Rewrite the expression with rational exponents as a radical expression.

Mathematics

1 answer:

Jlenok [28]3 years ago

6 0

Answer:

(cube√7x)^2

see above

(√7x)^3

(7√x)^3

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Maria want to make a footstool in the shape of a cylinder, as show below. She wants to fill the footstool with foam and cover it

dexar [7]

Answer:

She'll need 8143 cubic inches of foam and 1,809.6 square inches of fabric.

Step-by-step explanation:

Assuming you want to know how much foam and fabric she will need...

First the foam... so we need to determine the volume of that footstool. The Volume of a cylinder is given by:

V = π * r² * h

So, we plug in the numbers:

V = π * 12² * 18 = π * 144 * 18

V = 2,592 π = 8143 cubic inches.

Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.

The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool. The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.

So the lateral surface of the cylinder is:

LS = 18 * 75.14 = 1,357.2 sq inches.

Then we need to calculate the area of the top... which is easy:

A = π * r² = π * 12² = 144 π = 452.4 sq inches

So, to cover the lateral side of the footstool and its top, she needs to use:

TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.

8 0

3 years ago

Fine the area of the shaped trapezium in the rectangle below

Ksenya-84 [330]

At first find the area of rectangle:
(x + 4)*(x + 1) = x^2 + 5x + 4
Then find the area of triangle:
$\frac{(x+1)(x-3)}{2} = \frac{x^2-2x-3}{2}$
Then you must do like this
Area of rectangle - Area of triangle = Area of the shaded
x^2+5x+4 - ( $\frac{x^2-2x-3}{2}$ )