Answer:
![\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}](https://tex.z-dn.net/?f=%5Ctext%7B1%29%20%7D%5C%5C%5Ctext%7BCircumference%3A%20%7D24%5Cpi%20%5Ctext%7B%20m%7D%7D%2C%5C%5C%5Ctext%7BLength%20of%20bolded%20arc%3A%20%7D18%5Cpi%20%5Ctext%7B%20m%7D%5C%5C%5C%5C%5Ctext%7B3%29%7D%5C%5C%5Ctext%7BCircumference.%20%7D4%5Cpi%20%5Ctext%7B%20mi%7D%2C%5C%5C%5Ctext%7BLength%20of%20bolded%20arc%3A%20%7D%20%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%5Ctext%7B%20mi%7D)
Step-by-step explanation:
The circumference of a circle with radius
is given by
. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle
is equal to
.
Formulas at a glance:
- Circumference of a circle with radius
:
- Length of an arc with central angle
: ![\ell_{arc}=2\pi r\cdot \frac{\theta}{360}](https://tex.z-dn.net/?f=%5Cell_%7Barc%7D%3D2%5Cpi%20r%5Ccdot%20%5Cfrac%7B%5Ctheta%7D%7B360%7D)
<u>Question 1:</u>
The radius of the circle is 12 m. Therefore, the circumference is:
The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:
![\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}](https://tex.z-dn.net/?f=%5Cell_%7Barc%7D%3D24%5Cpi%20%5Ccdot%20%5Cfrac%7B270%7D%7B360%7D%2C%5C%5C%5C%5C%5Cell_%7Barc%7D%3D24%5Cpi%20%5Ccdot%20%5Cfrac%7B3%7D%7B4%7D%2C%5C%5C%5C%5C%5Cell_%7Barc%7D%3D%5Cboxed%7B18%5Cpi%5Ctext%7B%20m%7D%7D)
<u>Question 2:</u>
In the circle shown, the radius is marked as 2 miles. Substituting
into our circumference formula, we get:
![C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}](https://tex.z-dn.net/?f=C%3D2%28%5Cpi%29%282%29%2C%5C%5CC%3D%5Cboxed%7B4%5Cpi%5Ctext%7B%20mi%7D%7D)
The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:
![\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}](https://tex.z-dn.net/?f=%5Cell_%7Barc%7D%3D4%5Cpi%20%5Ccdot%20%5Cfrac%7B135%7D%7B360%7D%2C%5C%5C%5Cell_%7Barc%7D%3D1.5%5Cpi%3D%5Cboxed%7B%5Cfrac%7B3%5Cpi%7D%7B2%7D%5Ctext%7B%20mi%7D%7D)
Step-by-step explanation:
As we know that,
In area of triangle , breadth =6inch,similarily ,height =8inch
now ,
Area of triangle = 1/2 ×b×h
= 1/2 × 8 ×6
=24inch^2
also,
In another figure,we can say
a=10 inch,b=16 inch and h=9 inch
similarly,
Area of trapizium = 1/2 h(a+b)
= 1/2 ×9(10+16)
=9/2 ×26
=9×13
=117inch^2
now ,
total area of figure =117 +24 =141inch^2
therefore,total area of figure is 141 inch^2
Answer:
39
Step-by-step explanation:
65/2.5 then x 1.5
-2(5,6)-40 I think that's it
Answer:
$180,000 is 10% $9,000 is 5%
Step-by-step explanation:
To solve for this, you would set up a ratio and cross-multiply.
$18,000/$180,000 = x%/100%
(18,000)(100) = 180,000x
1,800,000 = 180,000x
10 = x
9,000/180,000 = x/100
900,000 = 180,000x
5 = x
OR
$18,000 ÷ 2 = $9,000
10% ÷ 2 = 5%