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:
.0668
Step-by-step explanation:
Formula:
z=(x-average)/standard deviation
(2.5-2.8)/.2= -1.5
Go to a ztable and find the value for 1.5 (.9332) and take the compliment of this (we can do this because the normal distribution is symmetrical)
1-.9332= .0668
The first one is the graph for 12 and the second one is 14. Hope this helps (:
Answer:
(t - 2)(t + 2)(t² + 4)
Step-by-step explanation:
Difference of Squares: a² - b² = (a - b)(a + b)
Step 1: Write expression
t⁴ - 16
Step 2: Difference of Squares
(t² - 4)(t² + 4)
Step 3: Difference of Squares
(t - 2)(t + 2)(t² + 4)
I can't speak to the cactus specifically, but any sphere has a surface area of
and a volume of
, so the area-to-volume ratio wold be
Where <em>r</em> is the radius of the sphere.