1)+(-1)(7)+0|}{\sqrt{3^2+(-1)^2}}=\dfrac{|-3-7|}{\sqrt{9+1}}=\dfrac{|-10|}{\sqrt{10}}=\dfrac{10\sqrt{10}}{\sqrt{10}\cdot\sqrt{10}}\\\\=\dfrac{10\sqrt{10}}{10}=\sqrt{10}$

<h3>Answer: d = √10</h3>