A triangle is placed in a semi circle with a radius of 9 mm find the area of the shaded region of the semi circle (not including the triangle)
Answers
The area of the shaded region will be 46.17 ft.²The number of unit squares that cover the surface of a closed-form is the figure's area.
What is the area?
The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
Given data;
Semicircle radius , r = 9 ft.
The height of the triangle, h=r=9 ft
The triangle is located where it is inscribed in the semicircle. The diameter of the semicircle is given as b, the base length of the triangle.
The diameter of the semicircle = 2 × The radius of the semicircle
D=2r
D= 2 × 9 ft
D= 18 ft.
Triangle base length,b = D= 18 ft.
The area of the triangle is found as;
[tex]\rm A= \frac{1}{2}bh \\\\ A = \frac{1}{2} \times 18 ft. \times 9 ft. \\\\ A = 81 \ ft^2[/tex]
[tex]A_{semi}={\rm \frac{A_{circle}}{2}} \\\\ A_{semi}= \frac{\pi \ r^2}{2}\\\\\ A_{semi}= \frac{3.14 \times 9^2}{2} \\\\ A_{semi} = 127.17 ft^2[/tex]
The area of the shaded region is;
a= 127.17 ft.² - 81 ft.²
a = 46.17 ft.²
Hence,the area of the shaded region will be 46.17 ft.²
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Related Questions
50 POINTS!!!! PLSSS HELPPP URGENTTTT!!!! Although 300° is a special angle on the unit circle, Amanda wanted to determine its coordinates using the sum and difference formulas.
Part A: Determine cos 300° using the cosine sum identity. Be sure to include all necessary work. (5 points)
Part B: Determine sin 300° using the sine difference identity. Be sure to include all necessary work. (5 points)
Answers
Answer:
a) 1/2, b) = - sqrt(3) / 2
Step-by-step explanation:
a) Let A = 120 degree, B = 180 degree
Using cosine sum is cos(120+180) = cos(120)*cos(180) - sin(120)* sin(180)
which will give you 1/2
b) Let A = 360, B = 60 degree
Using sine difference: sin(360-60) = sin(360) cos(60) - cos(360) sin (60)
gives you -sqrt(3)/2
Cos (300°) using the cosine sum identity is 1/2.
sin (300°) using the sine difference identity is √3/2.
What are Trigonometric Ratios?Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.
The main three trigonometric ratios are sine, cosine and tangent functions.
Part A :
The cosine sum identity is,
cos (A + B) = cos (A) cos (B) - sin (A) sin (B)
We can write cos (300°) as,
cos (300°) = cos (180° + 120°)
= cos (180°) cos (120°) - sin (180°) sin (120°)
sin (180°) = 0 and cos (180°) = -1
So, cos (300°) = -cos (120°) = -(-1/2) = 1/2
Part B :
Sine difference identity is,
Sin (A - B) = sin (A) cos (B) - cos(A) sin (B)
We can write sin (300°) as,
sin (300°) = sin (360° - 60°)
= sin (360°) cos(60°) - cos(360°) sin (60°)
= - sin (60°)
= -√3 / 2
Hence the value of Cos (300°) using the cosine sum identity is 1/2 and the sin (300°) using the sine difference identity is √3/2.
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an angle measures 122 degrees more than the measure of a supplementary angle. What is the measure of each angle?
Answers
Answer:
the measure of each angle is 75degrees
Match the average rates of change of f(x) to the corresponding intervals.
-3
-8
-7
[-5, -1]
[-4,-1]
[-3, 1]
[-2, 1]
Answers
The average rates of change of f(x) and their corresponding intervals are given as:
Interval Rate of Change
[-5, -1] -8
[-4, -1] -7
[-3, 1] -4
[-2, 1] -3.
What is the explanation for the above?Step 1 - See Table Attached
Step 2 - State the formula for rate of change
The formula for rate of change is given as:
= [change in f(x)] / [change in x]
a) For interval [5, -1] ⇒
Rate of Change - [ f(1) - f(-5) ] / [-1 - (-5)]
= [-1 - 35] / [-1+5]
= -36 / 4
= - 8
b) For interval [-4, -1] ⇒
rate of change = [ f(-1) - f(-4) ] / [ -1 - (-4) ]
= [3 - 24] / [-1 + 4]
= -21/3
= - 7
c) interval [-3,1] ⇒
rate of change = [ f(1) - f(-3) ] / [ 1 - (-3) ]
= [-1 - 15] / [1 + 3]
= -16/4
= - 4
d) interval [-2,1] ⇒
rate of change = [f (1) - f(-2)] / [1 - (-2)]
= [ -1 - 8] / [1 + 2]
= -9/3
= -3
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what is a factor of 84 but not a multiple of 3
Answers
Answer:
2
Step-by-step explanation:
jackson bought 3 pounds of candy for $9.60.
