Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.

Mathematics

1 answer:

kirza4 [7]3 years ago

8 0

Just take the second slot which is -3

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A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?

NeTakaya

A point (a, b) in the second Quadrant, is any point where a is negative and b is positive.

For example (-3, 5), (-189, 14) etc are all points in the 2.Quadrant

Rotating a point P(x, y) in the second Quadrant 180° counterclockwise, means rotating 180° counterclockwise about the origin, which maps point P to P'(-a, -b) in the fourth Quadrant.

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3 years ago

A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (ha

Neko [114]

Answer:

Volume: $\frac{2}{3}\pi r^3$

Ratio: $\frac{2}{9}r$

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

where

r is the radius of the sphere

V is the volume

Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is