Answer: Step 1
Find the scale factor
we know that
If the two cylinders are similar
then
The ratio between the circumference of the larger cylinder to the circumference of the smaller cylinder is equal to the scale factor
Step 2
Find the lateral area of the smaller cylinder
we know that
If the two cylinders are similar
then
The ratio between the lateral area of the larger cylinder to the lateral area of the smaller cylinder is equal to the scale factor squared
Let
x--------> the lateral area of the larger cylinder
y-------> the lateral area of the smaller cylinder
z--------> the scale factor
In this problem we have
substitute in the formula and solve for y
therefore
the answer is
33.6π mm2
The correct option is Option D: the lateral area of the smaller cylinder is 84π mm².
What is the lateral area of the cylinder?The lateral area of the cylinder is the area of the curved surface which can be calculated by the formula given below
lateral area of the cylinder= 2πrl
where r is the radius of the cylinder and l is the length of the cylinder.
Here given that the two cylinders are similar.
The larger cylinder has base of circumference = 60π mm
As we know the circumference of base of cylinder= 2πR
⇒60π= 2πr
⇒2πR= 60π
Given the lateral area of the larger cylinder is 210π mm²
From above formula, it is clear that the lateral area of the cylinder= 2πrl
⇒ 210π = 2πrl
⇒2πRl= 210π
⇒60πl= 210π (as from above it is derived that 2πr= 60π)
⇒l= 210π/ 60π= 7/2
⇒l= 3.5 mm
the smaller cylinder has base of circumference = 24π mm
⇒ 2πr= 24π mm
then the lateral area of the smaller cylinder is= 2πrl= 24π*3.5= 84π mm²
Therefore the correct option is Option D: the lateral area of the smaller cylinder is 84π mm².
Learn more about the lateral area of the cylinder
here: https://brainly.com/question/2292413
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The net of a solid is shown below:
Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square.
What is the surface area of the solid?
18 square inches
27 square inches
36 square inches
45 square inches
Answer:
The answer is 45 inches².
Step-by-step explanation:
First, you have to find the area of each triangle:
[tex]area = \frac{1}{2} \times base \times height[/tex]
[tex]let \: base = 3 \\ let \: height = 6[/tex]
[tex]area = \frac{1}{2} \times 3 \times 6[/tex]
[tex]area = \frac{1}{2} \times 18[/tex]
[tex]area = 9 \: \: {inches}^{2} [/tex]
Assuming that the formula for surface area of pyramid is Surface area = base area(area of square) × 4(area of triangle):
[tex]base \: area = 3 \times 3 = 9[/tex]
[tex]area \: of \: triangle = 9[/tex]
[tex]s.a = 9 + 4(9)[/tex]
[tex]s.a = 9 + 36[/tex]
[tex]s.a = 45 \: \: {inches}^{2} [/tex]
It takes 4 people 2 days to paint a wall. How long would it take if we got 8 people to do it?
Answer:
if it takes 4 people for 2 days
4+4= 8
so it would only take 8 people for 1 day
Answer:
1 day
Step-by-step explanation:
4 people = 2 days
→ Work out how long 1 person takes
4 people = 2 days
( ÷ 4 ) ( × 4 )
1 person = 8 days
→ Work out how long 8 people can do it
1 person = 8 days
( × 8 ) ( ÷ 8 )
8 people = 1 day
how to convert 0.16 to fraction
4/25
Step-by-step explanation:
16/100, 8/50, 4/25
Which expression can be used to find the surface area of the following square pyramid? I DONT KNOW HOW TO PUT A PHOTO ON PC!!! but it has 4 as the base and 3 as the height PLEASE HELP
Answer:
40 or 16+6+6+6+6
Step-by-step explanation:
To find the surface area of a 3d figure, we can imagine all of its faces laid down on a flat plane. In this case, we would have a square, and four congruent triangles. Now all we have to do is find the areas of each shape and add them up.
4 is the base of the pyramid, so it's also the square's side length. Since a square has four equal sides, our square's length and width are both 4.
