Could anyone help me with this? Thanks
1 answer:
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Answer:
C) horizontal compression and reflection across the y-axis
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached image below, to find more information about the graph
The original equation is:
f(x) = 2x
The new equation is:
f(-5x) = 2(-5x)
f(-5x) = -10*x
The answer is
C) horizontal compression and reflection across the y-axis
A. Every month Population will increase by a factor of 0.84%.
B. Every 3 months Population will increase by a factor of 2.5%.
C. Increase in population in every 20 months is 10% + 6.72% = 16.72%.
<u>Step-by-step explanation:</u>
Here, we have number of employees in a company has been growing exponentially by 10% each year. So , If we have population as x in year 2019 , an increase of 10% in population in 2020 as which is equivalent to
.
<u>A.</u>
For each month: We have 12 months in a year and so, distributing 10% in 12 months would be like . ∴ Every month Population will increase by a factor of 0.84%.
<u>B.</u>
In every 3 months: We have , 12 months in a year , in order to check for every 3 months and Now, Population increase in every 3 months is
. ∴ Every 3 months Population will increase by a factor of 2.5%.
<u>C.</u>
In every 20 months: We have , 12 months in a year in which increase in population is 10% . Left number of moths for which we have to calculate factor of increase in population is 20-12 = 8. For 1 month , there is 0.84% increase in population ∴ For 8 months , 8 × 0.84 = 6.72 %.
So , increase in population in every 20 months is 10% + 6.72% = 16.72%.
Step-by-step explanation:
First, graph the region. The first equation is x = 3y² − 2, which has a vertex at (-2,0). The second equation is x = y², which has a vertex at (0, 0). The two curves meet at the point (1, 1). The region should look kind of like a shark fin.
(a) Rotate the region about y = -1. Make vertical cuts and divide the volume into a stack of hollow disks (washers).
Between x=-2 and x=0, the outside radius of each washer is y₁ + 1, and the inside radius is 1. Between x=0 and x=1, the outside radius of each washer is y₁ + 1, and the inside radius is y₂ + 1.
The thickness of each washer is dx.
Solve for y in each equation:
y₁ = √(⅓(x + 2))
y₂ = √x
The volume is therefore:
∫₋₂⁰ {π[√(⅓(x+2)) + 1]² − π 1²} dx + ∫₀¹ {π[√(⅓(x+2)) + 1]² − π[√x + 1]²} dx
∫₋₂⁰ π[⅓(x+2) + 2√(⅓(x+2))] dx + ∫₀¹ π[⅓(x+2) + 2√(⅓(x+2)) − x − 2√x] dx
∫₋₂¹ π[⅓(x+2) + 2√(⅓(x+2))] dx − ∫₀¹ π(x + 2√x) dx
π[⅙(x+2)² + 4 (⅓(x+2))^(3/2)] |₋₂¹ − π[½x² + 4/3 x^(3/2)] |₀¹
π(3/2 + 4) − π(½ + 4/3)
11π/3
(b) This time, instead of slicing vertically, we'll divide the volume into concentric shells. The radius of each shell y + 1. The width of each shell is x₂ − x₁.
The thickness of each shell is dy.
The volume is therefore:
∫₀¹ 2π (y + 1) (x₂ − x₁) dy
∫₀¹ 2π (y + 1) (y² − (3y² − 2)) dy
∫₀¹ 2π (y + 1) (2 − 2y²) dy
4π ∫₀¹ (y + 1) (1 − y²) dy
4π ∫₀¹ (y − y³ + 1 − y²) dy
4π (½y² − ¼y⁴ + y − ⅓y³) |₀¹
4π (½ − ¼ + 1 − ⅓)
11π/3
As you can see, when given x = f(y) and a rotation axis of y = -1, it's easier to use shell method.
(c) Since we're given x = f(y), and the rotation axis is x = -4, we should use washer method.
Make horizontal slices and divide the volume into a stack of washers. The inside radius is 4 + x₁, and the outside radius is 4 + x₂.
The thickness of each washer is dy.
The volume is therefore:
∫₀¹ π [(4 + x₂)² − (4 + x₁)²] dy
∫₀¹ π [(4 + y²)² − (3y² + 2)²] dy
∫₀¹ π [(y⁴ + 8y² + 16) − (9y⁴ + 12y² + 4)] dy
∫₀¹ π (-8y⁴ − 4y² + 12) dy
-4π ∫₀¹ (2y⁴ + y² − 3) dy
-4π (⅖y⁵ + ⅓y³ − 3y) |₀¹
-4π (⅖ + ⅓ − 3)
136π/15
