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3 years ago

Find the slope and y-intercept of y=8x-7

1 answer:

5 0

$\bf \begin{array}{|c|ll}\cline{1-1}\textit{slope-intercept form}\\\cline{1-1}\\y=\stackrel{slope}{m}x+\stackrel{y-intercept}{b}\\\\\cline{1-1}\end{array}~\hspace{2em} y=\stackrel{slope}{8}x\stackrel{y-intercept}{-7}~~\begin{cases}m=8\\y-intercept = (0, -7)\end{cases}$

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Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y =

Dovator [93]

Answer:

V = π ∫₀² (y² − 8y + 6√(2y)) dy

V = π ∫₀² (6x − 5x² + x³) dx

Step-by-step explanation:

y₁ = 0.5x²

y₂ = x

First, find the intersections of the curves.

0.5x² = x

x² = 2x

x² − 2x = 0

x (x − 2) = 0

x = 0 or x = 2

So the points of intersection are (0, 0) and (2, 2).

When we revolve this region about the line x = 3, we get a hollow shape that looks like an upside-down funnel, or a volcano.

One option is to use washer method to find the volume, by cutting a thin horizontal slice of thickness dy, inner radius 3−x₁ = 3−√(2y), and outer radius of 3−x₂ = 3−y.

V = ∫₀² π [(3−y)² − (3−√(2y))²] dy

V = ∫₀² π (9 − 6y + y² − 9 + 6√(2y) − 2y) dy

V = π ∫₀² (y² − 8y + 6√(2y)) dy

Another option is to use shell method to find the volume, by cutting a thin vertical slice of thickness dx, radius 3−x, and height y₂−y₁ = x−0.5x².

V = ∫₀² 2π (3 − x) (x − 0.5x²) dx

V = ∫₀² 2π (3x − 1.5x² − x² + 0.5x³) dx

V = ∫₀² 2π (3x − 2.5x² + 0.5x³) dx

V = π ∫₀² (6x − 5x² + x³) dx

The second option is arguably easier to evaluate, but either one will get you the same answer (V = 8π/3).

7 0

3 years ago

Simplify this expression.

amm1812

Answer: 0.88

Step-by-step explanation:

Okay -5.37 + 8.14 = 2.77 ( you can simply plug this into the calculator or you could switch the problem around so it’s 8.14 - 5.37, either way you’ll get 2.77)

And then you take 2.77 -1.89 = 0.88

So 0.88 is your answer

7 0

2 years ago

The population of a town increases at a rate of 5% every year. The population of this town was 10,400 in 2017. What will the pop

galben [10]

Answer:

The population of the town in 2020 will approx. be 12,039.

Step-by-step explanation:

The initial population in the year 2017 = 10,400

Increase in population every yea r = 5%

Now, 5% of 10, 400 = $\frac{5}{100} \times 10, 400 = 520$

Hence, the population in the year 2018 = 10,400 + 520 = 10,920

Now, in the year 2019

5% of 10, 920 = $\frac{5}{100} \times 10, 920 = 546$

Hence, the population in the year 2019 = 10,920 + 546 = 11,466

Now, in the year 2020

5% of 11,466 = $\frac{5}{100} \times 11,466 = 573.3$

or, the population in the year 2020 = 11,466 + 573.3 = 12,039.3

The population of the town in 2020 will approx. be 12,039.

6 0

2 years ago

Solve each proportion. show your work. 2x/7 = 12/14

dybincka [34]

2x/7 = 12/14
Multiply both sides of the equation by 7:
2x = 84/14
Simplify:
2x = 6
Divide both sides by 2 and your answer is....
x = 3

8 0

3 years ago

What can you do to get the x alone on the left side of the equation? Fill in the blanks below to show what you would do. Then, s

Phantasy [73]

Answer:

Step-by-step explanation:

Equation: 82.5 + 2x = 338.5

--------------------------------------------------

2x ÷ _2__ = 256 ÷ _2__

x = _128__

7 0

1 year ago