Answer:
The coordinates of the triangle, (3, 6), (3, -3), and (3, 3), dilated by a magnitude of 3 is;
(9, 18), (9, -9), and (9, 9)
Step-by-step explanation:
The vertices of the given triangle are;
(3, 6), (3, -3), and (3, 3)
A dilation with a magnitude of 3 can be found as follows;
For each value of the x, and y-coordinates of the vertices, we multiply by the magnitude of dilation
As an example, the coordinate of the points on a line, (x₁, y₁) and (x₂, y₂), dilated by a scale factor of m, will become, (m·x₁, m·y₁) and (m·x₂, m·y₂)
Therefore, we have foe a magnitude of 3;
(3, 6), (3, -3), and (3, 3) becomes, (3×3, 3×6), (3×3, 3×(-3)), and (3×3, 3×3)
(9, 18), (9, -9), and (9, 9).
Answer:
(9, 18), (9, -9), and (9, 9)
Step-by-step explanation:
Mr. Conner is placing stone tiles to make a patio. Each tile is 1 square foot. The drawing shows the dimensions of his patio.
This question is incomplete
Complete Question
Mr. Conner is placing stone tiles to make a patio. Each tile is 1 square foot. The drawing shows the dimensions of his patio. A quadrilateral is broken into a triangle and rectangle. The triangle has a base of 20 feet and a height of 6 feet. The rectangle has a base of 20 feet and a height of 12 feet. How many total stone tiles will Mr. Connor need for the patio?
Answer:
300 tiles
Step-by-step explanation:
From the above question, we know that the patio is a combination of a triangle and a rectangle.
Step 1
Find the area of the shape
a) Area of the Triangle = 1/2 × Base × Height
Base = 20 feet
Height = 6 feet
Area = 1/2 × 20 × 6
Area = 60 square feet
b) Area of the rectangle
= Length × Breadth.
The rectangle has a
Base = Breadth = 20 feet
Height = Length = 12 feet
Area = 20 × 12 = 240 square feet.
Total Area of the patio
= Area of Triangle + Area of square
= 60 square feet + 240 square feet
= 300 square feet
Step 2
We are told that each stone tile = 1 square foot.
Hence, if the total area of the patio = 300 square feet, the number of stone tiles that would be used is
1 square foot = 1 stone tile
300 square feet = 300 stone tiles.
Therefore,the total stone tiles that Mr. Connor will need for the patio is 300 stone tiles.
Answer:
The answer is 300
Step-by-step explanation:
a^2 + b^2 + c^2 = 2(a − b − c) − 3. (1) Calculate the value of 2a − 3b + 4c.
Answer:
[tex]2a - 3b + 4c = 1[/tex]
Step-by-step explanation:
Given
[tex]a^2 + b^2 + c^2 = 2(a - b - c) - 3[/tex]
Required
Determine [tex]2a - 3b + 4c[/tex]
[tex]a^2 + b^2 + c^2 = 2(a - b - c) - 3[/tex]
Open bracket
[tex]a^2 + b^2 + c^2 = 2a - 2b - 2c - 3[/tex]
Equate the equation to 0
[tex]a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0[/tex]
Express 3 as 1 + 1 + 1
[tex]a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0[/tex]
Collect like terms
[tex]a^2 - 2a + 1 + b^2 + 2b + 1 + c^2 + 2c + 1 = 0[/tex]
Group each terms
[tex](a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
Factorize (starting with the first bracket)
[tex](a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex](a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + (b^2 + b+b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)(b + 1)) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + (c^2 + c+c + 1) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + (c(c + 1)+1(c + 1)) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + ((c + 1)(c + 1)) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + ((c + 1)^2) = 0[/tex]
Express 0 as 0 + 0 + 0
[tex](a - 1)^2 + (b + 1)^2 + (c + 1)^2 = 0 + 0+ 0[/tex]
By comparison
[tex](a - 1)^2 = 0[/tex]
[tex](b + 1)^2 = 0[/tex]
[tex](c + 1)^2 = 0[/tex]
Solving for [tex](a - 1)^2 = 0[/tex]
Take square root of both sides
[tex]a - 1 = 0[/tex]
Add 1 to both sides
[tex]a - 1 + 1 = 0 + 1[/tex]
[tex]a = 1[/tex]
Solving for [tex](b + 1)^2 = 0[/tex]
Take square root of both sides
[tex]b + 1 = 0[/tex]
Subtract 1 from both sides
[tex]b + 1 - 1 = 0 - 1[/tex]
[tex]b = -1[/tex]
Solving for [tex](c + 1)^2 = 0[/tex]
Take square root of both sides
[tex]c + 1 = 0[/tex]
Subtract 1 from both sides
[tex]c + 1 - 1 = 0 - 1[/tex]
[tex]c = -1[/tex]
Substitute the values of a, b and c in [tex]2a - 3b + 4c[/tex]
[tex]2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)[/tex]
[tex]2a - 3b + 4c = 2 +3 -4[/tex]
[tex]2a - 3b + 4c = 1[/tex]
HURRY I NEED IT NOW!!! What is the solution to this system of equations? x + 2 y = 4. 2 x minus 2 y = 5. (3, Negative 5 and one-half) (3, one-half) no solution infinitely many solutions
Answer:
(3, 1/2)
Step-by-step explanation:
set the equation up
x+2y=4
2x-2y=5
then solve
The correct option is B.[tex](3,\frac{1}{2})[/tex]
Given equations,
[tex]x+2y=4.....(1)\\2x-2y=5.....(2)[/tex]
The standard form for linear equations in two variables is [tex]Ax+By=C[/tex].
