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Volgvan
1 year ago
11

Need your help now please; the assignment is due tonight and this is the last problem I am having trouble with. The red box is t

he value I keep getting wrong
The region R is bounded by the x-axis, the straight line in the graph and the vertical line x=2.

Mathematics
1 answer:
Kobotan [32]1 year ago
3 0

The volume of the region R bounded by the x-axis is: \mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}

<h3>What is the volume of the solid (R) on the X-axis?</h3>

If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

From the given graph:

The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:

\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}

here:

  • (x₁, y₁) and (x₂, y₂) are two points on the straight line

Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8)  from the graph, we have:

\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}

y = 4x

Now, our region bounded by the three lines are:

  • y = 0
  • x = 2
  • y = 4x

Similarly, the change in polar coordinates is:

  • x = rcosθ,
  • y = rsinθ

where;

  • x² + y² = r²  and dA = rdrdθ

Therefore;

  • rsinθ = 0   i.e.  r = 0 or θ = 0
  • rcosθ = 2 i.e.   r  = 2/cosθ
  • rsinθ = 4(rcosθ)  ⇒ tan θ = 4;  θ = tan⁻¹ (4)

  • ⇒ r = 0   to   r = 2/cosθ
  •    θ = 0  to    θ = tan⁻¹ (4)

Then:

\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}

\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}

Learn more about the determining the volume of solids bounded by region R here:

brainly.com/question/14393123

#SPJ1

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HELPPPPPPP ASAPPPPP PLEASEEE
Kobotan [32]
<h3>Answer: </h3><h3>See the attached image below for the table</h3>

In column 1 we have the x values 0, 4, 8, 12

In column 2, we have the y values 1, 2, 3, 4

==================================================

Explanation:

We can start with any x value we want. I find that 0 is easiest to work with, so why not start at x = 0. For the sake of not repeating, I'll use y = 1 as the start value for y.

The first row of the table is x = 0 and y = 1.

A slope of 1/4 means rise/run = 1/4. So rise = 1 and run = 4.

A rise of 1 indicates y goes up by 1. A run of 4 means x increases by 4.

So put together, slope = 1/4 means each time x goes up by 4, y goes up by 1.

-----------

If we started at x = 0, then going up by 4 leads to x = 4. If y starts at y = 1, then going up by 1 leads to y = 2.

The second row of the table is x = 4 and y = 2

We'll repeat the pattern of "add 4 to x, add 1 to y" getting the third row having x = 8 and y = 3

We can repeat as many times as we want. Doing another "up 1, over to the right 4" movement lands us on (x,y) = (12, 4)

The completed table is shown below in the attached image.

-----------

If you were to use the slope formula with any two rows of the table, then you should get m = 1/4

Let's do the first two rows

m = (y2-y1)/(x2-x1)

m = (2-1)/(4-0)

m = 1/4

I'll let you check the other pairs of rows.

3 0
3 years ago
Samantha has a AA battery that is 51mm long. About how many centimeters long is it
Butoxors [25]

Answer:

5.1 cm

. . . . . .

All we have to do is convert our 51mm to centimeters.

We divide the length value by 10 to get our centimeters.

51 divided by 10 = 5.1

All we have to do is move our "invisible decimal"

In my way, every whole number has an invisible decimal at it's end.

For ex: '60.'

We can get into exponents. 10 is 10¹, any exponent is the number of zeros at the end of a number may have. Ex: '10² = 100'

We can move our decimal to the left since we are dividing. The amount of exponent numbers are the amount you move it, multiplying and dividing are different things with that.

Let's get back on topic.

Moving our decimal to the left with dividing is 5.1 since 10¹ has a "1" as it's exponent, making us move it "1" to the left.

Multiplying is going the right way.

I hope this helps.

5 0
3 years ago
8y : 10y in its simplest form
Harrizon [31]
4y:5y would be the simplest form 
5 0
3 years ago
Read 2 more answers
Julie has a jewlery box shaped like a cube. The volume of the jewlery box is v cubic inches. Write an
Stolb23 [73]

Answer: ∛v

Step-by-step explanation:

Since we know volume is measured height x width x length, we know the equation we'd use here would be:

___ x ___ x ___ =  v in³

If this was area, we would have ___ x ___ = v in², and it would be easy to find each blank. You would just find the square root of "v", making your answer √v.

When you have 3 things multiplied by each other (that are exactly the same, which is the situation here since this is a cube), you will want to find ∛x (if x is our unknown variable). This means that we are finding ONE-THIRD of the number ... sort of. So if x was equal to 8, then ∛x = 2, because 2 x 2 x 2 = 8.

In our situation here, x = v, and since we don't know the actual number, we will keep it as a square root, so the answer to your question is ∛v.

I really hope I was able to explain easy enough, feel free to ask anything else!

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