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3 years ago

Compute the radius of the circle with a circumference of 109.9 millimeters.

Mathematics

1 answer:

GarryVolchara [31]3 years ago

5 0

Answer:

The radius of the circle is 17.5 millimeters

Step-by-step explanation:

* Lets explain how to compute the radius of a circle from its

circumference

- Circle is the locus of all points equidistant from a given point,

this point is called the center of the circle.

- The distance from the center of the circle to a point on the circle is

called the radius of the circle

- The circumference of a circle is the length of the closed cure

- The relation between the radius of a circle and its circumference is

C = 2πr, where C is the circumference and r is the radius

* Lets solve the problem

- The circumference of a circle is 109.9 millimeters

- We need to find the radius of the circle

∵ The circumference of the circle = 109.9 millimeters

∵ The circumference of a circle = 2πr

- Substitute the value of the circumference in the equation above

∴ 109.9 = 2πr

- Divide both sides by 2

∴ 54.95 = πr

- Divide both sides by π (π ≅ 3.14)

∴ r = 17.49 ≅ 17.5

∴ The radius of the circle is 17.5 millimeters

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Step-by-step explanation:

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2 years ago

In the figure below, angle X is 35 degrees. What is the measure of angle Z?

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Answer:

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Step-by-step explanation:

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3 years ago

Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

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$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

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$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

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2 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

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grin007 [14]

Answer:

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Step-by-step explanation:

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