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4 years ago

How do you find the arc length of a partial circle

1 answer:

8 0

A circle is 360° all the way around; therefore, if you divide an arc's degree measure by 360°, you find the fraction of the circle's circumference that the arc makes up. Then, if you multiply the length all the way around the circle (the circle's circumference) by that fraction, you get the length along the arc.

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Alicia has 7 paintings she wants to hang side by side on her wall.

melisa1 [442]

The question is an illustration of permutation and combinations.

The number of ways she can choose 4 out of the 7 paintings is 35
The number of ways she can arrange 4 out of the 7 paintings is 840

The given parameters are:

$\mathbf{n = 7}$

$\mathbf{r = 4}$

(a) Choose 4 of 7 paintings

Choosing 4 of 7 paintings implies combination.

So, we have:

$\mathbf{^nC_r = \frac{n!}{(n - r)!r!}}$

Substitute values for n and r

$\mathbf{^7C_4 = \frac{7!}{(7 - 4)!4!}}$

$\mathbf{^7C_4 = \frac{7!}{3!4!}}$

Expand

$\mathbf{^7C_4 = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4 !}}$

$\mathbf{^7C_4 = 35}$

Hence, the number of ways she can choose 4 out of the 7 paintings is 35

(b) Arrange 4 of 7 paintings

Arranging 4 of 7 paintings implies permutation.

So, we have:

$\mathbf{^nP_r = \frac{n!}{(n - r)!}}$

Substitute values for n and r

$\mathbf{^7P_4 = \frac{7!}{(7 - 4)!}}$

$\mathbf{^7P_4 = \frac{7!}{3!}}$

Expand

$\mathbf{^7P_4 = \frac{7 \times 6 \times 5 \times 4 \times 3!}{3!}}$

$\mathbf{^7P_4 = 840}$

Hence, the number of ways she can arrange 4 out of the 7 paintings is 840

Read more about permutation and combinations at:

brainly.com/question/15301090

8 0

3 years ago

The circumference of a circle is 22pi in. What is the area, in square inches

Daniel [21]

Answer:

22π=2πr. Divide both sides by 2π so r=11. Area = πr^2=121π.

Step-by-step explanation:

6 0

3 years ago

How would I solve this?

givi [52]

Answer:

The valid value of x is x=-2

Step-by-step explanation:

we know that

The sum of the interior angles of any quadrilateral must be equal to 360 degrees

$(7x^{2}-24x)+100+(24-46x)+(3x^{2}+56)=360$

solve for x

Combine like terms

$10x^{2}-70x+180=360$

$10x^{2}-70x-180=0$

Divide by 10 both sides

$x^{2}-7x-18=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}-7x-18=0$

$a=1\\b=-7\\c=-18$

substitute in the formula

$x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(1)(-18)}} {2(1)}$

$x=\frac{7(+/-)\sqrt{121}} {2}$

$x=\frac{7(+/-)11} {2}$

$x=\frac{7(+)11} {2}=9$

$x=\frac{7(-)11} {2}=-2$

Remember that

The measure of the interior angle cannot be a negative number

For x=9

we have that the measure of one interior angle of quadrilateral is

$24-46x$

substitute the value of x

$24-46(9)=-390\°$

therefore

The value of x=9 cannot be a solution

For x=-2

The measure of the interior angles are

$(7(-2)^{2}-24(-2))=76\°\\100\°\\(3(-2)^{2}+56)=68\°\\24-46(-2)=116\°$

therefore

The valid value of x is x=-2

7 0

3 years ago

Your time in a 5k race. Is this discrete or continuous? Write a reasonable

Aneli [31]

Answer:

For intermediate runners (generally those who run 10 – 20 miles per week) an average 5K time would be around 20-25 minutes, which is an average speed of around 7-9mph over the course.

Step-by-step explanation:

https://www.ukfitnessevents.co.uk/event/5k-runs/average-5k-time

3 0

3 years ago

PLEASE HELP

vfiekz [6]

Let the hypotenuse of a 30-60-90 triangle = l
So, the leg which faces angel 60 = l sin 60 = (√3)/2 l // and the leg faces angel 30 = l sin 30 = 0.5 l //
∴ the longer leg = (√3)/2 l
∴ The ratio between the longer leg and hypotenuse = (√3)/2 l : l = (√3)/2 : 1 = √3 : 2 = 3 : 2√3
The correct choices will be C and E

8 0

4 years ago