Anwer: draw a square with side length equal to the square root of the area of the rectangle.
Explanation:
The rectangle that has the greatest perimeter given a fixed area is the square.
So, take the square root of the area and draw a square with that side length.
The demostration of that is done using the optimization concept from derivative. If you already studied derivatives you can follow the following demostration.
These are the steps:
1) dimensions of the rectangle:
length: l
width: w
perimeter formula: p = 2l + 2w
area formula: A = lw
2) solve l or w from the area formula: l = A / w
3) write the perimeter as a function of w:
p = 2 (A / w) + 2w
4) find the derivative of the perimeter, dp / dw = p'
p' = - 2A / w^2 + 2
5) The condition for optimization is p' = 0
=> -2A / w^2 + 2 = 0
=> 2A / w^2 = 2
=> w^2 = A
Which means that the dimensions of the rectangle are w*w, i.e. it is a rectangle of side length w = √A
The 2 to the power of 2 add the 4 will be in the parenthesis. This is just a tip for you, just try the parenthesis where you think is right and do the math. If it is not right then move the parenthesis.
Answer:
(96/5) mph, or 19.2 mph
Step-by-step explanation:
Average speed = (total distance traveled) / (total time elapsed)
Here we need to calculate the two elapsed times (going and returning)
Going: t1 = d/(24 mph)
Returning: t2 = d/(16 mph)
Less time is required for the outward bound trip.
16d + 24d
Total time elapsed: t = t1 + t2 = d/24 + d/16 = ------------------- = (5/48)*d hr
16*24
Thus, the average speed is (total distance traveled) / (total elapsed time)
2d
which here is --------------------- = (96/5) mph, or 19.2 mph
(5/48)d
Answer: d) (3, 3)
<u>Step-by-step explanation:</u>
Inverse is when you swap the x's and y's.
Let's look at the points and find their inverse:
f(x) f⁻¹(x)
(0, -2) --> (-2, 0)
(1, -1) --> (-1, 1)
(2, 0) --> (0, 2)
(3, 3) --> (3, 3) f(x) = f⁻¹(x) so this is where they intersect!
The sum of all 3 angles in a triangle is 180
180-44=136
And you know that angle A is over 90 degrees so I believe it is 100 leaving angle b to be 36