What was the price of this candy in cents per pound ?
PLS HELP ITS DU IN 5 MIN !!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
320 cents per pound
Step-by-step explanation:
so we do 9.60 divided by 3, which is 3.20. So, 3.20 for each pound. Now we need in cents. 3 dollars is 300 cents, plus another 20, so 320 cents. I hope this helped.
(01.06 LC)
Which number is not in scientific notation?
Answers
Answer:
[tex]0.95*10^8[/tex]
Step-by-step explanation:
Hello!
Rules for scientific notation format:
Has to be multiplied to a power of 10One factor has to be greater than 1 but less than 10[tex]\bold{0.95*10^8}[/tex]
There is a multiplication to a power of 10, but the other factor is less than 1.
This is NOT in Scientific Notation.
All the other options have a multiplication operation to a power of 10, and all the other factors are above 1 and less than 10.
Every day sandra eats 1/8 pound of a blueberries. If she does this for 9 days, how many pounds of blueberries did she eat?
Answers
Answer: 1.125 pounds of blueberries or [tex]1 \frac{1}{8}[/tex] or [tex]\frac{9}{8}[/tex]
Step-by-step explanation:
Since she will eat it for 9 days, just multiply or add the pounds.
The large rectangle below represents one whole.
A large rectangle with 25 equal sections, 11 of which are shaded
What percent is represented by the shaded area? is it 2.27
Answers
Answer:
See below
Step-by-step explanation:
If the whole rectangle were shaded (all 25 parts) that would be 100%
So, we can set up a proportion.
25 = 100%
11 = x
Then, cross-multiply to get,
25x = 1100
Divide both sides by 25 to solve for x
x = 44.
The x value represents the percentage shaded.
44%
Which of the following is equal to this expression?
(256·64)^1/4
A) 4·[tex]\sqrt[4]{4}[/tex]
B) 8·[tex]\sqrt[4]{4}[/tex]
C) 8·[tex]\sqrt[4]{2}[/tex]
D) 2·[tex]\sqrt[4]{2}[/tex]
Answers
Answer:
B) [tex]8\sqrt[4]{4}[/tex]
Step-by-step explanation:
[tex](2^{8} *2^{6} )^\frac{1}{4} = (2^{8+6} )^\frac{1}{4} =(2^{14} )^\frac{1}{4} =2^{\frac{7}{2} }=\sqrt{2^{7} } =2^{3} \sqrt{2} =8\sqrt{2} = 8\sqrt[4]{2^{2} } = 8\sqrt[4]{4}[/tex]
Arrange the samples in order starting with the sample that gives the least variation from the expected value and ending with the sample that gives the
greatest variation.
Tiles
sample A: a sample of
10 people
sample B: a sample of
50 people
sample C: a sample of
100 people
sample D: a sample of
20 people
Sequence
C
Answers
On the basis of least variation from the expected value is:
Sample A ⇒ Sample D ⇒ Sample B ⇒ Sample C
What is Variance?
Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.
Here, on the basis of least variation,
we had arranged the given sample as per their expected value.
Thus, On the basis of least variation from the expected value is:
Sample A ⇒ Sample D ⇒ Sample B ⇒ Sample C
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Find the average value of f over the region D. f(x, y) = 3xy, D is the triangle with vertices (0, 0), (1, 0), and (1, 9)
Answers
The average value of f over the region D is 243/4
To answer the question, we need to know what the average value of a function is
What is the average value of a function?The average value of a function f(x) over an interval [a,b] is given by
[tex]\frac{1}{b - a} \int\limits^b_a {f(x)} \, dx[/tex]
Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).
x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9
So, [tex]\frac{1}{b - a} \int\limits^b_a {f(x,y)} \, dA = \frac{1}{1 - 0} \int\limits^1_0 \int\limits^9_0 {3xy} \, dxdy \\= \frac{3}{1} \int\limits^1_0 {x} \,dx\int\limits^9_0 {y} \,dy\\ = \frac{3}{1} [\frac{x^{2} }{2} ]^{1}_{0}[\frac{y^{2} }{2} ]^{9}_{0} \\= 3[\frac{1^{2} }{2} - \frac{0^{2}}{2} ] [\frac{9^{2} }{2} - \frac{0^{2}}{2} ] \\= 3[\frac{1}{2} - 0 ][\frac{81}{2} - 0 ]\\= \frac{81}{2} X3 X \frac{1}{2} \\= \frac{243}{4}[/tex]
So, the average value of f over the region D is 243/4
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Donovan is paying for gym classes. Each type of class has its own weekly fee. He signed up for x weeks of yoga classes and y
weeks of kickboxing classes. He paid a total of $136. The equation below describes the relationship between the number of weeks
of yoga classes and the number of weeks of kickboxing classes Donovan signed up for.
