One ector of a circle ha an area of 121 quare centimeter and an arc meaure of 36'. What i the area of the circle to the nearet
quare centimeter
Answers
The Area of the circle will be = is 144.87 [tex]cm^{2}[/tex]
Given in the question,
The sector of the circle has an area of = 121 [tex]cm^{2}[/tex]
The measure of an arc = is 36 inches.
According to the attached figure,
Let us consider the arc length = L
Let radius = r
As per the question L = 36'
Let the radius be
To calculate the length of the arc we need to use the formula,
L = r x θ
36 = r x θ
θ = [tex]\frac{36}{r}[/tex] degrees ------- equation 1
Now according to the area of the sector of the circle,
A = [tex]r^{2}[/tex] x θ / 2
121 = [tex]r^{2}[/tex] x θ / 2
[tex]r^{2}[/tex] = 2 x 121 / ( [tex]\frac{36}{r}[/tex] )
[tex]r^{2}[/tex] = [tex]\frac{2 * 121 * r}{36}[/tex] ----- equation 2
r = [tex]\frac{2 * 121 }{36}[/tex]
r = 6.72 cm.
Now if the radius is = 6.72 cm
Diameter = 2 x radius
= 2 x 6.72
= 13.44 cm
Area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi[/tex] x 6.72 x 6.72
= 144.87 [tex]cm^{2}[/tex]
Therefore, the area of the circle = is 144.87 [tex]cm^{2}[/tex]
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Related Questions
In the figure below, ⎯⎯⎯⎯⎯⎯⎯⎯,⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯,
B
L
¯
,
A
M
¯
,
and ⎯⎯⎯⎯⎯⎯⎯⎯⎯
C
K
¯
are medians of △
△
A
B
C
. If AM = 21 and LO = 4, then AO =
Answers
Applying the definition of the median of a triangle, the length of AO is calculated as: 14 units.
What is the Median of a Triangle?The median of a triangle is a line segment that joins the midpoint of a side of a triangle and the opposite vertex to the side.
There are three medians in a triangle, and the three of them intersect at a point inside the triangle. This point of intersection is known as the centroid.
According to the centroid theorem of a triangle, the length from the vertex to the centroid is two-third of the length of a median.
Thus, the figure shows that triangle ABC has three medians, BL, AM, and CK, which intersect at point O. This means the centroid of the triangle is point O.
By implication, it means that:
Length of AO = 2/3 * (length of AM)
Plug in the value of AM:
Length of AO = 2/3 * (21) [centroid theorem]
AO = 2 * 7
AO = 14
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Urgent pls help guyssss
Answers
Answer: C
Step-by-step explanation:
I Need help with this question
Answers
However, when you roll multiple times, for example here 720 times, you have to multiply that probability by the number of rolls. So 720 x 2/3 = 480, and that’s the probability of getting a number less than 5 in 720 die rolls.
Answer is c
Answer:
720 / 6 = 120
120 * 4 = 480
P(1) = 120/720
P(2) = 120/720
P(3) = 120/720
P(4) = 120/720
P(5) = 120/720
P(6) = 120/720
P(1 + 2 + 3 + 4) = 480/720
C. 480 timesStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-use a double integral to find the area of the region. one loop of the rose r = 8 cos(3θ)
Answers
Using a double integral, the area of the region is [tex]\frac{\pi}{12}[/tex].
Consider the following polar equation:
r = 8cos3[tex]\theta[/tex]
What is a polar curve and how does it work?This is the process for measuring the intensity of light. Such intensity varies according to how close or far you are from LED light bulbs. Engineers use polar curves to plot the level of the intensity at any given point. In other words, a polar curve tells an engineer how LED light bulbs spread light across a room or surface.
The objective is to find the area of the region using double integral.
The sketch of the curve attached at the end of solution.
The intersection points of the curve with horizontal axis are given by,
8cos3[tex]\theta[/tex] = 0
cos3[tex]\theta[/tex] = 0
[tex]3 \theta & =\pm \frac{\pi}{2}[/tex]
[tex]\theta & =\pm \frac{\pi}{6}[/tex]
Therefore, the loop is given by the region,
[tex]D=\left\{(r, \theta) \mid-\frac{\pi}{6} \leq \theta \leq \frac{\pi}{6}, 0 \leq r \leq \cos 3 \theta\right\}[/tex]
Let A be the area of the curve.
