I got help on this one ty

The area of the sector formed by the 110 degree central angle is 50 units squared. What is the circumference of the circle

Mama L [17]

Answer:

The circumference of the circle is $C=45.346 \:units$ .

Step-by-step explanation:

A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

The area of a circle is given by $A_{circle}=\pi r^2$

The formula used to calculate the area of a sector of a circle is:

$A_{sector}=\frac{central \:angle}{360} \cdot {Area \:of \:whole \:circle}\\\\A_{sector}=\frac{\theta}{360} \cdot \pi r^2$

The circumference of a circle is the distance around the outside of the circle and its given by

$C=2\pi r$

We know the central angle $\theta$ = 110º and the area of the sector 50 units squared.

First, we use the formula to calculate the area of a sector to find the radius.

$50=\frac{110}{360} \cdot \pi r^2\\\\\frac{110}{360}\pi r^2=50\\\\\frac{11\pi }{36}r^2=50\\\\11\pi r^2=1800\\\\r^2=\frac{1800}{11\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{1800}{11\pi }},\:r=-\sqrt{\frac{1800}{11\pi }}$

The radius can't be negative. Therefore,

$r=\sqrt{\frac{1800}{11\pi }}\approx 7.217 \:units$

Next, we apply the formula for the circumference of a circle.

$C=2\pi (7.217)=45.346 \:units$

7 0

3 years ago

Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx x(l

Pepsi [2]

I'm assuming the integral is

$\displaystyle \int \frac{dx}{x (\ln(x^2))^5}$

We have

$\ln(x^2) = 2 \ln|x| \implies (\ln(x^2))^5 = 32 (\ln|x|)^5$

Then substituting $y=\ln|x|$ and $dy=\frac{dx}x$ , the integral transforms and reduces to

$\displaystyle \int \frac{dx}{x(\ln(x^2))^5} = \frac1{32} \int \frac{dy}{y^5} \\\\ ~~~~~~~~ = \frac1{32} \left(-\frac1{4y^4}\right) + C \\\\ ~~~~~~~~ = -\frac1{128(\ln|x|)^4} + C$

which we can rewrite as

$128 (\ln|x|)^4 = 8\cdot2^4(\ln|x|)^4 = 8 (2\ln|x|)^4 = 8 (\ln(x^2))^4$

and so

$\displaystyle \int \frac{dx}{x (\ln(x^2))^5} = \boxed{-\frac1{8(\ln(x^2))^4} + C}$

7 0

1 year ago

Simplify: 10(-5x+4) A 5x + 4 B - 50x + 4 - 50x + 40 5x + 40

ELEN [110]

Answer:

-50x+40

Step-by-step explanation:

4 0

2 years ago

The UAE Hope Probe is between 22,000 Km and 44,000 KM away from mars. This means its between _____________m and ______________m.

Marina86 [1]

Answer:

This means it is between 22000000 m and 44000000 m.

Step-by-step explanation:

From the question, the UAE Hope Pobe is between 22 000 km and 44 000 km away from Mars.

Since,

1 000 m = 1 km

Then,

22 000 km = 22 000 x 1000 m

= 22000000 m

also,

44000 km = 44000 x 1000 m

= 44000000 m

Therefore, the Probe is between 22000000 m and 44000000 m.

6 0

2 years ago

If a bill totals 123.85 with 5% tax and 18% tip what is the total bill

lianna [129]

Answer:

$152.33

Step-by-step explanation:

123.85 x 0.05 = $6.19

123.85 x 0.18 = $22.29

123.85 + 6.19 + 22.29 = $152.33

6 0

2 years ago