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Stella [2.4K]
3 years ago
11

A circle has an arc with a measure of 120 degrees and a lenght of 3π cm. What is the diameter of the circle

Mathematics
1 answer:
AnnZ [28]3 years ago
4 0

Answer:

9 cm

Step-by-step explanation:

Arc length = θ/360 × 2πr

A circle has an arc with a measure of 120 degrees and a lenght of 3π cm. What is the diameter of the circle

Hence,

3π = 120/360 × 2πr

Diameter = 2r

3π = 1/3 × 2πr

Cross Multiply

9π = 2πr

2r = 9π/π

Note that :

Diameter = 2r

Hence,

Diameter = 9 cm

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A triangle has one side measuring 5 feet and two sides measuring 7 feet. What kind of
Svetllana [295]

Answer:

isoceles but not equilateral

Step-by-step explanation:

it has two sides that are the same length, but not all three sides are the same length

An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal

8 0
3 years ago
Solve this quadratic equation by completing the square <br> x^2+6x=18
cestrela7 [59]

Answer:

( x + 3 )² - 27

Step-by-step explanation:

x² + 6x = 18

→ Minus 18 from both sides to get a quadratic equation

x² + 6x - 18

⇒Completed square from is ( x + a )² + b

⇒The value of 'a' will always be half the 'b' value in the equation

ax² + bx + c

→( x + 3 )² + b

Expand out the equation to find 'b'

x² + 6x + 9

We have do something to get from 9 to - 18 which -27

So the answer is ( x + 3 )² -27

4 0
3 years ago
Read 2 more answers
Write each expression as an algebraic​ (nontrigonometric) expression in​ u, u &gt; 0.
max2010maxim [7]

Answer:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

Step-by-step explanation:

We want to write the trignometric expression:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)

Take the secant of both sides:

\displaystyle \sec(\theta)=\frac{u}{10}

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}

By substitutition:

\displaystyle= \sin(2\theta)

Using an double-angle identity:

=2\sin(\theta)\cos(\theta)

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)

Simplify. Therefore:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

4 0
3 years ago
Can somebody plz help solve and find the correct answers!!<br> thanks so much!! :3
Naddik [55]

Answer:

m=32 p=42 r=24 x=45

Step-by-step explanation:

1. Multiply the answer with the denominator to find the missing number.

2. Check your answer by dividing the numerator and denominator to see if the equation is correct.

4 0
3 years ago
Jorge wants to be more generous and share his money with people in need. He decided that the first $10 he makes, he will give to
zalisa [80]

Answer:

it will be 634.24 because if you add 551.02 and 93.22 that will be 644.24 then you minus the 10 at the beginning.

7 0
3 years ago
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