The area of the loop is given by,
[tex]& A(D)=\iint_D d A \\[/tex]
[tex]& =\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \int_0^{\cos 3 \theta} r d r d \theta \\[/tex]
[tex]& =\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}}\left[\frac{r^2}{2}\right]_0^{\cos 3 \theta} d \theta \\[/tex]
[tex]& =\frac{1}{2} \int_{\frac{\pi}{6}}^{\frac{\pi}{6}} \cos ^2 3 \theta d \theta \\[/tex]
[tex]& =\frac{1}{2} \int_{-\frac{\pi}{6}}^{\frac{\pi}{6}}\left(\frac{1+\cos 6 \theta}{2}\right) d \theta \\[/tex]
[tex]& =\frac{1}{4}\left[\theta+\frac{1}{6} \sin 6 \theta\right]_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \\[/tex]
[tex]& =\frac{1}{4}\left[\left(\frac{\pi}{6}+\frac{1}{6} \sin \pi\right)-\left(-\frac{\pi}{6}+\frac{1}{6} \sin (-\pi)\right)\right] \\[/tex]
[tex]& =\frac{1}{4}\left(\frac{\pi}{3}\right) \\[/tex]
[tex]& =\frac{\pi}{12} \\[/tex]
Hence, the area of the one loop of the rose [tex]r = 8 \cos(3\theta)[/tex] is [tex]\frac{\pi}{12}[/tex].
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-x-7y-14
-4x-14y=28 solve by elimination
Answers
Answer:
x= -28
y= 6
Step-by-step explanation:
-x-7y = -14
-4x-14y=28
Let's find x first! First, we time the first equation by -2
2x + 14y = 28
-4x -14y = 28
Add them; you will get
-2x = 56
x = -28
Then put -28 back in the x, and you will get
y= 6
Which expreion have a quotient of 6? Select all that apply. 0. 48 ÷ 0. 8
4. 8 ÷ 8
0. 48 ÷ 0. 08
4. 8 ÷ 0. 8
4. 8/0. 8
Answers
Expreion have a quotient of 6 is 0. 48 ÷ 0. 08.
What is quotient?
In mathematics, the quotient is the result of performing division operations on two integers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
0. 48 ÷ 0. 8
=0.06
The solution for Long Division of [tex]$\frac{4.8}{8}$[/tex] is 0.6
The solution for Long Division of [tex]$\frac{0.48}{0.08}$[/tex] is 6.
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Which division problem can be described using this model?
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the number of miles mario can drive varies directly with the amount of gas that he has. he can drive 18 miles on ½ a gallon of gas. how many miles can mario drive with 9 gallons of gas?
Answers
There are 324 miles can Mario drive with 9 gallons of gas.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
He can drive 18 miles on ½ a gallon of gas.
Now,
Since, He can drive 18 miles on ½ a gallon of gas.
Let the number of miles cover with 9 gallons of gas = x
So, By definition of proportion, we get;
⇒ 18 / (1/2) = x / 9
⇒ 18 × 2 = x / 9
⇒ 36 × 9 = x
⇒ x = 324 miles
Thus, The number of miles cover with 9 gallons of gas = 324 miles
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What is 2 to the power of three halves equal to? square root of 8 cube root of 8 cube root of 16 square root of 16
Answers
The answer to 2 to the power of three halves equal to? is square root of 8 cube root of 8 cube root of 16 square root of 16 is [tex]\sqrt{8}[/tex]
How to find the square root of a number?In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.
From the question, we can simplify the question as
[tex]2^{\frac{3}{2} }[/tex]
simplifying further by simplifying the power
[tex]2^{\frac{3}{2} }[/tex] = [tex](2^{3})\frac{1}{2}[/tex]
= [tex]\sqrt{2^{3} }[/tex]
= [tex]\sqrt{8}[/tex]
hence, the solution to the problem is [tex]\sqrt{8}[/tex]
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a child of a parent with a mutation in collagen and displaying oi will have what probability of also having oi? 25% 50% 75% 100%
Answers
A child of a parent with a mutation in collagen and displaying OI will have 50% probability of also having OI.
