Question

Can someone explain this to me please.....

Answer 1

Explanation:

1. Perimeter of the rectangle= 2(l+b)

=
`2(4√(2)+5+√(6))`

=
`2(4(1.41)+5+2.44)`

=
`2(5.64+5+2.44)`

=
`2(13.08)`

=
`26.16`

2. The given equation is:

`4\sqrt[3]{3}(7+6\sqrt[3]{9})`

`4(1.44)(7+6(2.08))`

=
`5.768(7+12.48)`

=
`5.768(19.48)`

=
`112.36`

3. Area of the circle=
`{\pi}r^(2)`

`100{\pi}={\pi}r^(2)`

`r=10 feet`

Thus, the radius of the circle is 10 feet.

4. Volume of the cube=
`s^(3)`

`1536=s^(3)`

`s=11.53 in`

Thus, side length of the cube is=11.53 inches.

5. The given equation is:

`\sqrt[4]{2p+2}=3`

Squaring twice the both sides, we get

`2p+2=81`

`2p=79`

`p=39.5`

Thus, the value of p is 39.5.

Answer 2

1.

Perimeter of a rectangle is given by:

`P=2(l+b)`

Given:

Length of a rectangle(l) =
`4√(2)` unit and a width(w) of a rectangle =
`5+√(6)` units.

then;

`P= 2(4√(2)+5+√(6)) = 8√(2)+10+2√(6) = 10+8√(2)+2√(6)` units.

Therefore, the perimeter of a rectangle is
`10+8√(2)+2√(6)` units.

2.

Simplify:
`4\sqrt[3]{3}(7+6\sqrt[3]{9)}`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

then;

`28\sqrt[3]{7} + 36\sqrt[3]{27}`

`28\sqrt[3]{7} + 36 \cdot 3 = 28\sqrt[3]{7} + 108`

Therefore, the simplified given expression is,
`28\sqrt[3]{7} + 108`

3.

Area of a circle(A) is given by:

`A = \pi r^2` where r is the radius of the circle.

Given: Area of circle =
`100 \pi` square feet

then;

`100 \pi = \pi r^2`

⇒
`100 = r^2`

Simplify:

`r = √(100) = 10` ft.

Therefore, the radius of the circle is 10 ft.

4.

Volume of a cube is given by:

`V = s^3` where s is the side length of a cube.

Given: Volume of a cube = 1536 cubic inches.

Substitute the given value to find s;

`1536 = s^3`

Simplify:

`s=\sqrt[3]{1536} inches`

Therefore, the length of side of a cube is, 11.54 inches.

5.

Solve:
`\sqrt[4]{2p+2} = 3`

then;

`2p+2 = 3^4`

2p+2 = 81

Subtract 2 from both sides we get;

2p = 79

Divide 2 both sides we get;

p = 39.5

Therefore, the value of p is 39.5.