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:
9, 8, 11
Step-by-step explanation:
2, 5, 4, 7, 6, ...
+3 -1 +3 -1
The sequence goes +3 ,-1 +3 -1 and so on
The next term is will be +3
6+3 = 9
Then we will -1
9-1 =8
Answer:
D. 70 degrees.
Step-by-step explanation:
Because the 2 triangles are similar corresponding angles are congruent.
So m < P = m< X = 66 degrees.
And since there are 180 degrees in a triangle:
m < W = 180 - (m < V + m < X)
= 180 - (44 + 66)
= 70 degrees.