Answer:
x ∈ (-∞ , -2) ∪ (1, 3)
Step-by-step explanation:
The expression is already factored. Note that for the polynomial that appears in the numerator there are 2 roots:
For the polynomial that appears in the denominator there is 1 root:
Note that does not belong to the domain of f(x) because it zeroes the denominator of the function and the division between zero is not defined.
With these three roots we do the study of signs to find out when
Observe the attached image
Note that:
when
when
when
Finally, we have the solution:
x ∈ (-∞ , -2) ∪ (1, 3)
The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3
<h3>What is the Volume of a solid?</h3>
The volume of a solid, given by the function f(x), over an interval between a and b, is given by:
To find the area, integrate around that area. We're revolving around the x-axis so the area will be a circle;
V = ∫A(x)dx = ∫(πr²)dr
Then we subtract them from each others.
∫(πr₂² - πr₁²)dr
Now substitute the value and integrate;
∫(π(2)² - π(2x)²)dr
∫(4π - 4πx²)dr
4π∫(1 - x²)dr
Now integrate from 0 to 1 since that's where our boundary is.
V = 4π∫(1 - x²)dr = 8π/3
Therefore, The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3
Learn more about the volume here;
brainly.com/question/21080169
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Answer:
The missing factor is 5y-9
5y^2-4y-9=(y+1)(5y-9)
Step-by-step explanation:
We are given this expression:
Now let us factorise it using AC method of factorisation.
First taking product of 5 and -9
5*(-9)=-45
NOw we have to find two factors of -45 that add up to give -4
Two such factors are -9 and 5
So replacing -4y by -9y+5y,
Factoring by grouping,
So the missing factor will be 5y-9