The figure below is an isosceles trapezoid. If m∠K=73, find the missing angle

What is the <br> Number that the are talking about

anzhelika [568]

i can't comment so someone else is going to have to answer

but they need the whole page to answer this question.

4 0

3 years ago

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

2 years ago

An arithmetic sequence has t1 = 6 and common difference 2 find t12 and s12

Sergeeva-Olga [200]

Answer:

See below ~

Step-by-step explanation:

Finding t₁₂ :

⇒ t₁₂ = t₁ + 11d

⇒ t₁₂ = 6 + 11(2)

⇒ t₁₂ = 6 + 22

⇒ t₁₂ = 28

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

Finding S₁₂ :

⇒ S₁₂ = 12/2 × 2t₁ + (12 - 1)d

⇒ S₁₂ = 6 × 2(6) + 11(2)

⇒ S₁₂ = 6 × 12 + 22

⇒ S₁₂ = 6 × 34

⇒ S₁₂ = 204

4 0

1 year ago

How Do You Do This ? Please show work .

snow_tiger [21]

So basically you are going to line up your equations (already done). Next, you will just add each term. So x + 3x = 4x, then 2y - 2y = 0 (we wouldn't put anything) then 7 - 3 = 4
So then we have all of our terms figured out and will have 4x = 4 then divide 4x by 4 to get x alone and then you will also divide the four that is by itself by four to equal one. So, your answer is x = 1. I hope that helps!

5 0

3 years ago

Which perfect square equation represents x2+8x+11=0 by completing the square?

alexandr1967 [171]

Answer:

Solve the equation for x by finding a , b , and c

of the quadratic then applying the quadratic formula.

Exact Form:

x = − 4 ± √ 5

Decimal Form: x = − 1.76393202 … , − 6.23606797 …

7 0

2 years ago

The figure below is an isosceles trapezoid. If m∠K=73, find the missing angle​

The figure below is an isosceles trapezoid. If m∠K=73, find the missing angle