On comparing equation 1 and equation 2 with the standard form we get,
[tex]a_{1}=1, b_{1}=2, c_{1}=4\\a_{2}=2, b_{2}=-2,c_{2}=5[/tex]
Here,
[tex]\frac{a_{1} }{a_{2} } =\frac{1}{2} \\[/tex] and [tex]\frac{b_{1} }{b_{2} } =\frac{2}{-2} =-1[/tex]
Since [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex], So the given system of equation has a unique solution.
Now Adding equation 1 and 2 we get,
[tex]3x=9\\x=3[/tex]
putting the value of x in equation 1 we get,
[tex]3+2y=4\\2y=1\\y=\frac{1}{2}[/tex].
Hence the required solution of equation is [tex](3,\frac{1}{2})[/tex]. the correct option is B.[tex](3,\frac{1}{2})[/tex]
For more details follow the link:
https://brainly.com/question/11897796
Sales of a popular toy were about 20 million in 2000 and growing about 5% each year. At this growth rate, the function f(x) = 20(1.05)^x gives the annual number of toys sold in million in the xth year after 2000. Using this model, in about what year will the annual sales surpass 37 million?
===========================
Work Shown:
Plug in f(x) = 37. Solve for x. Use logarithms.
f(x) = 20(1.05)^x
37 = 20(1.05)^x
20(1.05)^x = 37
1.05^x = 37/20
1.05^x = 1.85
log( 1.05^x ) = log( 1.85 )
x*log( 1.05 ) = log( 1.85 )
x = log( 1.85 )/log( 1.05 )
x = 12.6088044498867
Round up to the nearest whole number to get x = 13.
In the year 2013, sales exceed 37 million.
HELP ME PLEASE!!!!!!!!!!!!!
A hospital found that a lower outside temperature indicates a higher number of patient visits. What can we determine from this information?
There is no correlation between outside temperature and number of patient visits.
There is a correlation between outside temperature and number of patient visits. However, there is no causation. This is because there is an increase in the number of patient visits with a decrease in the temperature outside.
There is a correlation between outside temperature and number of patient visits. There may or may not be causation. Further studies would have to be done to determine this.
Answer:
negative correlation
Step-by-step explanation:
Asked my teacher
Find the value of z.
Answer:
2
Step-by-step explanation:
opposite angles are the same
the shape opposite to 'z' is labelled with 2
which means that, that angle is 2 degrees
which also means that z would be 2 aswell.
The diagram shows two shapes A and B. Prove that both of them have equal perimeter.
Answer:
see explanation
Step-by-step explanation:
Calculate the perimeters by summing the measures of the sides.
Left figure ( starting with base and summing clockwise )
x + 5 + (x - 6) + (y - 5) + 6 + y ( brackets are the measure of the indents )
= x + 5 + x - 6 + y - 5 + 6 + y
= 2x + 2y
Right figure ( starting with base and summing clockwise )
x + 2 + (x - 3) + (y - 2) + 3 + y
= x + 2 + x - 3 + y - 2 + 3 + y
= 2x + 2y
Both figures have perimeters of 2x + 2y cm
At Camp Sunshine, 4 kids went home sick. Of the remaining campers, 18 kids went hiking and the other 41 kids spent the day swimming. How many kids started the day at Camp Sunshine?
Answer:
63 kids
Step-by-step explanation:
We can add up the number of students who went home sick, hiked, and swam to find the total amount of people.
[tex]4+18+41 = 63[/tex]
Therefore, 63 kids started their day at Camp Sunshine.
I get that feeling I oversimplified this one, let me know if I did. I'm not sure if this is right.
