Two prisms are similar with a scale factor of 1:4. Find the volume of the smaller prism given that the volume of the larger is 2
2 answers:
Answer: 37.5
Step-by-step explanation:
We are asked to find the volume of the smaller prism, and we know that the larger prism has a volume of 2400 cubic feet. We also know that the scale factor of the two prisms is 1:4. You may be tempted to set 1/4 equal to x/2400, but that is not what you should do. Remember that the volume ratio is , if the similarity ratio is a/b. Now, with this in mind, we know that the cube root of 2400 is 13.388659. Now, we can set 1/4 equal to x/13.388659. Solve for x by cross multiplying. 13.388659=4x. Divide both sides by 4. x=3.34716475. Then, we need to find the volume of the smaller prism, so we find the third power of x, or 3.34716475, which is approximately 37.5, which is your solution.
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Answer:
= 103 - 3n
Step-by-step explanation:
there is a common difference between consecutive terms , that is
97 - 100 = 94 - 97 = 91 - 94 = - 3
This indicates the sequence is arithmetic with explicit equation
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 100 and d = - 3 , then
= 100 - 3(n - 1) = 100 - 3n + 3 = 103 - 3n