Which of the following equations is the inverse of the function f(x)=4x-7/9
1 answer:
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Answer:
The system that models the situation is:
The solution is:
(9, 6)
Step-by-step explanation:
We must write the equations as indicated in the problem.
The sum of twice a number and another number is 24
<em>a number:</em> x
<em>other number:</em> y
Then
The difference of twice the first number and the other number is 12
<em>first number: </em> x
<em>other number:</em> y
Then:
The system that models the situation is:
To solve the system we add both equations to find the value of x
---------------------
The solution is:
(9, 6)
Answer:
π/10
Step-by-step explanation:
When we rotate the region about the y-axis, we get something that looks like a volcano, or a bundt cake. Instead of slicing this into flat washers, we'll slice it in concentric rings, or "shells".
Each shell has a radius x, a thickness dx, and a height y. The volume of an individual shell is:
dV = 2π r h t
dV = 2π x y dx
Since y = x² − x³:
dV = 2π x (x² − x³) dx
dV = 2π (x³ − x⁴) dx
The total volume is the sum of all the shells from x=0 to x=1.
V = ∫ dV
V = ∫₀¹ 2π (x³ − x⁴) dx
V = 2π (¼ x⁴ − ⅕ x⁵) |₀¹
V = 2π (¼ − ⅕)
V = π/10
