Answer: 90.51 square units
Explanation:
1) The rectangle has one length on the x-axis.
2) Call x, the x-coordinate of the right lower corner of the rectangle.
And the point is (x,0)
3) The x-coordinate of the lef lower corner will be - x.
And the point is (-x,0)
4) The right upper point of the rectangle will be (x,y) where y = 24 - x²
5) The left upper point of the rectangle will be (-x,y) where y = 24 - x² .
6) The area of such rectantle is the length of the base times the length of the height.
The length of the base is 2x
The lenght of the height is y
So, the area is A = 2x(y) = 2x(24 - x²) = 48x - 2x³
7) Now to find the maximum area you have to derivate the function and make it equal to zero:
dA
---- = A' = 48 - 6x² = 0 =>
dx
4x² = 48 => x² = 48/6 = 8 =>
x = (+/-)√8
Then, y = 24 - x² = 24 - (√8)² = 24 - 8 = 16
8) Therefore the area of the rectangle is
A = 2x(y) = 2(√8)(16) = 90.51.
9) You can see if x is a greater or smaller.
For example x = 2 and x = 3
x = 2 => y = 24 - (2)² = 20 => A = 2(2)(20) = 80 which is less than 90.51
x = 3 => y = 24 - (3)² = 15 => A = 2(3)(15) = 90 which is less than 90.51
So, that tells you that your result should be right.
Answer:
<h2>The slope of the line tangent to the function at x = 1 is 2.01 ≅2.</h2>
Step-by-step explanation:
Using the formula of derivative, it can be easily shown that, 
where 
.
Here we need to show that as per the instructions in the given table.
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = 
.
In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.
Hence, dividing Δy by Δx, we get, 
.
Let's examine this taking a smaller value.
If we take Δx = 0.001, then Δy = 
.
Thus, 
.
The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.
Both of them add up to 34!
I hope this helps.
Have a "AWESOME" day! :)
Answer:
n=m-18. Please Please Please Mark it as brainlist answer. Please I request to Mark it as brainlist answer..
Decrease = (original number - new number) / original number .....x 100
decrease = (49 - 22) / 49.....* 100 =
(27 / 49) * 100 =
2700 / 49 = 55% decrease
