A circle has a sector with area (3/2) pi and central angle of 60°.
What is the area of the circle?
Either enter an exact answer in terms of it or use 3.14 for it and enter your answer as a decimal.
Answers
Answer:
[tex]9\pi[/tex], which is approximately [tex]28.26[/tex].
Step-by-step explanation:
Consider two sectors in the same circle. The area of the two sectors is proportional to their central angles. In other words, if the central angle is [tex]\theta_1[/tex] for the first sector in this circle, and [tex]\theta_2[/tex] for the second, then:
[tex]\displaystyle \frac{\text{Area of Sector 1}}{\text{Area of Sector 2}} = \frac{\theta_1}{\theta_2}[/tex].
In this question, think about the whole circle as a sector. The central angle of this "sector" would be [tex]360^\circ[/tex] (a full circle.) Compare the area of this circle to that of the [tex]60^\circ[/tex]-sector in this circle:
[tex]\displaystyle \frac{\text{Area of Circle}}{\text{Area of $60^\circ$-Sector}} = \frac{360^\circ}{60^\circ} = 6[/tex].
In other words, the area of this circle is six times that of the [tex]60^\circ[/tex]-sector in it.
The area of that [tex]60^\circ[/tex]-sector is [tex]\displaystyle \frac{3}{2}\pi[/tex]. Therefore, the area of this full circle will be [tex]\displaystyle 6 \times \frac{3}{2}\pi = 9\pi \approx 28.26[/tex].
Related Questions
Dominique is building a flower box for her yard. The outline of the box is shown in the diagram. If she wants to cover the box with
burlap to protect it, how much burlap does she need to buy?
Highlight
00:03:11
Hide Tools
A)
6 sq. feet
B)
8 sq feet
C)
10 sq. feet
D)
12 sq. feet
Answers
Answer:
I promise it's C.) 10 sq. feet. It is not B.)
Answer:
Its C, I took the USA step prep
Please answer i'll give brainlist
AD and BE are diameters. What is the measure of arc EDC
A. 125 degrees
B. 145 degrees
C. 235 degrees
D. 215 degrees
Answers
Answer:
a
Step-by-step explanation:
how do u do this pls help me understand
Answers
Answer:
10.8
Step-by-step explanation:
5 times what gives 6? 5 times 1.2
So now you just do 9 times 1.2 which is 10.8
Answer:
10.8
Step-by-step explanation:
5*x=6
5*1.2=6
9*1.2=r
r=10.8
URGENT an athlete can lift a maximum of 80 pounds. if she uses 3 pound weights when she exercises, what percent is she lifting
Answers
Answer:
should be 3.75 percent
How many people can ride in 1 car? In 10 cars?
Answers
Answer:
depends on the car
Step-by-step explanation:
Answer:
It depends on how many sits the car have
Step-by-step explanation:
What is the area of the trapezoid?
8 m
110 m
12 m
80 m2
96 m2
100 m2
120 m2
Answers
Answer:
I think the answer is 96
Step-by-step explanation:
I think that u have to multiply eight times ten. The you add twelve and that is how I got the answer of 96. I am pretty sure that it is correct but just i case I am sorry if u don't get it right.
Answer:
100
Step-by-step explanation:
the formula is b1+b2 divided by 2 times the height. 8+12=20 divided by 2 is 10 times 10 is 100.
Find the center and radius when x^2+y^2+4x-4y=17
Answers
Answer:
the center is (-2,2) and the radius is 5
Answer:
Center: (-2,2)
Radius:5
Step-by-step explanation:
The first step in this problem is to complete the square and to find the equation of this circle in standard form.
[tex]x^2+y^2+4x-4y=17[/tex] can be rearranged to be:
[tex]x^2+4x+y^2-4y=17[/tex]
Now, you can begin to complete the square with both the x and the y:
[tex](x^2+4x+4)-4+(y^2-4y+4)-4=17[/tex]
Adding 8 to both sides and finishing the squares:
[tex](x+2)^2+(y-2)^2=25[/tex][tex](x+2)^2+(y-2)^2=25[/tex]
The coordinates of the center of the circle are (-2,2), and the radius is [tex]\sqrt{25}=5[/tex]. Hope this helps!
