find the volume of 4ft by 2ft by 3ft rectangular prism with a cylinder hole, radius 6 in., through the center

1 answer:

7 0

Just subtract the volume of the cylinder from the volume of the rectangular prism.

Volume of rectangular prism = l x w x h = 4 x 2 x 3 = 24 ft^3
Volume of cylinder = pir^2h = pi*(6/12)^2*3 = 3/4 pi

Thus the volume would be

24 - 3/4 pi = 21.64 ft^3.

The volume would be 21.64 ft3

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A parabola is graphed such that the axis of symmetry is x = 3. One of the x-intercepts is (5, 0). What is the other x-intercept?

Stells [14]

The axis of symmetry is the fold line that splits the parabola down the middle.

Now, since a parabola is symmetrical, every point, except the vertex, will have a mirror image of another point if we folded the parabola over the axis of symmetry.

So if we know the axis of symmetry is x = 3 and one of our points

has the coordinates (5, 0), the other point will have the coordinates (3, 0).

The axis of symmetry is always halfway between the x-intercepts.

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How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) =

rjkz [21]

The transformed equation $g(x)=\frac{1}{x+4}-6$ , the graph is shifted 4 units to the left and 6 units down.

Explanation:

The parent equation is $f(x)=\frac{1}{x}$

The transformed equation is $g(x)=\frac{1}{x+4}-6$

By using the function transformation rules, we can see that the parent function $f(x)=\frac{1}{x}$ is transformed into the function $g(x)=\frac{1}{x+4}-6$

Since, from the function transformation rules, we know that,

$f(x+b)$ shifts the function b units to the left.