Answer:
63 kids
Step-by-step explanation:
We know that there are some kids who went home sick, some went hiking and some went swimming.
The total number of kids that started the day at Camp Sunshine can be found by adding the number who went home sick, went hiking and went swimming.
sick + hiking + swimming
4 went home sick, 18 went hiking and 41 went swimming.
4+ 18 + 41
Add the numbers together
22+ 41
63
63 kids started the day at Camp Sunshine.
What is the equation of a circle with center (0, 5) and radius 8
Answer:
See below.
Step-by-step explanation:
Recall that the equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
We know the center is (0,5) and the radius is 8. Plug in the numbers:
[tex](x-(0))^2+(y-(5))^2=(8)^2[/tex]
We can remove the parentheses on the left. Therefore, the equation will be:
[tex]x^2+(y-5)^2=64[/tex]
Answer:
( x) ^2 + ( y-5) ^2 = 64
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x-0) ^2 + ( y-5) ^2 = 8^2
( x) ^2 + ( y-5) ^2 = 64
Find the area of the triangle. Round the answer to the nearest tenth. Triangle is SSA. a= 3.7 b= 3.7 β= 70° ----- A.4.4 square units B.5.2 square units C.6.8 square units D.8.8 square units
Answer:
A. 4.40 square units
Step-by-step explanation:
The triangle is isosceles with base angles of 70°. The a.pex angle will be ...
180° -2(70°) = 40°
The area of a triangle can be computed from two sides and the angle between them as ...
A = (1/2)ab·sin(γ)
A = (1/2)(3.7)(3.7)sin(40°) ≈ 4.40 . . . square units
write 4.83×10⁵ as an ordinary number
Answer:
483,000
Step-by-step explanation:
hope this helps :)
Answer:
The answer is 483,000 as an ordinary number
Step-by-step explanation:
A pair of linear equations is shown:
y=-3x + 5
y = x + 2
Which of the following statements best explains the steps to solve the pair of equations graphically?
O on a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = -3, and the second line has y-intercept = 2 and slope =
1.
O on a graph, find the point of intection of two lines; the first line has y-intercept = -3 and slope = 5, and the second line has y-intercept = 1 and slope =
2.
O On a graph, find the point of intersection of two lines; the first line has y-intercept = -5 and slope = 3, and the second line has y-intercept = -2 and slope =
-1.
O On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = -5, and the second line has y-intercept = -1 and slope =
-2.
Answer:
Hey there!
On on a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = -3, and the second line has y-intercept = 2 and slope = 1.
Hope this helps :)
The amount that two groups of students spent on snacks in one day is shown in the dot plots below. Which statements about the measures of center are true? Select three choices. The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B. The mode for Group A is less than the mode for Group B. The median for Group A is 2. The median for Group B is 3.
Answer:
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Step-by-step explanation:
First, we can find the measures of center for each group.
Group A
Mode: 1
Median: (1 + 2) / 2 = 3 / 2 = 1.5
Mean: (1 * 5 + 2 * 4 + 3) / 10 = (5 + 8 + 3) / 10 = 16 / 10 = 1.6
Group B
Mode: 3
Median: 92 + 3) / 2 = 5 / 2 = 2.5
Mean: (1 * 3 + 2 * 2 + 3 * 4 + 5) / 10 = (3 + 4 + 12 + 5) / 10 = 24 / 10 = 2.4
From here, we can see that...
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Hope this helps!
Answer:
ABC
Step-by-step explanation:
Solve for x. (x+2)/3+(2x-4)/4=3
Answer:
x=4
Step-by-step explanation:
First you need to factor the equation. You can do this by multiplying the numbers by eachother so they have a denominatior of 12.
You would come out to have this...
((x+2)*4)/12 + ((2x-4)*3)/4=3
At this point you can combine the numerators over the common denominator.
((x+2)*4+(2x-4)*3)/12=3
You can now rewrite the equation into factored form.
5x-2/6=3
Multiply both sides of the equation by 6.
5x-2=18
move the terms not containing x to the right
5x=20
and divide by 5
x=4
The average age of 15 students is 16 years. If teacher’s age is included the average increases
by 1. Find teacher’s age
31
because 15 +16 :31
[tex]. = y1 = \times [/tex]
Two planes make a 1750 mile flight, one flying 75 miles per hour faster than the other. The quicker plane makes the trip 3 hours faster. How long did it take the slower plane to complete the flight?