8x + 12y
-
136
The ordered pair (5,8) is a solution of the equation. What does the solution (5.8)
Answers
Considering the given function, the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.
What does the function represent?
The function that represents the relationship between the number x of yoga classes that Donovan signs up for and the number y of kickboxing classes is given by:
8x + 12y = 136.
Hence the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.
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Harry buys a ream of computer paper priced at $9.99 before a 6.0%
sales tax. He uses a coupon at checkout for a 10% discount. After the
purchase he mails in a form for a $5.00 rebate. What is Harry's final
cost?
Answers
Answer:
Step-by-step explanation:
Harry buys a ream of computer paper priced at $9.99 before a 6.0%
sales tax. He uses a coupon at checkout for a 10% discount. After the
purchase he mails in a form
A group of people were asked if they had run a red light in the last year. 218 responded "yes", and 270 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year.
Answers
# of desired outcomes / total # of outcomes
The total number of people that were surveyed is 270+218= 488 people.
218 have run a red light, our desired outcome.
So, the equation gives us 218/488, or approximately 44.67%.
1+ cos^4 x-sin^4 x = 2 cos² x
Answers
[tex]\text{L.H.S}\\\\=1+ \cos^4 x - \sin^4 x\\\\=1+ (\cos^2 x)^2 - (\sin^2 x)^2\\\\=1+(\cos^2 x + \sin^2 x)(\cos^2 x- \sin^2 x)\\\\=1+1\cdot(\cos 2x)\\\\=1+\cos 2x\\\\=2\cos^2 x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
can you help me with this question
Answers
Question 6(Multiple Choice Worth 1 points)
(02.02 MC)
Given the function f(x) = -5x² + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values.
O The value of f(1) cannot be compared to the value of f(2).
O The value of f(2) is larger than the value of f(1).
O The value of f(2) is smaller than the value of f(1).
O The value of f(1) is the same as the value of f(2). help
Answers
Answer:
O The value of f(2) is smaller than the value of f(1).
Step-by-step explanation:
First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)
A soccer league has $6,333 to buy new soccer balls. If each ball costs $3, how many balls can the league buy?
Answers
Answer: 2,111 soccer balls
Step-by-step explanation:
We will divide the total amount of money by the price per ball to find how many balls the league can buy.
$6,333 / $3 = 2,111
The league can buy 2,111 soccer balls.
3/4(2x-3) = 2/3 x+5 with detailed explanation
Answers
Answer:
x = 11
Step-by-step explanation:
3/(3(2x-3)) = 2/(3x+5)
3(2x-3) = 6x - 9
3/(6x-9) = 2/(3x+5)
3(3x+5) = 2(6x-9)
9x + 15 = 12x - 18
12x - 9x = 15 + 18
3x = 33
x = 11
Answer:
[tex]\mathrm x= \dfrac{87}{10} \quad or \quad 8.7[/tex]
Explanation:
[tex]\longrightarrow \sf \dfrac{3}{4} (2x-3)=\:\dfrac{2}{3}\:x+5[/tex]
Distribute inside parenthesis[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{9}{4} =\:\dfrac{2}{3}\:x+5[/tex]
Group the variables[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{2}{3}x=5+\dfrac{9}{4}[/tex]
Add or Subtract[tex]\longrightarrow \sf \dfrac{5}{6} x=\dfrac{29}{4}[/tex]
Cross Multiply[tex]\longrightarrow \sf x=\dfrac{29(6)}{4(5)}[/tex]
Simplify the following[tex]\longrightarrow \sf x=\dfrac{87}{10} \quad or \quad 8.7[/tex]
ZA and B are supplementary and vertical angles. What is m<B
A.180
B.135
C.45
D.90
Answers
Reason:
Vertical angles are equal to each other. Call them x. They must add to 180 degrees because they are supplementary (they are able to form a straight line).
x+x = 180
2x = 180
x = 180/2
x = 90
Find the missing side of this right triangle.
X
8
16
VI?]
X =
Enter the number that belongs in the green box.
