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3 years ago

How would you match these up?

Mathematics

1 answer:

TEA [102]3 years ago

5 0

<h3>Answer: Bottom right corner (ie southeast corner)</h3>

This 3D solid is a strange sideways bowl shape. Each cross section is a ring to show the empty space.

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Explanation:

Check out the diagram below. The graph was created with GeoGebra. We have y = x^2 in red and x = y^2 in blue.

The gray region is the region between the two curves. We spin this gray region around the horizontal green line y = 1 to generate the answer mentioned above.

Note how (1,1) is a fixed point that does not move as this is on the line y = 1. Every other point moves to sweep through 3D space to create the solid figure. One way you can think of it is to think of propeller blades. Or you can think of a revolving door (the door is "flat" so to speak, but it sweeps out a 3D solid cylinder).

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Because you want to prepare and serve the healthiest food possible you monitor the fat and calorie continent of items on your me

zavuch27 [327]

If there's a graph, maybe I could help...?

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2 years ago

Y = (1/4)x^2 - (1/2)lnx..over the interval (1, 7e) ...what is the arc length ?

xenn [34]

So, f[x] = 1/4x^2 - 1/2Ln(x)
<span>thus f'[x] = 1/4*2x - 1/2*(1/x) = x/2 - 1/2x </span>
<span>thus f'[x]^2 = (x^2)/4 - 2*(x/2)*(1/2x) + 1/(4x^2) = (x^2)/4 - 1/2 + 1/(4x^2) </span>
<span>thus f'[x]^2 + 1 = (x^2)/4 + 1/2 + 1/(4x^2) = (x/2 + 1/2x)^2 </span>
<span>thus Sqrt[...] = (x/2 + 1/2x) </span>

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3 years ago

Give the location of Berlin as an ordered pair X, Y

shusha [124]

The coordinates are based on two factors: the x coordinate and the y-coordinate.

The x coordinate is the position of the coordinate horizontally.

The y coordinate is the position of the coordinate vertically.

Berlin is at x-coordinate of 7 and y-coordinate of 8.

Thus the whole coordinate for Berlin is (7,8).

Hope that helped!

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2 years ago

The pythagorean theorem is true for some right triangles but not all

horrorfan [7]

The pythagorean theorem works for all right triangles. Just make sure it IS a right triangle.

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3 years ago

Read 2 more answers

We want to find the maximum and minimum values of f(x, y) = 10x2 + 11y on the disk D: x2 + y2 < 1.

dolphi86 [110]

If you're just focusing on the boundary, it's the circle $x^2+y^2=1$ . Parameterize it by taking $x=\cos t$ and $y=\sin t$ , with $0\le t\le2\pi$ . Then $f(x,y)$ reduces to a univariate function $g(t)$ :

$f(x,y)=10x^2+11y\iff g(t)=f(\cos t,\sin t)=10\cos^2t+11\sin t$

Then you can find any extrema on the boundary by checking the critical points of $g$ .

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3 years ago