Answer:
The slower plane is flying at 175 miles per hour and complete the trip in 10 hours
The faster plane is flying at 250 Miles per hour and complete the trip in 7 hours
Step-by-step explanation:
Let s= speed of the slower plane s+75= speed of the faster plane
The time it takes the slower plane to make the flight = 1750/s
The time it takes the faster plane to make the flight is=1750/(s+75)
The difference in these two times is 3 hours
1750/s - 1750/(s+7)=3
{(s+75) / (s+75) * (1750/s)} - {(s/s) * (1750/s+75)} =3
(1750s+131250 / s^2+75s) - (1750s/s^2+75s) =3
1750s+131,250-1750s / s^2+75d =3
131,250 / s^2+75s = 3
Cross product
131,250=3(s^2+75s)
131,250=3s^2+225s
43,750=s^2+75s
s^2+75s-43,750=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a=1
b=75
c= -43750
x= -b +or- √b^2-4ac / 2a
= -75 +or- √(75)^2 - (4)(1)(-43750) / (2)(1)
= -75 +or- √(5625) - (-175,000) / 2
= -75 +or- √180625) / 2
= -75 +or- 425 / 2
x= -75 + 425/2 OR -75- 425/2
=350/2 OR -500/2
x=175 OR -250
We will ignore the negative sign because the planes are not flying Backward
The slower plane is flying at 175 miles per hour and complete the trip in 1750/175= 10 hours
The faster plane is flying at 250 Miles per hour and complete the trip in 1750/250= 7 hours
If b = 1/2x −1/y, then what is an expression for 2/b in terms of x and y?
Answer:
2/xy
Step-by-step explanation:
you have to do the math but im not very sure on this
2 concentric circles have radii 2cm and 3cm respectively, calculate the ratio of their areas
Answer:For the first circle the radius is 2cm and for the second circle the radius is 3cm,by taking the ratio of their areas:
πr^2:πR^2
π cancels out and we are left with only r^2:R^2
r=2cm and R=3cm
Therefore r^2:R^2=2^2:3^2
=4:9
The answer is 4:9
Step-by-step explanation:
A small manufacturing company makes $125 on each stereo sound bar produces, and $100 profit on each flat screen TV makes. Each sound bar and TV must be processed by cutting machine (A), A fitting machine (B), and a polishing machine (C). each sound bar must be processed on machine A for one hour, Machine B for one hour machine C for four hours. each TV must be processed on machine A for two hours, machine B for one hour, machine C for one hour. Machine A is available for 16 hours, machine B for nine, machine C for 24. Using the information in the problem, right the constraints. Let X represent the number of sound bars made, and Y represent the number of TVs
Constraint Equations : [tex]X + 2Y \leq 16 , X + Y \leq 9 , 4X + Y \leq 24[/tex]
Time required for producing sound bar 'X' = 1 hour of machine A , 1 hour of machine B , 4 hour of machine C
Time required for producing flat screen TV 'Y' = 2 hours of machine A, 1 hour of machine B, 1 hour of machine C
So, constraint for machine A (needed for sound bar & flat screen TV) : [tex]1X + 2Y \leq 16[/tex]
Similarly, constraint for machine B (needed for X & Y) : [tex]1X + 1Y \leq 9[/tex]
Also, constraint for machine C = [tex]4X + 1Y \leq 24[/tex]
More for reference : https://brainly.com/question/9405925?referrer=searchResults
The linear function f (x) and g(x) are represented on the graph where g(x) is a tranfomation of f(x) I need help with part A part B and Part C
Answer:
see below
Step-by-step explanation:
Part A
We can shift f(x) to the left or we can shift f(x) up to make it become g(x)
Part B
y = f(x + k) k > 0 moves it left
Using the point ( 2,8) for f(x) and ( 0,8) for g(x)
k is 2 units
g(x) = f(x+2)
y = f(x) + k k > 0 moves it up
Using the point ( 0,-2) for f(x) and ( 0,8) for g(x)
The difference between -2 and 8 is 10
k = 10
g(x) = f(x) + 10
Part C
for the shift to the left g(x) = f(x+2)
for the shift up g(x) = f(x) + 10
What is the equation of the graphed line in standard form? y = 2x + 6 12x+y=6 12x−y=−6 −2x+y=6
Answer:
THe standard form of equation for a line is -2x+y=6
Step-by-step explanation:
THe standard equation has a form of Ax+ By=C, where A, B and C are constants.
12x-y=-6 is not a standard form of a line equation, because the value near you is negative, but should be positive. It would be this form if we would change it a little bit to the form:
-12x=y=6
Daniel is a very good television salesperson. His annual sales average at $187,400. His commission on sales is 30% and his annual base salary is $40,000. On average what is his annual gross income?
