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evablogger [386]
2 years ago
11

What is the measure of the central angle of a circle with radius 15 ft that intercepts a 10 ft arc?

Mathematics
1 answer:
olga2289 [7]2 years ago
5 0
  • L=10ft
  • R=15ft
  • We have to find theta

\Large{\underline{\sf Solution:-}}

\\ \sf\dashrightarrow L=\dfrac{\Theta}{180}\times \pi r

\\ \sf\dashrightarrow 10=\dfrac{\Theta}{180}\times 3.14\times 15

\\ \sf\dashrightarrow 10=\dfrac{\Theta}{180}\times 47.1

\\ \sf\dashrightarrow \Theta=\dfrac{10(180)}{47.1}

\\ \sf\dashrightarrow \Theta=\dfrac{1800}{47.1}

\\ \sf\dashrightarrow \Theta=38.2°

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anzhelika [568]

Answer: 5x^2y - 30xy^2 - 35y^3=5y(x+y)(x-7y)

Step-by-step explanation:

GCF = Greatest common factor.

For example: 6 is the GCF of 12 and 18.

The given expression: 5x^2y - 30xy^2 - 35y^3

It can be written as

5x^2y - (5\times6)x( y\times y) - (5\times7)(y^2\times y)

Taking out common factor  5y , we get

5y(x^2-6xy-7y^2)\\\\ =5y(x^2+xy-7xy-7y^2)\  \ [\because-6xy=xy-7xy]\\\\=5y(x(x+y)-7y(x+y))\\\\= 5y((x+y)(x-7y))\\\\=5y(x+y)(x-7y)

Hence, 5x^2y - 30xy^2 - 35y^3=5y(x+y)(x-7y)

3 0
3 years ago
Let g(x)= -3x and h(x) x^2+3 Find (g°h)(0)
raketka [301]
<h3>Answer is   -9</h3>

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Work Shown:

(g°h)(x) is the same as g(h(x))

So, (g°h)(0) = g(h(0))

Effectively h(x) is the input to g(x). Let's first find h(0)

h(x) = x^2+3

h(0) = 0^2+3

h(0) = 3

So g(h(x)) becomes g(h(0)) after we replace x with 0, then it updates to g(3) when we replace h(0) with 3.

Now let's find g(3)

g(x) = -3x

g(3) = -3*3

g(3) = -9

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alternatively, you can plug h(x) algebraically into the g(x) function

g(x) = -3x

g( h(x) ) = -3*( h(x) ) ... replace all x terms with h(x)

g( h(x) ) = -3*(x^2 + 3) ... replace h(x) on right side with x^2+3

g( h(x) ) = -3x^2 - 9

Next we can plug in x = 0

g( h(0) )  = -3(0)^2 - 9

g( h(0) ) = -9

we get the same result.

7 0
3 years ago
Andrew received a raise from $14,580.00 per year to $25,317.40 per year. He received
skelet666 [1.2K]

Answer:

Step-by-step explanation:

$25,317.40 is about 57.5% higher than $14,580.00

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A 2% raise would be $14,871.60 per year.

A 3% raise would be $15,017.40 per year.

A 7.4% raise would be $15,658.92 per year.

A 29% raise would be $18,808.20 per year.

I hope this helps

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