What are the answers to a, b, c, d?

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

Olivia decides to hire an electrician. The electrician charges $35 to come out to Olivia's

atroni [7]

Answer:

Step-by-step explanation:

Total cost

C (x) = 35+ 60x

Where,

Fixed cost= $35

Variable cost = 60x

x= number of hours of work

Total cost is the addition of fixed and variable cost

C (x) = 35+ 60x

C(5)= 35 + 60(5)

= 35 + 300

=335

C(5) = 335

C(5) = 335 is Olivia's total cost of hiring the electrician

x=5 is the electrician's number of hours of work

35= fixed cost of hiring the electrician

60(5) = 300 is the variable cost of hiring the electrician for 5 hours

5 0

2 years ago

Use the balanced scale to find the conversion factor that can be used to convert the number of blocks to the weight of the block

Sedbober [7]

Answer:

A. 1.5 pounds per block

Step-by-step explanation:

The conversion factor shows 2 blocks on the right and three 1 pound blocks on the left. It takes two 1 pound blocks to make 2 and then you get your 3rd block, making it 3 (.5 more than 2.5) needing another block to add a .5

8 0

2 years ago

Read 2 more answers

Please help me with this

Cerrena [4.2K]

Answer:

Yes;Each side of triangle PQR is the same length as the corresponding side of triangle STU

Step-by-step explanation:

You can observe the sides of both triangles to see if this property holds

Lets check the length of AB

A(0,3) and B(0,-1)

$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\\\\\AB=\sqrt{(0-0)^2+(-1-3)^2} \\\\\\\\AB=\sqrt{0^2+-4^2} \\\\\\AB=\sqrt{16} =4units$