What is Osteogenesis Imperfecta (OI)?Osteogenesis imperfecta (OI) is an inherited or genetic bone disorder which is present at birth. It is also known as brittle bone disease. A child born with OI may have soft bones which fracture easily, bones which are not formed normally, and other problems. Signs and symptoms may range from mild to severe.
Life expectancy for OI babies vary greatly depending on OI type. Babies with Type II generally die soon after birth. Children with Type III may live longer, but mostly only until around age 10.
About 90% of OI cases are caused by autosomal dominant mutations in the type I collagen genes. Mutations in one or the other of these genes cause the body to make either abnormally formed collagen or too little collagen. Mutations in these genes cause OI Types I through IV.
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Choose the equation of a line parallel to the given equation and passing through a point P. x + 2 y =5 ; ( 2,-5)
A.) Y = 2 x -4
B.) Y = -1/2x -1
C.) Y = -1/2x -4
D.) Y = -2 x -1
Answers
Answer:
The correct answer is C: Y = -1/2x - 4.The slope of the given line is -1/2, so any line that is parallel to it will have the same slope. In order to find the equation of a line with the same slope that passes through the point (2, -5), we can use the point-slope form of the equation of a line.The point-slope form of the equation of a line is:y - y1 = m(x - x1)where m is the slope of the line, and (x1, y1) is a point on the line.In this case, we can plug in the values m = -1/2, x1 = 2, and y1 = -5 to get:y + 5 = -1/2(x - 2)Solving for y, we get:y = -1/2x - 4Therefore, the equation of the line that is parallel to the given line and passes through the point (2, -5) is Y = -1/2x - 4.
If your parabola has a vertex going through the point (2,13), the axis of symmetry would be?
Answers
The axis of symmetry of the parabola would be x = 2
How to determine the axis of symmetryFrom the question, we have the following parameters that can be used in our computation:
Vertex = (2, 13)
Rewrite the vertex as follows
So, we have the following representation
(x, y) = (2, 13)
Remove the y-coordinates
This gives
x = 2
This represents the axis of symmetry
Hence, the axis of symmetry is x =2
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mateo is playing a word game where he's trying to make 444-letter words by rearranging the letters in the word iron. how many unique ways are there to arrange the letters in the word iron?
Answers
The word IRON can be arranged is 24 unique ways.
Given:
The word = IRON
The number of unique ways in which the letters in the word IRON can be arranged = ?
The number of letters in IRON = 4
The number of positions = 4
In the first position, any one of the 4 letters can be placed
In the second position any one of the remaining 3 letters can be placed
In the third position any one of the remaining 2 letters can be placed
The fourth position can be filled with the left over letter
So the total number arrangement in unique way
= (Number of ways to fill in 1st position)* (Number of ways to fill in 2nd position)* (Number of ways to fill in 3rd position)* (Number of ways to fill in 4th position)
=> 4 *3*2*1
= 24 ways
Hence, The word IRON can be arranged is 24 unique ways.
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Select all the values of x that make the equation | 3x + 4 | − 9 = 0 true.
A . 1 2/3
B. -1 2/3
C. 4 1/3
D. -4 1/3
E. 5 2/3
F. -5 2/3
Answers
[tex]|3x+4|-9=0[/tex]
Add 9 to both sides:
[tex]|3x+4|-9+9=0+9[/tex]
[tex]|3x+4|=9[/tex]
Solve the Absolute Value:
[tex]3x+4=9or3x+4=-9[/tex]
__________________________________________________________
[tex]3x+4=9[/tex]
Subtract 4 from both sides:
[tex]3x+4-4=9-4[/tex]
[tex]3x=5[/tex]
Divide both sides by 3:
[tex]\dfrac{3x}{3} =\dfrac{5}{3}[/tex]
[tex]\fbox{x = $\dfrac{5}{3} $ or 1$\dfrac{2}{3}$}[/tex]
__________________________________________________________
[tex]3x+4=-9[/tex]
Subtract 4 from both sides:
[tex]3x+4-4=-9-4[/tex]
[tex]3x=-13[/tex]
Divide both sides by 3:
[tex]\dfrac{3x}{3} =\dfrac{-13}{3}[/tex]
[tex]\fbox{x = $\dfrac{13}{3} $ or -4$\dfrac{1}{3} $}[/tex]
________________________________________________________
[tex]\fbox{Options A and D}[/tex]
(a) Given that f(x) = 2x + 1, find the nearest whole number of f(2.99), f(2.999) f(3.01), f(3.001). What conclusion can you draw from these results?
Answers
Step-by-step explanation:
since f(x) = 2×x + 1
therefore f(2.99) = 2×2.99 + 1 = 6.98 ≈ 7
therefore f(2.999) = 2×2.999 + 1 = 6.998 ≈ 7
therefore f(3.01) = 2×3.01 + 1 = 7.02 ≈ 7
therefore f(3.001) = 2×3.001 + 1 = 7.002 ≈ 7
now for the what conclusion can you draw from these results i dont 100% know but i think he wants that
the point x = 3 and the point y = 7
since f(x) = y
and since we have the approximate of x 3
This number line models the division problem 1/4÷5 what is the quotient
15 points!
Answers
Answer: 1/20
Step-by-step explanation:
....................................
At a real estate agency, an agent sold a house for $306,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The agency made (answers) on the house
Answers
Answer:
.......................
Answer:
$22,950, $4,590
Step-by-step explanation:
Divide 306,000 by 100. This equals 3060, or one percent of the profit.
Multiply this profit by 7.5 to get $22,950, which is the amount to agency makes.
To find what the agent makes, divide 22,950 by 10 to get 2,295, or ten percent of the agency's profits. Double it and it will 20 percent or $4,590, the amount the agent makes.
draw the mail carrier's position-versus-time graph. assume that x=0m at t=0s.
Answers
The position of mailbox after 10s is equal to sum displacements is 14m.
The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).
Given velocity time graph understand in three parts.
1. first 6s mailbox have constant velocity 3m/s
the displacement covered by it = area under v-t graph(square shape)
s1=3 x 6 =18m
2. the mailbox at rest at 6-8 s.
the displacement covered by it s2=0
3. the mail returned with constant velocity 2m/s
Displacement is defined to be the change in position of an object. It can be defined mathematically with the following equation:
Displacement=Δx=[tex]x_{f} - x_{0}[/tex]
[tex]x_{f}[/tex]=refers to the value of the final position.
[tex]x_{0}[/tex]= refers to the value of the initial position.
Δx is the symbol used to represent displacement
the displacement covered by it s3 =(10-8) (-2) =-4m
the position of mailbox after 10s is equal to sum displacements=s1+s2+s3 =18+0-4=14m the displacement - time graph.
Therefore, the position of mailbox after 10s is equal to sum displacements is 14m.
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Draw the mail carrier's position-versus-time graph. Assume that x=0m at t=0s
What is the position of the mailbox?
86 crayons in the basket are broken. The basket has 182 crayons. How many crayons are NOT broken?
Answers
Answer: 96 crayons
Step-by-step explanation:
Take 182 subtract 86 = 96 crayons
96 crayons are not broken
In what ways were the causes and the effects of revolutions between 1750 and 1900 similar and different?.
Answers
From 1750 to 1900, Europe's strength and dominance over the world grew dramatically.
New western political concepts developed strong, centralized states that directed empires all around the world, while industrialization created unprecedented wealth.
The following are the reasons and impacts of the various revolutions that occurred between 1750 and 1900:
The globe became really autonomous as a result of industrialization.
Such countries, in quest of raw supplies and markets, encroached on other countries' economic interests.Many people migrated to big cities as a result of population expansion.Slaves and serfs were liberated because free-wage work was favored over forced labor.In comparison to men, women were paid significantly less.This drove women to struggle for their own political rights.People from the working class arrived as a force for change.They were able to push for changes to their terrible working conditions through the formation of unions.
