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KATRIN_1 [288]
3 years ago
7

Find the volume of the solid generated when R​ (shaded region) is revolved about the given line. x=6−3sec y​, x=6​, y= π 3​, and

y=​0; about x= 6

Mathematics
1 answer:
Dmitrij [34]3 years ago
6 0

Answer:

V=9\pi\sqrt{3}

Step-by-step explanation:

In order to solve this problem we must start by graphing the given function and finding the differential area we will use to set our integral up. (See attached picture).

The formula we will use for this problem is the following:

V=\int\limits^b_a {\pi r^{2}} \, dy

where:

r=6-(6-3 sec(y))

r=3 sec(y)

a=0

b=\frac{\pi}{3}

so the volume becomes:

V=\int\limits^\frac{\pi}{3}_0 {\pi (3 sec(y))^{2}} \, dy

This can be simplified to:

V=\int\limits^\frac{\pi}{3}_0 {9\pi sec^{2}(y)} \, dy

and the integral can be rewritten like this:

V=9\pi\int\limits^\frac{\pi}{3}_0 {sec^{2}(y)} \, dy

which is a standard integral so we solve it to:

V=9\pi[tan y]\limits^\frac{\pi}{3}_0

so we get:

V=9\pi[tan \frac{\pi}{3} - tan 0]

which yields:

V=9\pi\sqrt{3}]

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Katena32 [7]

Answer:

64

Step-by-step explanation:

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2 years ago
Please help me<br> Show your work
GrogVix [38]

<u>ANSWER TO PART A</u>

The given triangle has vertices J(-4,1), K(-4,-2),L(-3,-1)


The mapping for rotation through 90\degree counterclockwise has the mapping


(x,y)\rightarrow (-y,x)


Therefore

J(-4,1)\rightarrow J'(-1,-4)


K(-4,-2)\rightarrow K'(2,-4)


L(-3,-1)\rightarrow L'(1,-3)


We plot all this point and connect them with straight lines.


ANSWER TO PART B


For a reflection across the y-axis we negate the x coordinates.


The mapping is



(x,y)\rightarrow (-x,y)


Therefore

J(-4,1)\rightarrow J''(4,1)


K(-4,-2)\rightarrow K''(4,-2)


L(-3,-1)\rightarrow L''(3,-1)


We plot all this point and connect them with straight lines.


See graph in attachment







7 0
3 years ago
The length of a sticky note measures 77 millimeters.express this length in meters explain your thinking include an equation with
Eva8 [605]

The length of the sticky notes is \bf77\times{10^{-3}}{\text{meter}}.

Further explanation:

Given:

The length of sticky notes is measured as 77 millimeters.

Calculation:

Since 1 meter contains 1000 mm, it can be written as follows:

\begin{aligned}1000{\text{mm}}&\to{\text{1meter}}\\{\text{1mm}}&\to\frac{{\text{1}}}{{1000}}{\text{meter}}\\{\text{1mm}}&\to{10^{-3}}{\text{meter}}\\x\,{\text{mm}}&\to x \times {10^{-3}}{\text{meter}} \\ \end{aligned}

Now, substitute 77 for x in above expression to obtain the length of sticky notes in meter as follows:

77\,{\text{mm}}\to77\times{10^{-3}}{\text{meter}}

Thus, the length of the sticky notes is \bf77\times{10^{-3}}{\text{meter}}.

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brainly.com/question/1632445  

2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12  

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3. what are the domain and range of the function f(x) = 3x + 5?  

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Answer Details :

Grade: Middle School

Subject: Mathematics

Chapter: linear equation

Keywords:

Millimeters, meter, equation, sticky notes, measurements, length, function, substitution, Mexico, site, direct substitution, elimination, graph, middle term factorization, scientific notation.

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Step-by-step explanation:

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Answer:

C≈37.7

Step-by-step explanation:

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