X2+Y2−8X+6Y+21=0 Use the process of completing the square to rewrite the equation above as the equation of a circle in standard form , and identify the center and radius . The center is at the point ( , ) The radius is
Answers
Answer:
Step-by-step explanation:
hello : here is an solution
A jar of marbles has 3 blue marbles,
4 red marbles, and 2 green marbles.
What is the probability of drawing a
marble that is green or not red?
Answers
Answer:
50/50
Step-by-step explanation:
the other person said it and it makes sense smh
The area of a garden is 30 square feet. The perimeter is 26 feet. What are the measurements of each side?
Answers
Answer:
So there are two possibilities:
x = 3, y = 10
x = 10, y = 3
Step-by-step explanation:
Make two equations:
Length = x
Width = y
xy = 30
2x + 2y = 26
You can simplify the second equation to:
x + y = 13
x = 13 - y
(13 - y) * y = 30
13y - y^2 = 30
y^2 - 13y + 30 = 0
Factor:
(y - 3)(y - 10) = 0
y = 3, y = 10
So there are two possibilities:
x = 3, y = 10
x = 10, y = 3
54 out of 72 is what percent
Answers
Answer:
the answer is 75 percent
If a population has a mean of 128 and samples of size 50 from this population have a standard deviation in their sample means of 3.8, then which of the following sample mean would not be within the margin of error when sampling from this population?
A) 119.7
B) 122.8
C) 134.9
D) 135.2
Answers
How many ways can Gary, Cayla, and
Pinak finish a bicycling race in first, second,
and third place?
Answers
Answer:
6
Step-by-step explanation:
G,C,P
C,P,G
P,G,C
G,P,C
P,C,G
C,G,P
Carlos keeps track of his math scores of tests. His scores on his math tests are
the following: 100, 88, 50, 50, 90, 70, 80 What is the:
Median?
Mode?
Mean?
Range?
Answers
Answer:
Median: 75
Mode: 50
Mean: ≈ 75.4
Range: 50
Step-by-step explanation:
Median:Arrange the numbers in order:
50, 50, 70, 80, 88, 90, 100
There is no exact middle number.
[tex]70 + 80 = 150\\150/2 = 75[/tex]
The median is about 75.
Mode:50, 50, 70, 80, 88, 90, 100
"50" appears the most.
The mode is 50.
Mean:Add all numbers in the set.
[tex]100+88+50+50+90+70+80 = 528[/tex]
Divide by the number of values in the set.
[tex]528/7 = 75.4285714286[/tex]
75.4285714286 ≈ 75.4
The mean is about 75.4.
Range:Subtract the smallest number in the data set from the largest number in the data set.
[tex]100-50=50[/tex]
The range is 50.
Brainilest appreciated.
Find the area of a triangle whose sides are 12 cm 6 cm and 14 cm
Answers
Answer:
32
Step-by-step explanation:
add 12 + 6 + 14
Can someone give me three possible solutions?
Answers
How milliliters will there be?
Answers
Answer: Conver 9.7 liters into milliliters!
Me: Ok
Can Yo explain: You
Me: multiply the volume value by 1000
Me: is 9700
Wow Thanks! Goodbye! :You
Me: I am smarter!
Bob has taken out a loan of $15,000 for a term of 48 months (4 years) at an interest rate of 6.5%. Using the amortization table provided, what will be his total finance charge over the course of his loan?
Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77 $30.88 $23.95 $19.80
7.5% $86.76 $45.00 $31.11 $24.18 $20.04
8.0% $86.99 $45.23 $31.34 $24.41 $20.28
8.5% $87.22 $45.46 $24.65 $24.65 $20.52
9.0% $87.45 $45.68 $31.80 $24.89 $20.76
A.
$355.65
B.
$975.00
C.
$1,682.40
D.
$2,071.20
E.
$17,071.20
Answers
The total finance charge over the course of his loan is $2071.20.
It is required to find the total finance charge.
What is simple & compound interest?Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time. Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. Formula. S.I. = (P × T × R) ⁄ 100.
Given that:
Loan= $15,000
The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be 23.71 per thousand borrowed.
The sum of those 48 payments is ...
=48 × $23.71 =
=$1138.08
That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000.
so his total finance charge will be
= 15 × $138.08
= $2071.20
Therefore, the total finance charge over the course of his loan is $2071.20.
Learn more about simple & compound interest here:
https://brainly.com/question/16666364
#SPJ5
Answer:
D.
