<u>Answer:</u>
3/5
<u>Step-by-step explanation:</u>
We are to find the similarity ratio of a cube with volume
to a cube with volume
.
We know the formula for the ratio of two cubes:
where
is the similarity ratio of the two cubes.
Substituting the given values in the formula to find
:




Therefore, the similarity ratio of the two cubes is 3/5.
Step-by-step explanation:
Close. You correctly set up the integrals. When integrating e²ˣ:
∫ e²ˣ dx
½ ∫ 2 e²ˣ dx
½ e²ˣ + C
So the coefficient should be ½, not 2.
[eˣ − ½ e²ˣ]₋₁⁰ + [½ e²ˣ − eˣ]₀¹
[(e⁰ − ½ e⁰) − (e⁻¹ − ½ e⁻²)] + [(½ e² − e) − (½ e⁰ − e⁰)]
1 − ½ − e⁻¹ + ½ e⁻² + ½ e² − e − ½ + 1
-e⁻¹ + ½ e⁻² + ½ e² − e + 1
I'll use subscript notation for brevity, i.e.

3.




By the chain rule,


4.



By the chain rule,


