Answer:
<h2>√512 by √512 </h2>
Step-by-step explanation:
Length the length and breadth of the rectangle be x and y.
Area of the rectangle A = Length * breadth
Perimeter P = 2(Length + Breadth)
A = xy and P = 2(x+y)
If the area of the rectangle is 512m², then 512 = xy
x = 512/y
Substituting x = 512/y into the formula for calculating the perimeter;
P = 2(512/y + y)
P = 1024/y + 2y
To get the value of y, we will set dP/dy to zero and solve.
dP/dy = -1024y⁻² + 2
-1024y⁻² + 2 = 0
-1024y⁻² = -2
512y⁻² = 1
y⁻² = 1/512
1/y² = 1/512
y² = 512
y = √512 m
On testing for minimum, we must know that the perimeter is at the minimum when y = √512
From xy = 512
x(√512) = 512
x = 512/√512
On rationalizing, x = 512/√512 * √512 /√512
x = 512√512 /512
x = √512 m
Hence, the dimensions of a rectangle is √512 m by √512 m
Answer:
(6^-4)^-4, (6^-2)^-8, (6^8)^2
Answer:
Step-by-step explanation:
When we solve for an equation, our goal is to find the value of the variable. Any variable can be used, but for the time being let’s assume we use 
.
We can algebraeically solve equations until we get the value of x - in which we will have x equal to something.
Say we have the equation 
. Our goal is to find the value of . <u>We can do this by getting x isolated on one side so we have something equal to x</u>.
We can subtract 5 from both sides and divide both sides by 5.
We now know the value of since it’s on one side of the equation.
Hope this helped!