4*4 = 16
For every triangle we have, the base is 4 and the height is 3. The area of a triangle can be found using the formula A=(bh)/2. We plug in the values:
A = (4*3)/2
A = (12)/2
A = 6
Since we have 4 triangles, the surface area is:
16+6+6+6+6 = 40
Answer:
16+6+6+6+6
Step-by-step explanation:
KHan
Find the product. (5p + 2)2^
Answer:
25p^2 + 4 + 20p
Step-by-step explanation:
(5p + 2)^2 = (5p)^2 + (2)^2 + 2 × 5p × 2
= 25p^2 + 4 + 20p
One day I found a strange thing happening to my watch,the minute hand & the hour hand were coming together every 65 minutes.I decided to get it checked. Was my watch gaining or losing time, and how much per hour?
Answer:
Step-by-step explanation:
The minute hand of a clock overtakes the hour hand at intervalsof M minutes of correct time. The clock gains or loses in a day by=(720/11−M)(60×24/M) minutes.
Here M = 64. The clock gains or losses in a day by
=(720/11−M)(60×24/M)=(720/11−64)(60×24/64)
=16/11(60×3/8)=2/11(60×3)=360/11=32(8/11) minutes.
Tom and Harry live 24km from each other, which on the map is 5 cm Given that the distance on the map between Harry and the Sea view is 4cm Find the actual distance between Harry and the Sea view.
Answer:
19.5 km
Step-by-step explanation:
the actual distance between Harry and the Sea view:
if 24 km is 5 cm on map
24*4/5= 19.5 km
I REALLY NEED HELP FOR THIS ONE
Answer:
A = 27(2√3-π) cm² ≈ 8.71 cm²Step-by-step explanation:
Area of shaded region it is area of hexagon minus area of circle.
A regular hexagon is comprised of six equilateral triangles (of the same sides).
So its area: [tex]A_1=6\cdot\dfrac{S^2\sqrt3}{4}=\dfrac{3S^2\sqrt3}2[/tex] {S = side of the triangle}
Height (H) of such a triangle is equal to radius (R) of a circle inscribed in the hexagon:
[tex]R = H = \dfrac{S\sqrt3}{2}[/tex]
Area of shaded region:
[tex]A=A_1-A_\circ=\dfrac{3S^2\sqrt3}2-\pi R^2=\dfrac{6S^2\sqrt3}4-\pi\left(\dfrac{S\sqrt3}2\right)^2=\dfrac{S^2(6\sqrt3-3\pi)}4[/tex]
S = 6 cm
so:
[tex]A=\dfrac{6^2(6\sqrt3-3\pi)}4=\dfrac{36(6\sqrt3-3\pi)}4=9(6\sqrt3-3\pi)=27(2\sqrt3-\pi)\ cm^2\\\\A=27(2\sqrt3-\pi)\ cm^2\approx8.71\ cm^2[/tex]
Please help.. ty if you do
Answer:B
Step-by-step explanation: x is less than 1 so it is a open circle on the graph and x is greater than or equal to -1 so it is a closed circle on -1, B has both of these so B is the answer
II NEED HELP!!!!!!!! Are the graphs of the lines in the pair parallel? Explain. y = 2/3x– 17 4x – 6y = –6 4x-6y=-6 Yes, since the slopes are the same and the y-intercepts are the same. A )No, since the y-intercepts are different. B)No, since the slopes are different. C)Yes, since the slopes are the same and the y-intercepts are different.
Answer:
A
Step-by-step explanation:
Compare 1/11 to 11/20 using least to greatest
Answer:
0.09
0.55
Step-by-step explanation:
to write least to greatest firstly, start comparing both number
so the answer will be=0.09,0.55
it least to greatest or in assending order.
I need Help!!! Will give Brainliest ABC≅DEF Find the following: 1. x = 2. CB = 3. FE = 4. y = 5. ED = 6. FD = 7. AB = 8. AC = 9. Area =
Answer:
ABC≅DEF
x = 2
CB = 3
FE = 4
y = 5
ED = 6
FD = 7
AB = 8
AC = 9
In triangle ABC=
Side AC= 9 cm
Side CB= 3 cm
Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
=13.5 cm^2
In triangle DEF=
Side FE= 4 cm
Side FD= 7 cm
Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
=14 cm^2
Does this graph represent a function? Why or why not?
