Answer:
Part 1) 
Part 2) 
Step-by-step explanation:
we know that
The volume of a cube is equal to

where
s is the length of the cube
Part 1)
we have

substitute in the formula


Part 2)
we have

substitute in the formula


Answer:
She should make a rectangle with dimensions 14.4 cm by 4.2 cm.
Step-by-step explanation:
- The diagonal of a rectangle is represented by
. - Area of rectangle is = length×width
- Perimeter of a rectangle = 2(length+width).
Assume x be the width of the rectangle.
The length of the rectangle is to be 6 cm more than twice the width.
The length of the rectangle is= (2x+6) cm
Then the diagonal of the rectangle is 


cm
According to the problem,

Squaring both sides




⇒5x²+45x-21x-189=0
⇒5x(x+9)-21(x+9)=0
⇒(x+9)(5x-21)=0
⇒x+9=0 or, 5x-21=0

⇒x= -9, 4.2
Since the width of a rectangle can not negative.
So, x=4.2 cm
The width of rectangle is = 4.2 cm
The length of the rectangle is =(2×4.2+6)
=14.4 cm
She should make a rectangle with dimensions 14.4 cm by 4.2 cm.
Answer:
The second one I think
Step-by-step explanation:
Answer:
x=6
Step-by-step explanation:
81^x = 27 ^(x+2)
81 = 3^4 and 27 =3^3 so replace 81 and 27 in the equation
3^4^x = 3^3^(x+2)
When we have a power to a power we can multiply the exponents
a ^b^c = a^(b*c)
3^(4x) = 3^(3*(x+2))
Since the bases are the same, the exponents have to be the same
a^b = a^c means b=c
4x = 3(x+2)
Now we can solve for x
Distribute
4x = 3x+6
Subtract 3x from each side
4x-3x = 3x-3x+6
x = 6