$2,071.20
Step-by-step explanation:
what does "cross the line, change the sign" means.
Answers
Answer: i believe its like with fractions if you have to cross the line to add or subtract it means that
Step-by-step explanation:
are you working with fractions
Joe is looking for a new laptop case. His computer is 18 x 13.5 inches. What is the perimeter and area of the laptop case?
Perimeter:
Area:
Answers
Answer:
Perimeter =63 inches
Area = 243in²
Step-by-step explanation:
Given data
Length of computer = 18in
Width of computer = 13.5in
From the given data the computer has a rectangular shape
Perimeter of the computer = L+L+W+W= 2L+2W
Perimeter = 2(18)+ 2(13.5)
Perimeter = 36+27=63 inches
Area of rectangular shape = L*W
Area = 18 x 13.5= 243in²
Answer:
Perimeter: 63 inches
Area : 243 square inches
Step-by-step explanation:
Hi, to answer this question w eave to apply the next formulas:
Perimeter of a rectangle: (2 x width) + (2 x length )
Area of a rectangle: width x length
Replacing with the values given:
Perimeter: 2(18) +2(13.5) = 36+27 = 63 inches
Area = 18 x 13.5 = 243 square inches
Feel free to ask for more if needed or if you did not understand something.
Which two values are greater than 3/5
1/4
0.68
2/3
0.599
1/2
Answers
A cylinder shaped juice pitcher has a diameter of 12 cm and a height of 25 cm.
What volume of juice does the pitcher contain when it is 25% full?
Use 3.14 to approximate pi.
Enter your answer as a decimal to the tenths place in the box.
cm
Answers
Answer:
radius of pitcher = 12/2 = 6cm
Volume of pitcher = pi x r^2 x h = 3.14 x 6^2 x 25 = 2,826 cm^3
Volume when pitcher is 25% full = 0.25 x 2,826 = 706.5 cm^3
Step-by-step explanation:
Write down first five multiples of 7.
Answers
Answer:
7, 14, 21, 28, 35
Step-by-step explanation:
Answer:
7,14,21,28,35.
Step-by-step explanation:
7+7=14
14+7=21
21+7=28
Add 7 to each term to get the next or multiply 7 by 5 same answer
i need help thanks in advance
Answers
Answer:
36
Step-by-step explanation:
The reciprocal of the cosine is the ___.
A. secant
B. tangent
C. sine
D. cotangent
Answers
Answer:
The correct answer is A
Step-by-step explanation:
The secant is the distance from the center to the vertical tangent in a certain direction.
Answer:
A. secant
Step-by-step explanation:
For trigonometric ratios, we know that cosine is [tex]\frac{adjacent}{hypotenuse}[/tex]. The reciprocal of something is just flipped over. So the reciprocal of cosine is [tex]\frac{hypotenuse}{adjacent}[/tex], which is the ratio for secant.
Another way we can remember this is [tex]sec x = \frac{1}{cos x} \\\\cos x = \frac{1}{sec x}[/tex]
The ratio of the number of left handers to the number of right handers in a middle school is 6:15. If there are 120 left handers, how many right handers are there? (WILL GIVE BRAINLIEST)
Answers
Answer:
300
Step-by-step explanation:
there are 9 15's in 120 which means its going by 15's 3 x 5= 15 and if it says 6 that means its timesed by 2. 15 x 2= 30 then 30 x 10= 300
What is the lcm of 3,8
Answers
Answer: 24
Step-by-step explanation: The LCM of 3 and 8 is 24.
3 6 9 12 15 `18 21 24
8 16 24
Electronics unlimited sells tvs. There are 110 tvs on display in the showroom, and each tv is turned on to a random channel from a set of 11 channels, 7 sport channels, 3 news channels, and one movie channel. Which statement best predicts how many tvs will not be showing a sports channel?
Answers
Answer:
b
Step-by-step explanation:
khan
The coordinates for a quadrilateral are (0, 0), (-1, 2), (1, 6) and (2, 4). Determine the type of quadrilateral.
Group of answer choices
Parallelogram
Square
Rhombus
Rectangle
Answers
Answer:D is a rectangle
Step-by-step explanation:
9(p-4) = -18 Please help guys!
Answers
Answer:
Step-by-step explanation:
