Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
!
Answer: 8 (Pi - sqrt(3))
Discussion:
The area of the shaded region is that of the semicircle minus the area of the triangle..
Area of semicircle = 1/2 * Pi * R^2
Where R^2 is the square of the radius of the circle. In our case, R ( = OC)
= 4 so the semicircle area is
(1/2) * Pi * (4^2) = (1/2) * Pi * 16 = 8 Pi
Area of triangle.
First of all, angle ACB is a right angle ( i.e. 90 degrees).
* This is the Theorem of Thales from elementary Plane Geometry. *
so by Pythagoras
AC^2 + BC^2 = AB^2
But CB = 4 (given) and AB = 4*2 = 8 ( the diameter is twice the radius).
Substituting these in Pythagoras gives
AC^2 + 4^2 = 8^2 or
AC^2 = 8^2 - 4^2- = 64 - 16 = 48
Hence AC = sqrt(48) = sqrt (16*3) = 4 * sqrt(3)
We are almost done! The area of the triangle is given by
(1/2) b * h = (1/2) BC * AC = (1/2) 4 * (4 * sqrt(3)) = 8 sqrt(3)
We conclude the area area of the shaded part is
8 PI - 8 sqrt(3) = 8 (Pi - sqrt(3))
Note that sqrt(3) is approx 1.7 so (PI - sqrt(3)) is a positive number, as it better well be!
Related Questions
Ms. Nina wants to buy candy mix for $1.00 per pound. If she already bought 50 pounds of candy for $1.20 per pound, how many pounds that costs 80 cents per pound must she buy?
Answers
Answer:
She must buy 50 pounds of the other candy in order to have a mix that costs $1 per pound.
Step-by-step explanation:
Her goal is to have a candy mix that has a cost of $ 1.00 per pound, therefore the relation [tex]\frac{\text{total cost}}{\text{total weigh}}[/tex] must be equal to 1. She already bought a total of 50 pounds of a $1.2 per pound candy, therefore she spent:
[tex]\text{spent first candy} = 50*1.2 = 60[/tex]
She wants to buy "x" of a 80 cents per pound candy, therefore if we sum it's weigh "x" with 50 pounds, then it must be equal to it's value summed with 60. We have:
[tex]50 + x = 60 + 0.8*x\\x - 0.8*x = 60 - 50\\0.2*x = 10\\x = \frac{10}{0.2} = 50\\[/tex]
She must buy 50 pounds of the other candy in order to have a mix that costs $1 per pound.
HELP!! The measure of two supplementary angles are in the ratio 4:2. Find the two angles.
Answers
Hey there!
Supplementary angles always equal 180° when combined. We have our ratio which is 4:2. When we combine them, we have six. This is on a different scale than 180, so we need to divide 180 by six to see how much bigger we need to make our ratio so we can find the angles.
180/6=30
As we can see, our parts of the ratio are 1/30 the size of our actual angle. To find our angles now, we multiply each number by 30.
4(30):2(30)=120:60
As you can see, if we add 120 and 60, it equals 80, and if you simplify the ratio it is still 4:2.
Your angles are 120° and 60°.
I hope this helps!
The measure of the two angles is 120 and 60 degrees if the angles are in the ratio of 4:2.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
The measure of two supplementary angles are in the ratio 4:2.
From the question:
4x + 2x = 180
6x = 180/6
x = 30
The first angle = 4x = 4(30) = 120 degrees
The second angle = 2(30) = 60 degrees
Thus, the measure of the two angles is 120 and 60 degrees if the angles are in the ratio of 4:2.
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Johnny claims that a horizontal line had no slope. is he correct? Why or why not.
Answers
Without drawing the graph of the function y=1.2x−7, see if the graph passes through points: (100; 113)
Answers
Answer:
(100,113) is on the graph of y = 1.2x -7
Step-by-step explanation:
y=1.2x−7
Substitute the point in and see if the equation is true
113 = 1.2 (100) -7
113 =120 - 7
113 = 113
This is true, so the point is on the graph
Find the volume of the composite solid. Please explain how you got your answer
Answers
Answer:
To find the volume of the composite solid you must learn how to find the surface and the volume of a composite solid, prism, pyramid, cones, cylinders and spheres. In order to find the surface area and the volume
Step-by-step explanation:
Tell me if you still need help.
Hope this helps.
plus help me asap thank you the first answer choices are 8 5 4 and 2 the second answer choices are 2 5 4 8 and then the third ones are greater than equal to less than and then the last one is equal to greater than or less than
Answers
Answer:
2
5
less than
<
Step-by-step explanation:
gotchu fam
A number divided by three, then increased by four is nine.
(As an equation)
Answers
Answer:
5
Step-by-step explanation:
Which is the correct calculation for the volume of the prism?
A prism has a length of 8 millimeters, height of 2 and one-half millimeters, and width of 8 and one-half millimeters.
2 and one-half + 8 + 8 and one-half = 19 mm3
2 and one-half times 8 + 8 and one-half = 28.5 mm3
8 times 8 and one-half = 68 mm3
2 and one-half times 8 times 8 and one-half = 170 mm3
Answers
Answer:
its D
Step-by-step explanation:
The correct calculation for the volume of the prism is 2 and one-half times 8 times 8 and one-half = 170 mm3
What is a volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of cube or cubes.
The volume will be calculated as:-
V = L x W x H
V = [tex]2\dfrac{1}2}[/tex] x 8 x [tex]8\dfrac{1}{2}[/tex]
V = ( 5/2) x 8 x ( 17/2 )
V = 170 mm³
Therefore correct calculation for the volume of the prism is 2 and one-half times 8 times 8 and one-half = 170 mm3
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please help :(((((((((((((((((((((((
Answers
Answer:
6.5 feet
Step-by-step explanation:
Answer:
6 in = 0.5 ft
If model is 1 /13 then original is
height = 0.5 ft / 1/13 = (0.5 *13)/1
height = 6.5 ft
Step-by-step explanation:
Write a variable expression for each. Tell what the variable represents I NEED HELP!!!
1. $16 less than last week's income
2. 5ft longer than the width of the wall
3. The amount of a car loan separated into 48 equal payments
Answers
2. x + 5
3. x divided by 48 (I don’t have the division symbol.)
PLEASEE I NEED HELPP Which statement is true about the solutions for the equation 5y + 8 = −2? (5 points)
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Answers
Answer:
it has one solution
Step-by-step explanation:
5y+8= -2
5y= -2-8
5y= -10
divide both sides by 5
-10/2= -2
y= -2
Answer:
It has one solution.
Step-by-step explanation:
I took the test and I got a 100 on the test.
Trust me, the answer is It has one solution.
You are welcome.
You just bought ten trees and want to plant them in 5 rows with 4 trees in each row. How will you plant the trees?
Answers
Answer:
You can't you have to use 20 trees since 20 divided by 5 is 4.
So using 10 would make it 10 divided by 5 which is 2.
And the trees can't be halve so it's 20. 10 is impossible.
Step-by-step explanation:
if the mean of the data set is 35 apples, find the number of apples on the Granny Smith tree,
apples
Answers
Answer:
can i please have more details please?
Step-by-step explanation:
PLSSSSSSSSSSS HELP ME RQ
Answers
Answer:
they spent more on signs than on flower boxes
Step-by-step explanation:
2/9 = 16/72
5/8= 45/72
11/72
All of the guests at a school dance choose one option for their dinner - rice and chicken, the pizza, or pasta. 45% of the guests chose the rice and chicken
option. 260 guests chose the pizza option. 25% of the guests chose the pasta option. How many guests chose rice and chicken as their dinner option?
Answers
Step by step:
45% chose rice and chicken and 25% chose pasta. So that means 30% chose pizza option.
If 30% is equal to 260 then 45% would be 260/30*45=390
Find the surface area of the regular pyramid. The surface area is square inches.
Answers
Answer:225 square inches
Step-by-step explanation:
Answer:
225
Step-by-step explanation:
15. You want to wrap a paperweight shaped like the
triangular prism shown. How many square inches
of wrapping paper do you need to completely
cover the prism?
Answers
Answer: 110
Step-by-step explanation: This is actually very simple. Al you have to do is to find the area of the 3 rectangles, which adds up to be 96, and find the area of the triangles, which adds up to be 14. You then have to add 96 and 14, which results in 110.
Estimate the solution to the following system of equations by graphing.
-41 + 5y = 8
61 - y = 11
Answers
Answer:
Sorry but what's the question
The solution of equation is (5/2, 7/2)
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
-4x + 5y = 8
6x - y = 11
Now, using the graphical method the lines of the equation intersect at
x = 2.5 and y = 3.5.
So, the solution of equation is (5/2, 7/2)
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For what value of x the relation S: {(x2+3,4), (5,2)} is not a function?
Answers
Answer:
x = ±sqrt(2)
Step-by-step explanation:
It is not a function if the same input goes to 2 different outputs
x^2 +3 =5 would cause the same input to go to 2 different outputs
Subtract 3 from each side
x^2 +3-3 =5-3
x^2 = 2
Take the square root of each side
sqrt(x^2) = ±sqrt(2)
x = ±sqrt(2)
Answer:
x = sqrt(2), -sqrt(2)
Step-by-step explanation:
For a function, there cannot be multiple outputs for the same input, therefore x²+3 should not be 5
x² + 3 = 5
x² = 2
x = +/- sqrt(2)
Two objects that are the same shape but not the same size are?
Answers
Answer:
Similar
Step-by-step explanation:
Objects that have the same shape but not size are defined to be similar.
Objects with the same shape and size are defined as congruent.
Anything that is congruent is ALSO similar.
Answer:
SimilarStep-by-step explanation:
Two angles are congruent if they have the same measure. Two figures are similar if they have the same shape but not necessarily the same size. All of the figures below are congruent since they all have the same shape and size.
The art teacher wrote down how many flower pots each child painted last week. The results are shown here.
How many students are there in all?
A) 21
B) 25
C) 35
D) 41
Answers
Answer:
41 students
Step-by-step explanation:
5+3+8+9+4+2+10 = 41
Who Would Like To Help Me??
Answers
Answer:
The answer is 128 bunches because 1027/8 = 128.375
Then I multiplied 128*8
which is equal to 1024
So the left over is 3 after subtracting the initial.
graph : f(x) = 2[x] + 1
PLEASEEEE + step by step
Answers
Answer:
x=1/2
x=-o.5, x=-2
Step-by-step explanation:
To find x intercept/zero, substitue f(x)= 0-0 which gives you 0=2x+1. Then you solve for x to get x=-1/2 which is the answer. x=-o.5, x=-2 is the alterative form. Pls mark as brainlist if right.
A triangle has these coordinates Point A:(1,5)Point B:(1,9)Point C:(8,5)Enter the length of side AC
Answers
Answer:I think the answer is 180 or 360
Step-by-step explanation:
The triangles will always be the same answer even if it looks different.
Martha has 27 quilt patches with animals and
27 patches with flowers. She wants her quilt
to have rows of 6 patches. How many rows
will the quilt have?
Answers
She will make 9 rows because 27 + 27 = 54 and divided by 6 =9
Analyze the diagram below and complete the instructions that follow.
Answers
Answer:
c) 5 and 9, 6 and 7
Step-by-step explanation:
The pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles
Answer:
5 and 9, 6 and 7
Took test
Step-by-step explanation:
For each of the following p-values, state whether you would "reject" or " fail to reject" H0 for the given a level.
1) P-value = 0.234 when a = 0.05
2) P-value = 0.024 when a = 0.05
3) P-value = 0.024 when a = 0.01
4) P-value = 0.024 when a = 0.10
Answers
Step-by-step explanation:
if we help you then make me brain list answer plsWhich of the following pairs of triangles can be proven congruent through SSS?
Answers
Answer:
B
Step-by-step explanation:
In figure C) segment AB is similar to segment DF, segment BC is similar to segment EF, and segment AC is similar to segment DE. So, both the triangles are congruent by SSS similarity.
Check all the options in order to determine the correct pairs of triangles can be proven congruent through SSS.
A) According to the given figure, segment AB is similar to segment XY and segment YZ. Also, segment AC is similar to segment XZ.
Therefore, this option is incorrect.
B) According to the given figure, angle A is congruent to angle X, angle B is congruent to angle Y, and angle C is congruent to angle Z. So, both the triangles are congruent by AAA similarity.
Therefore, this option is incorrect.
C) According to the given figure, segment AB is similar to segment DF, segment BC is similar to segment EF, and segment AC is similar to segment DE. So, both the triangles are congruent by SSS similarity.
Therefore, this option is correct.
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Which is true about the data shown in the scatter plot?
A)
The data have no clusters and outliers.
B)
The data cluster along a line and there is no outlier.
C)
The data cluster along a curve and there is no outlier.
D)
The data cluster along a line. The point (10, 6) is an outlier.
Answers
Answer:
D.
Step-by-step explanation:
The line is going in positive linear association and the outlier is (10,6) because that is the coordinate farthest from the line.
Answer:
I would answer but that ain't enough points...
Step-by-step explanation:
Please help me and then solve for angle 2 please I really need help
Answers
Answer:
Angle 1 is 45
Angle 2 is 90
Step-by-step explanation:
ABCD is a square, so by definition, all of its angles equal 90:
∠ABC = ∠BCD = ∠CDA = ∠DAB = 90
We also see that AC and BD are diagonals of the square, and by definition, these diagonals bisect those angles. In other words, these diagonals cut those angles in half.
∠DAB = ∠DAE + ∠BAE
That means ∠DAE = ∠BAE = 90/2 = 45 degrees, which also means angle 1 is 45 degrees.
Also by definition, when the diagonals intersect, they form a right angle. In other words, angle 2 will be 90 degrees.
Thus, the answer is angle 1 is 45 and angle 2 is 90.
Answer:
1: 45°
2: 90°
Step-by-step explanation:
Diagonals of a square are Perpendicular bisectors of each other, hence AEB is an isosceles right angle triangle
Angle at E = 90
Angle at A = (180-90)/2 = 45