The perimeter of base dhgc is 30 inches, and the perimeter of base swvr is 20 inches. Complete the table with the ratios of the heights, surface areas, and volumes of these two similar rectangular prisms. Assume the ratios are written in the form figure 1 : figure 2.
Answers
Answer:
Ratio of heights: 3 : 2
Ratio of surface areas: 9 : 4
Ratio of volumes: 27 : 8
Step-by-step explanation:
Since both cuboids are proportional, then we must derive expressions for the ratios of heights, surface areas and volumes from the following identities:
Perimeter
[tex]p' = k_{p}\cdot p[/tex] (1)
Surface area
[tex]A'_{s} = k_{A_{s}}\cdot A_{s}[/tex] (2)
Volume
[tex]V' = k_{V}\cdot V[/tex] (3)
Where:
[tex]p[/tex], [tex]p'[/tex] - Perimeters of the small cuboid and the big cuboid, in inches.
[tex]A_{s}[/tex], [tex]A'_{s}[/tex] - Surface areas of the small cuboid and the big cuboid, in square inches.
[tex]V[/tex], [tex]V'[/tex] - Volumes of the small cuboid and the big cuboid, in cubic inches.
By means of geometry formulas we expand the system of equations below:
Perimeter
[tex]4\cdot (w' + h' + l') = k_{p}\cdot [4\cdot (w + h + l)][/tex]
[tex]4\cdot (k\cdot w'+ k\cdot h' + k\cdot l) = k_{p}\cdot [4\cdot (w+h+l)][/tex]
[tex]k_{p} = k[/tex]
Surface area
[tex]2\cdot (w'\cdot h' + l'\cdot w' + l' \cdot h') = k_{A_{s}}\cdot [2 \cdot(w\cdot h + l \cdot w + l\cdot h)][/tex]
[tex]2\cdot [(k\cdot w')\cdot (k\cdot h') + (k\cdot l)\cdot (k\cdot w) + (k\cdot l)\cdot (k\cdot h)] = k_{A_{s}}\cdot [2\cdot (w\cdot h + l\cdot w + l\cdot h)][/tex]
[tex]k_{A_{s}} = k^{2}[/tex]
Volume
[tex]w'\cdot h' \cdot l' = k_{V}\cdot (w\cdot h \cdot l)[/tex]
[tex](k\cdot w)\cdot (k \cdot h)\cdot (k \cdot l) = k_{V}\cdot (w\cdot h \cdot l)[/tex]
[tex]k_{V} = k^{3}[/tex]
Where [tex]k = \frac{p'}{p}[/tex].
If we know that [tex]p' = 30\,in[/tex] and [tex]p = 20\,in[/tex], then we proceed to calculate all the ratios:
[tex]k_{p} = \frac{30\,in}{20\,in}[/tex]
[tex]k_{p} = \frac{3}{2}[/tex]
[tex]k_{A_{s}} = \frac{9}{4}[/tex]
[tex]k_{V} = \frac{27}{8}[/tex]
Answer:
ratio of heights: (3/2)
Ratio of surface area: (9/4)
Ratio of volumes: (27/8)
Step-by-step explanation:
got this right, hope it helps :)
Related Questions
Maria is saving money to buy a bike. She has $42 and is going to save an additional $ 7 each week. The bike costs $133. In how many
weeks will she have enough money to buy the bike?
Answers
Answer:
Maria will have enough money to buy the bike in 13 weeks.
Step-by-step explanation:
w = weeks
42 + 7w = 133
take away 42 frim each side
7w = 91
divide each side by 7
w = 13
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How much would you have paid on the Constant Usage plan? $22.37 $21.83 $21.65 $22.08
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Answer: 22.08
Step-by-step explanation:
Answer: 22.08
Step-by-step explanation:
ABC and ADC are triangles. The area of triangle ADC is 52m^2. Work out the length of AB
Answers
Answer:
Tthe length of AB is 13.6 cm
Step-by-step explanation:
Step 1: calculate length CD using the area of a triangle
[tex]A = \frac{1}{2} \times (AD \times CD) \times \ sine (D)\\\\52 = \frac{1}{2} \times (12 \times CD) \times \ sine (102)\\\\52 = 6CD \times 0.978\\\\52 = 5.868CD\\\\CD = \frac{52}{5.868} \\\\CD = 8.862 \ cm[/tex]
Step 2: calculate length AC using Cosine rule;
[tex]AC^2 = AD^2 + CD^2 - 2(AD \times CD)cos (D)\\\\AC^2 = 12^2 + 8.862^2 - 2(12 \times 8.862)cos(102)\\\\AC^2 = 222.535 - 2(-22.11)\\\\AC^2 = 222.535 + 44.22\\\\AC^2 = 266.755\\\\AC = \sqrt{266.755} \\\\AC = 16.33 \ cm[/tex]
Step 3: Apply sine rule to calculate length AB;
[tex]\frac{AB}{sin \ 46} = \frac{AC}{sin \ 120} \\\\AB = \frac{sin \ 46 \ \ \times \ \ AC}{sin \ 120} \\\\AB = \frac{sin \ 46 \ \ \times \ \ 16.33}{sin \ 120} \\\\AB = 13.56 \ cm \\\\AB = 13.6 \ cm[/tex]
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There were 780 fish in the lake. After a year, the population increases by 23% How many fish are in the lake? Round tot he nearest whole number.
Answers
Answer:
There are 959 fish in the lake.
