Answer:
a) 8π
b) 8/3 π
c) 32/5 π
d) 176/15 π
Step-by-step explanation:
Given lines : y = √x, y = 2, x = 0.
<u>a) The x-axis </u>
using the shell method
y = √x = , x = y^2
h = y^2 , p = y
vol = ( 2π ) 
= 
∴ Vol = 8π
<u>b) The line y = 2 ( using the shell method )</u>
p = 2 - y
h = y^2
vol = ( 2π )
= 
= ( 2π ) * [ 2/3 * y^3 - y^4 / 4 ] ²₀
∴ Vol = 8/3 π
<u>c) The y-axis ( using shell method )</u>
h = 2-y = h = 2 - √x
p = x
vol = 
= 
= ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀
vol = ( 2π ) ( 16/5 ) = 32/5 π
<u>d) The line x = -1 (using shell method )</u>
p = 1 + x
h = 2√x
vol =
Hence vol = 176/15 π
attached below is the graphical representation of P and h
2 Answers: Choice B and Choice C
The rate of change is 2.
The rate of change is constant.
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Explanation:
The first point on the left is when x = 1.5 and it has a height of y = 1
The point (1.5, 1) is on the line.
So is the point (3,4) for similar reasoning.
Compute the slope between those points
m = (y2-y1)/(x2-x1)
m = (4-1)/(3-1.5)
m = 3/(1.5)
m = 2
The slope is 2, which is the same as saying the rate of change is 2. This only applies when x > 1 of which the interval 1.5 ≤ x ≤ 3 is a part of.
Since the slope stays at 2 on the interval 1.5 ≤ x ≤ 3, this means we consider the slope to be constant. If the curve bended at all on this interval, then it wouldn't be a constant slope.
Answer:
i do
Step-by-step explanation:
The discriminant is b<span>²-4ac
We can rewrite x</span>² = 4 to x<span>² + 0x - 4 = 0
So a = 1, b = 0, c = -4
</span>Δ = 0 - 4 * 1 * -4
Δ = 16
The answer is B