Answer:
B
Step-by-step explanation:
it is not a function because it fails the vertical line test,
A vertical line intersect the graph no more than once.
Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below.
Answer:
0
Step-by-step explanation:
Answer: it's C. 0
Also Happy early Christmas
Which expression is equivalent to -80
Answer:
what expressions?
Step-by-step explanation:
look at the pattern below.How should the tird shape be labeled
Answer:
You havent showed us the pattern
What is the difference between a parallelogram and a rectangle? a Both pairs of opposite sides are congruent and parallel. b Contains four right angles. c The diagonals bisect each other. d Both pairs of opposite angles are congruent.
Answer:
b. Contains four right angles.
Step-by-step explanation:
A parallelogram has two pairs of opposite sides that are both congruent and parallel, as does a rectangle.
A parallelogram usually does NOT have four right angles, but a rectangle does. b Contains four right angles is the difference between a parallelogram and a rectangle.
The diagonals of a parallelogram bisect each other, and so do the rectangle's diagonals.
The opposite angles of parallelograms are congruent, and all four angles of a rectangle are congruent, so this is a similar aspect of both a parallelogram and a rectangle.
Hope this helps!
(OFFERING ALL THE POINTS I HAVE) Word Problem. Please help!! Part 1 of problem: The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number and use 3.14 for Pi. (Use sphere volume formula) Part 2: The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up? Part 3: Using the information from part 2, answer the following question by filling in the blank: The volume of the actual tank is __% of the mock-up of the tank.
Answer:
Part 1: 359,007 ft³
Part 2: 216 times smaller
Part 3: 21600%
Step-by-step explanation:
Part 1:
The parameters for the tank are;
The radius of the tank = 70 feet
The volume of a sphere = 4/3·π·r³
Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere
The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3
Plugging in the value for the radius gives
Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.
Part 2:
The dimension of the scale model = 1/6 × Actual dimension
Therefore, we have the radius of the sphere of the scale model = 1/6 × 70
Which gives;
The radius of the sphere of the scale model = 35/3 = 11.67 feet
The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³
The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times
The number of times smaller the scale model is than the actual volume = 216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.
Part 3:
The percentage of the mock-up, x, to the volume of the actual tank is given as follows
x/100 × 1662 = 359,007
∴ x = 216 × 100 = 21600%
The percentage of the mock-up, to the volume of the actual tank is 21600%.
Answer:
Part 1: 359,007 ft³
Part 2: 216 times smaller
Part 3: 21600%
Step-by-step explanation:
Part 1:
The parameters for the tank are;
The radius of the tank = 70 feet
The volume of a sphere = 4/3·π·r³
Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere
The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3
Plugging in the value for the radius gives
Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.
Part 2:
The dimension of the scale model = 1/6 × Actual dimension
Therefore, we have the radius of the sphere of the scale model = 1/6 × 70
Which gives;
The radius of the sphere of the scale model = 35/3 = 11.67 feet
The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³
The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times
The number of times smaller the scale model is than the actual volume = 216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.
Part 3:
The percentage of the mock-up, x, to the volume of the actual tank is given as follows
x/100 × 1662 = 359,007
∴ x = 216 × 100 = 21600%
The percentage of the mock-up, to the volume of the actual tank is 21600%.
What is the probability that a randomly selected male will have a foot length between 8 and 12.5 inches? P(8 < r < 12.5)= ____ or ____%
Answer:
0.8185 or 81.85%
Step-by-step explanation:
The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.
The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean the z sore is negative. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.
