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3 years ago

What is the expression in radical form?

Mathematics

1 answer:

BabaBlast [244]3 years ago

3 0

Answer:

32x^9y^6/5

Step-by-step explanation:

Factor (4x^3y^2)^3 and get 2^6(x^3)^3(y^2)^3

Factor 10: 2 x 5

Then get 2^6(x^3)^3(y^2)^3/2 x 5

Cancel the common factor, 2

2^5(x^3)^3(y^2)^3/5

(x^3)^3=x^9

2^5x^9(y^2)^3/5

(y^2)^3=y^6

2^5x^9y^6/5

2^5=32

32x^9y^6/5

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A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from th

jeyben [28]

Consider a circle with radius $r$ centered at some point $(R+r,0)$ on the $x$ -axis. This circle has equation

$(x-(R+r))^2+y^2=r^2$

Revolve the region bounded by this circle across the $y$ -axis to get a torus. Using the shell method, the volume of the resulting torus is

$\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx$

where $2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}$ .

So the volume is

$\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx$

Substitute

$x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt$

and the integral becomes

$\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt$

Notice that $\sin t\cos^2t$ is an odd function, so the integral over $\left[-\frac\pi2,\frac\pi2\right]$ is 0. This leaves us with

$\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt$

Write

$\cos^2t=\dfrac{1+\cos(2t)}2$

so the volume is

$\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}$

6 0

3 years ago

Ughhh please helpppp!!!!

Rom4ik [11]

Answer:

$\frac{2}{3}$

Step-by-step explanation:

4 : 6 = 2/3

8/3 : 4 = 2/3

16/9 : 8/3 = 2/3

4 0

2 years ago

Help!

alexira [117]

Answer:

410 student and 436 adult tickets

Step-by-step explanation:

x is the number of student tickets and y is the number of adult tickets sold. we now that a total of 846 tickets were sold so x+y=846=>x=846-y. we also now that their worth was 3 846usd so 3*x+6*y=3846. we substitute x and are left with the following equation:3x+6*(846-x)=3846

5076-3x=3846

3x=1230

x=410

=>y=846-410=436

4 0

2 years ago

Please Simplify 60/105 to lowest form

svlad2 [7]

4/7. Divide the numerator and denominator by 15.

7 0

3 years ago

What is the missing statement for step 7 in this proof? A. ΔDGH ≅ ΔFEH B. ΔGHF ≅ ΔEHD C. ΔDGF ≅ ΔFED D. ΔDEF ≅ ΔEDG

sergij07 [2.7K]

Answer:

A. ΔDGH ≅ ΔFEH

Step-by-step explanation:

We are given the proof of GH ≅ EH and DH ≅ FH.

Now, previous to step 7, we have obtained,

Step 5: ∠HGD ≅ ∠HEF and ∠HDG ≅ ∠HFE

Step 6: DG ≅ EF as opposite sides of a parallelogram are congruent.

Since, we have that two angles of the triangles are congruent and their including sides are also congruent.

Thus, by Step 7 i.e. ASA criterion for congruence, we get that the corresponding triangles are also congruent.

Hence, we get, ΔDGH ≅ ΔFEH.

Step-by-step explanation:

7 0

3 years ago