Answer:
0.089
Step-by-step explanation:
f(x) = -ln(x) and g(x) = x²
Start by graphing the region. The two curves intersect at about (0.653, 0.426), with g(x) on the left and f(x) on the right. The region is the triangular area between the curves and above the x-axis.
If we were to cut the region horizontally (perpendicular to the y-axis), the resulting line is the width of the square cross section. The thickness of this square is dy. So the volume of the square is:
dV = A dy
dV = s² dy
dV = (x₂ − x₁)² dy
dV = (e⁻ʸ − √y)² dy
The total volume is the sum of all the squares from y=0 to y=0.426.
V = ∫ dV
V = ∫₀⁰'⁴²⁶ (e⁻ʸ − √y)² dy
Evaluate with a calculator:
V ≈ 0.089
Answer:
2x-106
Step-by-step explanation:
-7(x+10)+9(x-4)
Expand parentheses:
-7x-70+9x-36
Combine like terms:
2x-106
Hope this helps!
Answer:
x+6
Step-by-step explanation:
Answer:
Step-by-step explanation:
According to the Polynomial Remainder Theorem, when dividing a polynomial P(<em>x</em>) by a binomial in the form (<em>x - </em>a), the remainder will be given by P(a).
We are given the polynomial:
And it is divided by the binomial:
The remainder is 21.
Rewriting the divisor yields:
So, <em>a</em> = -1.
Then by the PRT:
Simplify:
Solve for <em>k: </em>
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