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4 years ago

Jack is 4 times as old as lacy. 4 years ago the sum of their ages was 22. How old are they now

Mathematics

1 answer:

r-ruslan [8.4K]4 years ago

3 0

4 x 22 =?

the question mark is how old they'll be.

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What Is the percent equal to 3/10

lianna [129]

30 %
3/10 * 10 = 30/100
30/100= 30%

6 0

3 years ago

Find x. Give reasons to justify your solution

katrin [286]

Answer: x = 28

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

Explanation:

The angles COE, EOF, and FOB combine to form angle COB

angle COB = (angleCOE)+(angleEOF)+(angleFOB)

angle COB = (3x)+(x)+(x+12)

angle COB = 5x+12

----------

Angles AOD and COB are vertical angles, so they are congruent

angle COB = angle AOD

5x+12 = 152

5x = 152-12

5x = 140

x = 140/5

x = 28

7 0

3 years ago

What is the actual distance of 23cm

Vera_Pavlovna [14]

Answer:

23 cm = 0.23 m or 9.055118 inches

Step-by-step explanation:

5 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

3 years ago

A rectangular tank with a square base, an open top, and a volume of 8 comma 7888,788 ft cubedft3 is to be constructed of sheet

Vlad [161]

Answer:

26 ft square by 13 ft high

Step-by-step explanation:

The tank will have minimum surface area when opposite sides have the same total area as the square bottom. That is, their height is half their width. This makes the tank half a cube. Said cube would have a volume of ...

2·(8788 ft^3) = (26 ft)^3

The square bottom of the tank is 26 ft square, and its height is 13 ft.

_____

<em>Solution using derivatives</em>

If x is the side length of the square bottom, the height is 8788/x^2 and the area is ...

x^2 + 4x(8788/x^2) = x^2 +35152/x

The derivative of this is zero when area is minimized:

2x -35152/x^2 = 0

x^3 = 17576 = 26^3 . . . . . multiply by x^2/2, add 17576

x = 26

_____

As the attached graph shows, a graphing calculator can also provide the solution.

5 0

3 years ago