Answers
The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Related Questions
3. If a = 2, b = -5 and c = 3, determine the value of b(a)+c
Answers
-5*2=-10
-10+3=-7
The answer is -7
Origami paper is always in the shape of a square. If you take the top corner of either side of a 9 x 11-inch piece of paper and fold it to the lower opposite side and trim off the excess paper, this creates the square that we need. Then fold the top corner to the opposite corner to create a diagonal, which is a typical first step to most origami designs. What are the dimensions of your square? What is the length of the diagonal? Write your answer in exact and decimal form.
Answers
Answer:
Dimensions are nine by nine, the diagonal is the square root of 162.
Step-by-step explanation:
The resulting square will have the same width as before, with a height to match, (9,9) The diagonal can be found using the pathagyreon theorom.
9^2 + 9^2 = x^2.
The dimensions of the square would be nine by nine, the diagonal is the square root of 162.
The square will have the same width as before, with a height to match, (9,9)
The diagonal can be found using the Pythagorean theory.
9^2 + 9^2 = x^2.
What is the Pythagorean theorem?This theorem states that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
What is the Pythagorean theorem and what is it used for?The Pythagorean Theorem is a useful tool that shows how the sum of the areas of three intersecting squares can determine the side lengths of a right triangle.
Learn more about Pythagorean Theorem here:https://brainly.com/question/231802
#SPJ2
Let's Apply Solve for the surface area of the following figures.
Answers
Answer:
1. 864in^2
2. 331.2581cm^2
3. 201.0619m^2
4. 516.548m^2
5. 2827.4334mm^2
22. The population, P, of the city of Hazelton has grown according to the mathematical model
P = 65,000(1.075)', where t is the number of years since 2005.
a) At what percentage is the population growing? [1 mark]
Answers
Answer:
7.5%
Step-by-step explanation:
The exponent 't' is applied to 1.0751.075 is the rate at which it increasesDecimal → % = x 1001.075 × 100 = 107.5%107.5% - 100% = 7.5%find the missing length of a rectangle with a width of 7b^3 and an area of 77a^8b^8
Answers
Answer:
Step-by-step explanation:
What is the equation to this graph using Y=MX+B. Show Work.
Answers
Answer:
y = 2x + 9
Step-by-step explanation:
Y = mx + b indicates slope-intercept equation.
"b" represents y -intercept/beginning.
"mx" represent slope/constant of variation/rate of change
x-intercept represents the end of the graph. (in stories using money its the ending amount).
The y-intercept is always when the x-value is 0. The point of the y-intercept is on the y-axis. The line on the graph starts at the point (0,9). It can be located on the point right above the number labeled under the 9 which is 8. Since the x-value is 0,
The y-intercept is 9.
To find the slope, we have to find two points on the graph to use.
Two points on the graph are:
(1.5, 13) , (2, 14)
Using the slope formula:
y2-y1/x2-x1
Plug in:
14-13/2-1.5
Complete:
1/0.5
divide:
The numbers in 1 divided by 1/2 are labeled below:
1 = whole number
1 = numerator
2 = denominator
To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:
1 x 2/1 = 2/1
Thus, the answer to 1 divided by 1/2 in fraction form is:
2/1
To make the answer to 1 divided by 1/2 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
2 / 1 = 2
The answer is rounded to the nearest two decimal points if necessary.
2/1 is an improper fraction and should be written as 2.
So now that we have the y-intercept and slope:
Y-intercept: 9
Slope: 2
Equation: y = 2x + 9
Terms: Linear Equations 8th Grade
Which expression correctly shows the difference between the product of 8 and 5 and the sum of 8 and 7?
O 8 x (5-8) +7
O (8 x 5) + (8 + 7)
O 8x (5+8)+7
O (8 x 5) - (8 + 7)
feel
Wacom
aer
Answers
Answer:
D. (8 x 5) - (8 + 7)
Step-by-step explanation:
Evaluate the word problem.
The difference (we will be subtracting.) between the product of 8 and 5 (8 * 5) and the sum of 8 and 7 (8 + 7)?
So set it up.
(8 * 5) - (8 + 7)
This is the correct answer because we are taking the difference of the product of 8 and 5 and the sum of 8 and 7.
Use the volume formula to find the volume of the prism.
help!!
20 points!!
Answers
Answer:
B. 9 cubic units
Length×width×height
1. you make a deposits of a 467,00 into an ordinary annuity earning 5.75.7. compounded moyenthly, how many deposits must you make so that you will have atleast & 196.000?
Answers
answer? i give vrainlist
Answers
Answer:
3 I think
Step-by-step explanation:
1/3 opposite is 3/1 or 3
At a dance school, 18 students attend class on Tuesday. Six of those students are boys. What is the ratio of girls
to total students attending class on Tuesday?
Answers
Answer:
= 12 : 18
Step-by-step explanation:
• 18 - 6 = 12
• girls = 12
• total students = 18
• girls to total students
= 12 : 18
Answer:
12:18
Step-by-step explanation:
The data set below shows the weights of some puppies, in pounds, at a kennel:
10, 11, 12, 12, 13, 13, 14, 15, 15
Which histogram represents the data set?