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find constant rate of change
Answers
Answer: B
Step-by-step explanation:
The constant rate of change or slope is rise/run
Let's pick 2 points ( 4, 12) ( 10, 0)
We see that the y decreases by 12 and the x increase by 6, so our slope is
-12/6 = -2 hours per person
So the answer is B
find the area of the region bounded by the hyperbola 9x2 − 4y2 = 36 and the line x = 3.
Answers
Refer to the photos taken.
Find the percent of sugar in the concentration:
A syrup made of 10kg of water and 2kg of sugar
Answers
Answer: 2/12= 16.67% four sig fig
Step-by-step explanation:
Using (mass of sugar)/(total mass)
and total mass equals (mass of sugar) + (mass of water)
get a total mass of 12kg
Therefore percentage is 2/12=1/6=16.666666%
Answer:
The percentage of sugar in the syrup is 16.66...%
Step-by-step explanation:
lmk
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
m=riserun=ΔyΔx
m=y2−y1x2−x1
m=0−2−2−2
m=−2−4
m=12
The answer is :
m = 0.5
Smith City received 2. 45 inche of rain on Monday and 1. 72 inche of rain on Tueday. Write an equation howing a way to etimate to the nearet inch the total rainfall for the two day
Answers
an equation showing a way to estimate to the neasrt inch the total rainfall for the two day 2.45 + 1.72 ≈ 4.2 inches
1. Add the two amounts of rainfall together: 2.45 + 1.72
2. Round the answer to the nearest inch: 4.2 inches
3. The equation to estimate the total rainfall for the two days is 2.45 + 1.72 ≈ 4.2 inches.
This equation provides a simple way to estimate the total rainfall for two days. By adding the two amounts of rainfall, we can then round the answer to the nearest inch to obtain the estimated total rainfall. This equation can be used to quickly and accurately estimate rainfall totals for any two-day period.
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if f'(x)=cos(x^2) and f(3)=7 then f(2)=
Answers
The value of function f(2) if f'(x)= cos(x²), and f(3) = 7 is [tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{4}{\pi }}\right)+C[/tex].
What is function?The relationship between a set of potential outputs and a set of potential inputs is called a function, and it has one relationship per output between each input. This indicates that a function f will map an object x to exactly one object f(x) in the set of potential outputs if it is present in the set of inputs, also known as the domain (called the co-domain).
Given:
f'(x )= cos(x²),
f(3) = 7
Calculate the integration of the following function as shown below,
∫ f'(x) = 3∫cos(x²)
The integral is the Fresnel integral function, C(x)+C
[tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{2}{\pi }}x\right)+C[/tex]
f(3) = 7
[tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{2}{\pi }}3\right)+C[/tex]
Calculate the value of f(2) as shown below,
f(2) = [tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{2}{\pi }}\times 2\right)+C[/tex]
f(2) = [tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{4}{\pi }}\right)+C[/tex]
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Last year a community had 32 incidents of vandalism.
This year they only had 23 incidents of vandalism.
Answers
Answer: 22%
Step-by-step explanation:
The volume of a large can of tuna fish can be calculated using the formula V = πr²h. Write an equation to find the radius, r, in terms of V and H.
Answers
Answer:
[tex] r = \sqrt{\dfrac{V}{\pi h}} [/tex]
Step-by-step explanation:
V = πr²h
Switch sides.
πr²h = V
Divide both sides by πh.
r² = V/(πh)
Take the square root of both sides.
r = √[V/(πh)]
[tex] r = \sqrt{\dfrac{V}{\pi h}} [/tex]
Help aspp please thank you
Answers
The equation of the line would be y = (-3/4)x + 5.
What is the slope-point form of the line?
For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be
y - y1 = m(x - x1)
The given equation is [tex]y=-\frac{3}{4}x-17[/tex]
The required line is parallel to the given line.
and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4
And the required line passes through (8, -1)
so by using slope - point form of the line,
y - (-1) = (-3/4)(x - 8)
y + 1 = (-3/4)x - (-3/4)8
y + 1 = (-3/4)x + 24/4
y = (-3/4)x + (12/2 - 1)
y = (-3/4)x + 5
Hence, the equation of the line would be y = (-3/4)x + 5.
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What is the linear regression equation for the data given? (Round to the nearest tenths place.)
Answers
a = 3.47
b = 13.27
r^2 = .85
r = .92