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3 years ago

4 [-2a - 6b + 5a - 1]

Mathematics

1 answer:

Paha777 [63]3 years ago

3 0

Answer:

Step-by-step explanation:

$4 [-2a - 6b + 5a - 1]\\\\Simplify\:\\-2a - 6b + 5a - 1 : 3a-6b-1\\\\=4\left(3a-6b-1\right)$

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The area enclosed by the graphs of y = 1/x, y = 1, and x = 3 is rotated about the line y = -1. Find the volume and show steps.

Natalija [7]

Answer:

$A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\approx9.8524$

Step-by-step explanation:

Use the Washer Method $A=\pi\displaystyle \int\limits_{a}^{b}{\bigr[R(x)^2-r(x)^2\bigr] \, dx$ where $R(x)$ is the outer radius and $r(x)$ is the inner radius.

If we sketch out the graph, we see that $y=1$ intersects points $(1,1)$ and $(3,1)$ , which will be our bounds of integration.

Here, our outer radius will be $R(x)=(-1-1)=-2$ and our inner radius will be $r(x)=-1-\frac{1}{x}$ .

Thus, we can compute the integral and find the volume:

$A=\pi\displaystyle\int\limits^{3}_{1} {(-2)^2-\biggr(-1-\frac{1}{x}\biggr)^2 } \, dx\\ \\A=\pi\displaystyle\int\limits^{3}_{1} {4-\biggr(1+\frac{2}{x}+\frac{1}{x^2} \biggr) } \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {4-1-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {3-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\biggr[3x-2\ln(|x|)+\frac{1}{x}\biggr]\Biggr|_{1}^{3}\\$

$A=\pi\displaystyle\biggr[\biggr(3(3)-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3(1)-2\ln(|1|)+\frac{1}{1}\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(9-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3+1\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(\frac{28}{3}-2\ln(|3|)\biggr)-\biggr(4\biggr)\biggr]\\A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\\A\approx9.8524$

In conclusion, the volume of the solid of revolution will be about 9.8524 cubic units. See the attached graph for a helpful visual!

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1 year ago

Square root of 1536 with divison method

11111nata11111 [884]

Answer:

39.191835884531

this is the square root

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3 years ago

Write y=2|x+2|−3 as a piecewise function.

hichkok12 [17]

Answer:

Below.

Step-by-step explanation:

f(x) = 2(x + 2) - 3 when x ≥ -2

f(x) = -2(x + 2) - 3 when x < -2

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2 years ago

A boat is sighted from a 50-meter observation tower on the shoreline at an angle of depression of 4 degrees moving directly towa

MAXImum [283]

Answer:

5.76 km/h

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides of a right triangle. Here, we are given the side opposite the angle (angle of depression), and we want to find the adjacent side (distance from shore).

Tan = Opposite/Adjacent

tan(4°) = (height of tower)/(distance from shore)

tan(4°) = (50 m)/(distance from shore)

Then the distance from shore is ...

distance from shore = (50 m)/tan(4°) ≈ 715.03 m

At the second sighting, the distance from shore is ...

distance from shore = (50 m)/tan(12°) ≈ 235.23 m

So, the distance traveled in 1/12 hour is ...

715.03 m - 235.23 m = 479.80 m

and the speed in km per hour is ...

speed = 0.4798 km/(1/12 h) = 5.7576 km/h

The speed of the boat is about 5.76 km per hour.

4 0

3 years ago

I really need someone to help me with this question ASAP.

ra1l [238]

Answer:

a=2, b=-20

Step-by-step explanation:

4(2xsquared -5x+3)= 8xsquared -20x +12

4 0

3 years ago

4 [-2a - 6b + 5a - 1]​

4 [-2a - 6b + 5a - 1]