Step-by-step explanation:
According to the information provided, to be able to find the number of fish in the lake, you have to calculate 23% of the amount of fish in the lake and add that result to the amount of fish in the lake:
780*23%=179
780+179=959
According to this, the answer is that there are 959 fish in the lake.
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Answers
Answer:
The total number of combinations that include cheddar and turkey is 2.
Step-by-step explanation:
Since the meat and cheese of the sandwich have already been locked in, the different number of sandwiches with cheddar and turkey is down to the number of bread. Since there are two types of bread: white and rye, that means there are two different combinations that include cheddar and turkey.
Plz it’s for my finals!!
Answers
Good luck on your finals!
Find the Area.
help sos I need it please I have 15 minutes left to complete this
Answers
Answer:
95
Step-by-step explanation:
6 x 10 = 60
7 x 10 / 2 = 35
35 + 60 = 95
Henry has 2 six-sided number cubes, one red, and one blue. The faces of the red cube are numbered 1-6. The faces of the blue cube are numbered 7-12. If Henry tosses both number cubes, what is the probability that the sum of the two cubes will be a prime number? Show and explain how you got your answer.
Answers
Answer:
babylonia and lseral i thik so
The probability that the sum of the two cubes will be a prime number is 0.33.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Henry has 2 six-sided number cubes, one red, and one blue.
The faces of the red cube are numbered 1-6.
The faces of the blue cube are numbered 7-12.
Henry tosses both number cubes.
Sample space for the experiment = {(1, 7), (1, 8), .........., (1, 12), (2, 7), (2, 8), ......., (2, 12), .........., (6, 7), ...........,(6, 12)}
Total number of outcomes = 36
Least sum is 1 + 7 = 8 and greatest sum is 6 + 12 = 18
Prime numbers in between 8 and 18 are 11, 13 and 17.
Sum will be prime numbers for the outcomes,
{(1, 10), (1, 12), (2, 9), (2, 11), (3, 8), (3, 10), (4, 7), (4, 9), (5, 8), (5, 12), (6, 7), (6, 11).
Number of outcomes which sum are prime numbers = 12
Probability = 12/36 = 1/3 = 0.333
Hence the probability is 0.33.
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Help please
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The first rectangle will be the small piece sticking out in the right. The length is 8 and the width would be 4 since 10 (whole length of the side)- 6 (known length of the side being cut off) = 4. That would make the area of that 32 since lxw=area.
Then the next rectangle would be the one on the left. This would be the 6 times the whole 20 that is given which is 120.
Add the 2 to get the whole area which would be 152 inches.
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Answer:
Mia khalifa
Step-by-step explanation:
H3ntai g hhuh
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Answer:
Hello! answer: 186
7 3/4 × 2 × 12 = 186
Hope that helps!
The scale of a map is 0.5 inches :10 km. Find the actual distance corresponding to the map distance of 10 inches.
Answers
Answer:
200 km
Step-by-step explanation:
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[tex]\frac{0.5}{10}[/tex] = [tex]\frac{10}{x}[/tex]
Cross multiply and solve for x:
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Answers
Answer:
g(x)=-8(3^x)
Step-by-step explanation:
Given: f(x)=3^x
Multiply by 8: f(x)=8(3^x)
Negate function: g(x)=-8(3^x)
The function represents the exponential function f(x) = 3x after a vertical stretch by a factor of 8 and a reflection across the x-axis will be g(x)=-8(3ˣ).
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x.where a is a constant and a>1
It is given that, the function represents the exponential function f(x) = 3x.
We have to find the function after a vertical stretch by a factor of 8 and a reflection across the x-axis.
We have to do geometric transformation, It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
Thus, the function represents the exponential function f(x) = 3x after a vertical stretch by a factor of 8 and a reflection across the x-axis will be g(x)=-8(3ˣ).
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Answers
Answer: D on Edge.
Step-by-step explanation:
The domain of the absolute value function is (-∞, +∞).
Here,
In the given figure,
The line of the absolute value function extend in both direction of the
x- axis.
We have to find the domain of the absolute value function which shown in graph.
What is Domain?
The Domain is the set of all x-values. It is the horizontal line In a Cartesian Plane.
Now,
In the given figure,
The line of the absolute value function extend in both direction of the
x- axis.
This shows that, the function can take any of the x values as its input.
That's mean all the real number.
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Option 4 is true.
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Answer:
its C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
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length = 3 + width
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3 +x + x = 17
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Answer:
If the diameter or radius of one circle is the same as another circle they are congruent.
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3
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answer:
-3x^2+16x+64
Step-by-step explanation:
First, you need to find the area of both areas (the total area and the area of the unshaded part). Let's find the total area.
(x+8)(x+8)=x^2+16x+64
The total area is x^2+16x+64
(2x)(2x)=4x^2
The area of the unshaded part is 4x^2
Now we have to subtract to find the area of the shaded part.
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That is the answer
Hope this helped!! :D
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Answers
Answer:
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Step-by-step explanation:
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Answers
there is not enough info given to tell how long it would take
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Answers
Answer:
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Step-by-step explanation:
got it right
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4(2x + 11
Answers
Answer:
habla no espanyol
Step-by-step explanation:
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if you can answer this ill give you brainlist
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Answer:
option 1
Step-by-step explanation:
the pattern will continue like this:
50 - 25
answer 1 is the correct answer!
Answer:The first question is the true statement <3
Step-by-step explanation
<3