Iam in desperate need of . i'd also appreciate if you could explain to me how you got the answer. i dont quite understand how the teacher explained it. you.

V₂ = 810 cm³

Step-by-step explanation:

Given data : a₁ = 2 cm, V₁ = 30 cm³  and a₂ = 6 cm, V₂ = ?

If two prisms are similar then their corresponding sides are proportional.

First way:

Since we know the volume of the smaller prism and the volume of the larger is required and we know that the volume is calculated using the following formula:

V = a · b · c (cm³)

Accordingly, we will make following proportion:

2³ : 6³ = 30 : V₂ =>  8 : 216 = 30 : V₂ =>   8 · V₂ = 216 · 30 =>

V₂ = 6480/8 = 810 cm³

V₂ = 810 cm³

Second way:

We will assume that the sides of the first smaller prism are the following:

a₁ = 2cm, b₁= 5cm and c₁ = 3cm

V₁ = a₁ · b₁ · c₁ = 2 · 5 · 3 = 30 cm³  which is given value.

Accordingly, we will make following proportion:

a₂ : a₁ = b₂ : b₁ = c₂ : c₁ =>  6 : 2 = b₂ : 5 = c₂ : 3  =>  6/2 = b₂/5 = c₂/3 = 3 =>

b₂/5 = 3 and  c₂/3 = 3 => b₂ = 5 · 3 = 15 cm  and c₂ = 3 · 3 = 9 cm

Finally we get

V₂ = a₂ · b₂ · c₂ = 6 · 15 · 9= 810 cm³

V₂ = 810 cm³

God with you!!!

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.