Answers
Step-by-step explanation:
the missing side is given by sqrt(16² - 8²)
hence,
the number that belongs in the green box is 192
How many liters each of a 24% iodine solution in a 40% iodine solution must be used to produce a total make sure of 100 L of 28% iodine solution
Answers
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
How to determine the volume associated with a given concentrationPhysically speaking, concentration is equal to the amount of solute divided by the volume of solution. We have two solutions with same solute and different concentration and can find the right proportion between the 24 % solution and the 40 % solution by concept of weighted average:
x · 24 + (1 - x) · 40 = 28
40 - 16 · x = 28
16 · x = 40 - 28
16 · x = 12
x = 3/4
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
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Question 4 of 10
If ƒ(x) = 3(x+5) +−, what is f(a+2)?
Answers
[tex]f(x) = 3(x+5)\\\\f(a+2) = 3(a+2 +5) \\\\~~~~~~~~~~~~=3(a+7)\\\\~~~~~~~~~~~~=3a+21[/tex]
The solution to an absolute value inequality is shown on the graph below.
-5-4-3-2-1 0 1 2 3 4 5
What is another way to show the solution?
O x>-3 or x < 2
O {x|x <-3 orx <2}
O [-3, 2]
O (-3,2)
Answers
The solution to the absolute value inequality is (-3,-2)
How to determine the absolute inequality?On the absolute value inequality, we have:
Interval = -3 to 2
The intervals are represented with open circles.
This means that -3 and 2 are exclusive of the values of the inequality.
So, we have:
-3 < x < 2
As an interval notation, we have:
(-3,-2)
Hence, the solution to the absolute value inequality is (-3,-2)
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Determine the area, in square centimeters, of
this quarter circle with a radius of 8 cm. Use 3.14
for π and round your answer to the nearest
hundredth.
Answers
Step-by-step explanation:
quarter circle means that you just find the are and then divide it by 4.
hence,
(3.14 × 8²) ÷ 4 = answer
the answer is 50.24 cm²
hope this helps.
Answer: 6.28
Step-by-step explanation: In order to get your answer, the equation that you need to do is 8 X 3.14 / 4 to get your answer.
A bag has 9 blue cubes, 11 red cubes, and 5 green cubes. If you
draw a cube and replace it in the bag 250 times, which of the
following amounts would you expect to pull?
Answers
The numbers that can be pulled based on the probability of the calls will be 90, 110, and 50.
How to depict the probability?From the information given, the bag has 9 blue cubes, 11 red cubes, and 5 green cubes and when one draws a cube and replace it in the bag 250 times, the number of blue balls that can be gotten will be:
= 9/(9+ 11 + 5) × 250
= 9/25 × 250
= 90
The number of red balls that can be gotten will be:
= 11/25 × 250
= 110
The number of green balls that can be gotten will be:
= 5/25 × 250
= 50
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One number is 2 less than a second number. Twice the second number is 7 less than 3 times the first. Find the two numbers.
Answers
Answer : 11 and 13
Step-by-step explanation:
Let the numbers be X and Y then,
By question
X= Y - 2 .....................(i)
2Y = 3X - 7 ...............(ii)
putting the value of X from (i) on equation (ii) we get,
2Y = 3(Y - 2) - 7
2Y = 3Y - 6 - 7
2Y - 3y = - 13
-Y = - 13
Y = 13
now putting value of Y in equation (i)
X = 13 - 2= 11
hence those numbers are 11 and 13 respectively
How might an architect use geometry in their work?
Answers
Answer:
Architects use geometry to study and divide space as well as draft detailed building plans. Builders and engineers rely on geometric principles to create structures safely. Designers apply geometry (along with color and scale) to make the aesthetically pleasing spaces inside. Applying geometry in design is unavoidable.
ustrating the fine basic
1. Future Value or Present Value of a Single Sum
Compute the future value of $2,250 at a 17 percent annual rate for
30 years.
Answers
Answer:$249895.46
Step-by-step explanation:
Well, if 2250 dollars increase by 17% every year for 30 years, then it will be 2250*(1.17)^30
which would be $249895.46
so if you could increase money by 17% every year, 2250 dollars now will be worth a lot in 30 years!
The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below: Step 1: 2(y + 6) = 4y Step 2: 2y + 8 = 4y Step 3: 2y = 8 Step 4: y = 4 Which of the following explains how to correct Step 2 and shows the correct value of y? (5 points) a 2 should be distributed as 2y + 12; y = 6 b 2 should be distributed as 2y + 12; y = 3 c The equation should be y + 6 = 4y after division by 2; y = 2 d The equation should be y + 6 = 4y after division by 2; y = 1
Answers
Step-by-step explanation:
The wording is slightly confusing so I will just solve the equation.
2 (y + 6) = 4y
We expand the bracket
2y + 12 = 4y
We subtract 2y from both sides
12 = 2y
We divide both sides by 2
6 = y