Answers
Answer:
The second histogram. and this is because of the arrangement of data which is the puppies
Answer:
I think its A)
Step-by-step explanation:
The line plot shows the heights of the players on a basketball team, in inches.
Part B
he next year, a player who is
71
inches tall is replaced by a player who is
73
inches tall. Otherwise the team remains the same. Is
74
an outlier the next year? Explain.
Answers
A: based on the given dot plot are: statements B, D, and E.
B: A. No. 74 is not an outlier because it is not different from the other heights in the dot plot.
What is a Dot Plot?In a dot plot, frequencies of each data point is represented as dots.
Part A:
Thus, in the dot plot given:
Players of 70 1/2 in. tall and above are 7 in number. This is half of the number of the total players. (option B is true).
Players with height of 69 1/2 in. (3 players) are more than those that are 70 in. tall (1). (option A is not true).
One of the player is 68 1/2. (option C is not true).
Four of the players are 74 in. tall (option D is true).
The team has 6 different heights as shown in the dot plot given (option E is correct).
Therefore, the statements that are correct based on the given dot plot are: statements B, D, and E.
Part B:
If a player of 73 in. tall replaces a player of 71 in, tall, 73 is close to 74.
Therefore, we can conclude that: A. No. 74 is not an outlier because it is not different from the otehr heights in the dot plot.
Learn more about dot plots on:
https://brainly.com/question/25957672
What does 5 in = how many feet/foot?
Answers
Answer:
5/12
Step-by-step explanation:
Since 12 inches is one foot, the number has to be a fraction number. The answer is 5/12 feet.
1in = 1/12
5 x 1/12
=5/12
Which expression is equivalent to StartFraction 5 y cubed Over (5 y) Superscript negative 2 Baseline EndFraction?
y5
y6
125y3
125y5
Answers
Answer:
125y3
Step-by-step explanation:
12x5=y
y3/2 = y26 - 5 =y
Answer:
D should be right
Step-by-step explanation:
What number can be divided into 2 equal groups whit out a reminder
Answers
all even numbers
hope it really helps...!!!
Answer:
all even numbers. because when divisible by two there is no reminder
f(x) =2x^3 + 3x^2 - 7x + 2 g(x) = 2x-5 find (f+g)(x)
Answers
Answer:
Step-by-step explanation:
Remark
The way this is written, the notation is directing you to add the right hand sides of the two given polynomials.
Givens
f(x) = 2x^3 + 3x^2 + 7x + 2
g(x) = 2x - 5 Add
Solution and Answer
Answer: (f + g)(x) = 2x^3 + 3x^2 + 9x -3
Be careful with that - 5. The result is -5 + 2 = - 3
Answer: It's (f+g)(x)=2x^3+3x^2-5x+3
Step-by-step explanation: I just did it.
Which of the following statements is not true?
- the median is not affected by outliers as much as the mean.
- the mode is the most frequently occurring value(s) in a data set.
- the best measure of central tendency depends on the data set.
- the mean is the middle value of a data set.
Answers
Answer:
the mean is the middle value of the data set.
Step-by-step explanation:
the mean is the average of all the data, so i would say the last statement is incorrect.
Answer:
the mean is the middle value of a data set
Mike is working on solving the exponential equation 74^x = 37; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.
Answers
Answer:
Method 1
[tex]74^x = 37[/tex]
Take natural logs of both sides:
[tex]\implies \ln74^x = \ln37[/tex]
Apply the log power rule: [tex]\ln(a)^b=b \ln (a)[/tex]
[tex]\implies x\ln74 = \ln37[/tex]
Divide both sides by ln 74:
[tex]\implies \dfrac{x\ln74}{\ln74} = \dfrac{\ln37}{\ln74}[/tex]
[tex]\implies x= \dfrac{\ln37}{\ln74}[/tex]
[tex]\implies x=0.8389552282...[/tex]
Method 1
[tex]74^x = 37[/tex]
Take logs of base 74 of both sides:
[tex]\implies \log_{74}74^x = \log_{74}37[/tex]
Apply the log power rule: [tex]\log_am^n=n\log_am[/tex]
[tex]\implies x\log_{74}74= \log_{74}37[/tex]
Apply log of the same number as base rule: [tex]\log_aa=1[/tex]
[tex]\implies x= \log_{74}37[/tex]
[tex]\implies x=0.8389552282...[/tex]
Answer:
[tex]x = \log_{74}(37) [/tex]
Step-by-step explanation:
we want to solve the following exponential equation:
[tex] \iff {74}^{x} = 37[/tex]
Taking common logarithm of both sides yields:
[tex]\iff \log{74}^{x} = \log37[/tex]
recall that,
[tex] log( {a}^{x} ) = x log(a) [/tex]utilizing it yields:
[tex] \iff x \cdot\log{74} = \log37[/tex]
divide both sides by log74:
[tex]\iff \dfrac{ x \cdot\log{74}}{ \log(74)} = \dfrac{ \log37}{ \log(74) }[/tex]
remember that,
[tex] log_b( {a} ) = \frac{log(a)}{log(b)} [/tex]
hence,
[tex]x = \boxed{ \log_{74}(37)} [/tex]
What’s the following sum?