For 8 inches:
[tex]z=\frac{x-\mu}{\sigma}=\frac{8-11}{1.5}=-2[/tex]
For 12.5 inches:
[tex]z=\frac{x-\mu}{\sigma}=\frac{12.5-11}{1.5}=1[/tex]
From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%
C equal 3x - 2 of x=5 than what does c equal
Answer:
i need help this too
Step-by-step explanation:
Answer:
13Step-by-step explanation:
Given,
x = 5
Now, let's find the value of C
[tex]c = 3x - 2[/tex]
plug the value of x
[tex] = 3 \times 5 - 2[/tex]
Multiply the numbers
[tex] = 15 - 2[/tex]
Calculate the difference
[tex] = 13[/tex]
Hope this helps..
Best regards!!
pls let me know what you get for the question below
Answer:
233.37
Step-by-step explanation:
so between each gondola is 20.95 so you will multiply it by 35 not 36 (because between the first you go round and come back to the same first you started so no space between first and last) then get circumference as 733.25 using
[tex]c = \pi \: d[/tex]
you get diameter
Please help me, im in desperate need of help for these questions
Answer:
For the first one, answer is dilation of 2
Step-by-step explanation:
you see the coordinates for triangle A'B'C' are all doubled the coordinates of triangle ABC
Instructions: Given the preimage reflect over the x-axis then they axis. Find
the new coordinates.
10
8
6
1012
А
-12 -10 8 6 4-2
-2
B
-4
D
-6
С
-12
The coordinates of the preimage are:
A(-8, -2)
B(-4, -3)
C(-2,-8)
D(-10, -6)
Now let's find the coordinates after the reflection over the x-axis.
A'(-8,
B' (-4,
C'(-2,
D' (-10,
Answer:
The coordinates are;
For reflection over the x-axis
A'(-8, 2)
B'(-4, 3)
C'(-2, 8)
D'(-10, 6)
For reflection over the y-axis;
A''(8, 2)
B''(4, 3)
C''(2, 8)
D''(10, 6)
Step-by-step explanation:
When a point (x, y) is reflected over the x, axis, we have;
Coordinates of the pre-image = (x, y)
Coordinates of the image after reflection = (x, -y)
Therefore, for the points A, B, C, D we have;
Pre-image A(-8, -2), Image A'(-8, 2)
Pre-image B(-4, -3), Image B'(-4, 3)
Pre-image C(-2, -8), Image C'(-2, 8)
Pre-image D(-10, -6), Image D'(-10, 6)
When a point (x, y) is reflected over the y, axis, we have;
Coordinates of the pre-image = (x, y)
Coordinates of the image after reflection = (-x, y)
Therefore, for the points A', B', C', D' we have;
Pre-image A'(-8, 2), Image A''(8, 2)
Pre-image B'(-4, 3), Image B''(4, 3)
Pre-image C'(-2, 8), Image C''(2, 8)
Pre-image D'(-10, 6), Image D''(10, 6).
I really need help with this question, and I would really appreciate it! I will mark brainliest!
Answer:
These are two equilateral triangles and all the sides of an equilateral triangle are equal. The question even says so so that's the answer, all the sides of the equilateral triangles are equal so all the sides equate to each other
La suma de dos números es 50 y la diferencia es 22. ¿Cuáles son los números?
Answer:
(3,2)
Step-by-step explanation:
Just took the test
The graph shows the distance Ted traveled from the market in miles (y) as a function of time in seconds (x). The graph is divided into four segments labeled P, Q.
R. and S
S
Distance
(mi)
R
P
Time (sec)
Which segment shows Ted waiting for a cab?
A) P
B) Q
C) R
D) S
Explanation:
The flat horizontal portion S is where the distance (y) does not increase or decrease. So Ted is stationary during this time frame.
In terms of speed, we would say speed = distance/time = (change in y)/(change in x). Note how this is the slope.
Rise = 0 because the horizontal line does not go up or down. The run is any positive number, though convention usually has Run = 1. Therefore, slope = rise/run = 0/1 = 0. All flat horizontal lines have a slope of 0 to indicate no upward or downward movement.
Added to Six Flags St. Louis in the Colossus is a giant Ferris wheel. Its diameter is 165 feet, it rotates at a rate of about 1.6 revolutions per minute, and the bottom of the wheel is 15 feet above the ground. Determine an equation that relates a rider's height above the ground at time . Assume the passenger begins the ride at the bottom of the wheel.