Answer: $96,220
Step-by-step explanation:
From the questionwe are we informed that Daniel is a very good television salesperson and that his annual sales average at $187,400 and his commission on sales is 30% while his annual base salary is $40,000.
His annual gross income will be his annual base salary plus commission annually. This will be:
= $40,000 + (30% × $187,400)
= $40,000 + (0.3 × $187,400)
= $40,000 + $56,220
= $96,220
Please help I really need to get it right
Answer:
Alternate interior angles.
17x + 6 = 18x - 1.
x = 7.
Step-by-step explanation:
According to the diagram below, the angles are alternate interior angles.
Since they are alternate interior angles, they are congruent. So, 17x + 6 = 18x - 1.
17x + 6 = 18x - 1
18x - 1 = 17x + 6
x = 7
Hope this helps!
Jennifer wants to see if the color of the testing room causes test anxiety. She asks 100 participants to come to a modified classroom, and as they walk in, she asks each person to choose either a testing cubicle painted bright red or a testing cubicle painted off white. On the basis of their choices, participants spend 20 minutes in one or the other cubicle solving challenging math problems. Then, they complete a survey asking them questions about how anxious they were during the math test. What's wrong with Jennifer's experiment?
Answer: Jennifer didn't randomly assign participants to the control and experimental group.
Step-by-step explanation: In the scenario discussed above, Jennifer failed to perform a random assignment of the participants who took part in the survey, that is the experimental group, those who receive the treatment and the control group, those who don't. Random assignment is required in other to address the issue of bias in our experiment. She was supposed to perform a random assignment of the participants to the two groups instead of asking them to make a choice.
Agrid shows the positions of a subway stop and your house. The
subway stop is located at (-7,8) and your house is located at (6,4).
What is the distance, to the nearest unit, between your house and
the subway stop?
Answer: about 13u
Step-by-step explanation:
Distance can be calculated as [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\sqrt{(6-(-7))^2+(4-8)^2}\\\\\\\sqrt{(13)^2+(-4)^2}\\\\\\\sqrt{185}\\\\13[/tex]
Hope it helps <3
What is 37 ÷ 100 × 9 =
Answer: 3.33
Step-by-step explanation:
Multiplication and division should be solved left to right.
[tex]37/100*9\\\\Divide(100)\\\\0.37*9\\\\Multiply(9)\\\\3.33[/tex]
Hope it helps <3
Answer:
=37/100×9=.
=divide 37 by 100
=0.37 ×9
=3.33
Which of the following graphs is the graph of
Answer:
Graph A is the one that represents the given piecewise function.
Step-by-step explanation:
Notice that the Domain of the given function has been partitioned in three sections:
[tex]-2\leq x<0\,\,; \,\,\,x = 0\,\,;\,\,\,0<x\leq 2[/tex]
in the first section we have that the function responds to [tex]f(x)=x-1[/tex], which is a line of positive slope (ascending line) equal to "1", and y-intercept at y= -1.
This line should therefore start at the point (-2, -3) (when x = -2) and end at y almost equal to -1, when x approaches the value zero; and an empty dot should be seen in the position (0, -1)
For x = 0 we should see a solid dot located at the position (0, 1) on the plane.
And finally for the third section we should see a horizontal segment (that represents a constant value of 3, starting with an empty dot at the point (0, 3), and ending on a solid dot located at (2, 3).
This is what we see represented by the graph labeled A in the list of answer options.
Answer:
B
Step-by-step explanation:
please help!!! Its not a super hard question i just want to make sure im right
Answer:
D
Step-by-step explanation:
If you put the equation into a graphing calculator it will give ou a function than is a straight line that is stretched vertically by 3 units
What is the shape name
please do fast.
Answer:
[tex]\boxed{\sf Parallelogram}[/tex]
Step-by-step explanation:
A parallelogram has opposite parallel sides and it is a quadrilateral.
Answer:
This is a parallelogram
Step-by-step explanation:
This is also a quadrilateral.
Hope this helps.
A metal cube
of
side 4.4cm was melted
and the molten material used to make a Sphere
Find to 3 significant figures the radius of
the
sphere [take It - 22/7].
Answer: 2.73 cm
Step-by-step explanation:
Given that :
Side (a) of cube = 4.4cm
Volume of a cube (V) = a^3
V = 4.4^3
V = 85.184cm^3
Therefore, volume of the sphere made = 85.184cm^3
Volume of sphere = 4/3 πr^3
Where r = radius
85.184 = (4/3)*(22/7)*r^3
85.184 = (88/21)*r^3
85.184 = 4.1905 * r^3
r^3 = 85.184 / 4.1905
r^3 = 20.327884
Take the cube root of both sides
r = 2.73 cm