Answers
[tex] \huge{ \orange{ \boxed{ \bold{6 \sqrt{5} }}}}[/tex]
EXPLAINATION :
By following the rule in finding the sum or difference of similar radicals
[tex] \green{a \sqrt{c} \: + \: b \sqrt{c} \: = (a + b) \sqrt{c} }[/tex]
Answer:
3.73
Step-by-step explanation:
HELP QUICKLY PLEASE
31. Tony is borrowing $10 from his mom every week for buying more toy cars for his Hot Wheels collection. How much money does he owe at the end of 7 weeks?
33. Linda borrowed $7 a day until she had borrowed a total of $56. For how many days did she borrow money?
34. The temperature increased 2o per hour for six hours. How many degrees did the temperature raise after six hours?
35. Max lost 24 pounds in 8 weeks on his new weight-loss plan. What was his average change in weight per week?
Answers
Answer:
the answer to 33 is 8 7×8=56 or 56÷7
What is the solution to 3x/4 =7/3
Answers
Answer:
[tex]x=\frac{28}{9}[/tex]
Step-by-step explanation:
[tex]\frac{3x}{4} =\frac{7}{4}[/tex]
[tex]\Longleftrightarrow \left( 3x\right) \times 3=7\times 4[/tex]
[tex]\Longleftrightarrow 9x=28[/tex]
[tex]\Longleftrightarrow x=\frac{28}{9}[/tex]
Help help ASAP math math
Answers
Answer:
-25
Step-by-step explanation:
f(-12) means x = -12
so you just plug it in the equation and solve for x
[tex]f(x) = 3(-12)+11\\f(x) = -36+11\\f(x) = -25[/tex]
Where do 2x - y = 4 and 4x + y = 9 intersect?
Answers
Answer: They intersect at [tex](2\frac{1}{6}, \frac{1}{3} )[/tex]
Step-by-step explanation:
We can solve this system of equations through elimination
Add (4x+y=9) with (2x-y=4)
[tex]4x+y=9\\+2x-y=4\\=\\6x+0=13[/tex]
Now that y is canceled out we can solve for x
[tex]6x=13\\\frac{6x}{6}=\frac{13}{6} \\x=2\frac{1}{6}[/tex]
Now sub back x into one of the original equations to find the value of y
[tex]4(2\frac{1}{6} )+y=9\\8\frac{2}{3} +y=9\\8\frac{2}{3}-8\frac{2}{3}+y=9-8\frac{2}{3}\\y=\frac{1}{3}[/tex]
Maya is building a model of her city's downtown area. She is constructing part of an office building, as shown below. Each cube has an edge length of 1/6 foot.
The volume of the model building is cubic foot?
A.2/3
B.1/36
C.1/4
D.1/9
E.1/2
Answers
Answer:
B I think my bad if its wrong
Answer: the answer is e
Step-by-step explanation: 1 over 6 multiplied by 9 cubes will give 1.5 which is 1 over 2 . 4 cubes are the length and 2 the width and 3 height s o equal 9 . 9 times 1 over 6 equals 1.5 which is the last one. hope it helps buddy .
Please please give brainliest !!! Thanks .
What is the perimeter of a rectangle 5cm by 8cm?
Answers
Answer:26
Step-by-step explanation:
how is 0.136 written as a fraction in simpilist form. is my answer correct?
Answers
Answer:
Yes you are
Step-by-step explanation:
case as) the repeating decimal is 36
Multiply x by a power of , one that keeps the decimal part of the number the same:
Subtract from
The repeating decimals should cancel out
solve for x
Divide by both sides
Simplify
Divide by both numerator and denominator
therefore
the answer case a) is
The fraction in easyiest form is
case b) the repeating decimal is 136
Let
Multiply x by a power of, one that keeps the decimal part of the number the same:
Subtract from
The repeating decimals should cancel out
solve for x
Divide by both sides
-----> irreducible
therefore
the answer case b) is
The fraction in simplest form is
136/999
Please help asap!
Which of the graphs has the greatest rate of change?
A) Graph A
B) Graph B
C) Graph C
D) Graph D
Answers
Answer:
B) Graph B
Step-by-step explanation:
Your food costs are $2,000.
Your total food sales are $8,500. What percent of your food sales do the food costs represent?
Answers
Answer:
23.53%
Step-by-step explanation:
Given :
food costs = $2,000total food sales = $8,500Solving :
Food costs / Total Food Sales2000/85004/170.235323.53%How to calculate percentage profit?
Answers
Answer:
Profit/Cost Price*100
Step-by-step explanation
Calculated by working out the difference between the cost price and the selling price, which is then divided by the original price and multiplied by 100, giving you a percentage. Cost price is the original price for good which the retailer has bought for.