Answer:
The height of the rider as a function of time is [tex]h(t) = 15 + 82.5\cdot (1-\cos 0.168t) \,[ft][/tex], where time is measured in seconds.
Step-by-step explanation:
Given that Ferris wheel rotates at constant rate and rider begins at the bottom of the wheel, the height of the rider as a function of time is modelled after this expression:
[tex]h(t) = h_{bottom} + (1-\cos \omega t)\cdot r_{w}[/tex]
Where:
[tex]h_{bottom}[/tex] - Height of the bottom with respect to ground, measured in feet.
[tex]\omega[/tex] - Angular speed of the ferris wheel, measured in radians per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]r_{w}[/tex] - Radius of the Ferris wheel, measured in feet.
The angular speed of the ferris wheel, measured in radians per second, is obtained from the following expression:
[tex]\omega = \frac{\pi}{30}\cdot \dot n[/tex]
Where:
[tex]\dot n[/tex] - Angular speed of the ferris wheel, measured in revolutions per minute.
If [tex]\dot n = 1.6\,rpm[/tex], then:
[tex]\omega = \frac{\pi}{30}\cdot (1.6\,rpm)[/tex]
[tex]\omega \approx 0.168\,\frac{rad}{s}[/tex]
Now, given that [tex]h_{bottom} = 15\,ft[/tex], [tex]r_{w} = 82.5\,ft[/tex] and [tex]\omega \approx 0.168\,\frac{rad}{s}[/tex], the height of the rider as a function of time is:
[tex]h(t) = 15 + 82.5\cdot (1-\cos 0.168t) \,[ft][/tex]
The perimeter of a rectangle is 141 feet, and the length is twice the width. What are the dimensions ?
Answer:
The width is 23.5 ft and the length is 47 ft
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w)
141 = 2(l+w)
The length is twice the width
l = 2w
141 = 2 ( 2w+w)
141 = 2( 3w)
141 = 6w
Divide each side by 6
141/6 = 6w/6
23.5 = w
l = 2w = 2(23.5) = 47
The width is 23.5 ft and the length is 47 ft
Answer:
[tex]\boxed{Width = 23.5 \ feet}[/tex]
[tex]\boxed{Length = 47 \ feet}[/tex]
Step-by-step explanation:
Let Length be l and Width be w
Perimeter = 2(Length) + 2(Width)
Condition # 1:
2l+2w = P
=> 2 l + 2 w = 141
Condition # 2:
=> l = 2w
Putting the second equation in the first one
=> 2(2w)+2w = 141
=> 4w + 2w = 141
=> 6w = 141
Dividing both sides by 6
=> Width = 23.5 feet
Given that
=> l = 2w
=> l = 2(23.5)
=> Length = 47 feet
PLSSSS HELPPP. The price of a tennis racquet is inversely proportional to its weight. If a 20 oz. racquet cost $30.00, what would a 25 oz. racquet cost?
Answer:
$24 will be the cost of tennis racquet with weight 25 oz.
Step-by-step explanation:
Given that Price of racquet is inversely proportional to its weight.
i.e.
[tex]Price \propto \dfrac{1}{Weight}[/tex]
We can replace the proportional sign with a constant of proportionality.
[tex]Price = \dfrac{C}{Weight}[/tex]
Where C is a constant named as constant of proportionality.
Given that cost of 20 oz. racquet is $30.00
Putting both the values :
[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]
So, the equation becomes:
[tex]Price = \dfrac{600}{Weight}[/tex]
Now, we have to find the price of 25 oz. racquet.
Putting Weight = 25 oz and finding Price:
[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]
So, $24 will be the cost of tennis racquet with weight 25 oz.
PRST is a trapezium. PQR and PTU are
straight lines. Find the values of x and y.
Answer:
x = 56 degrees
y = 62 degrees
Step-by-step explanation:
Given TS || PR
x = 56 ................. corresponding angles TS, PR parallel sides of trapezium.
VSK = x ...................... correspoinding angles given TU || SV
y = 118 - VSK .......... given VSR = 118
= 118 - 56
= 62