Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
Hello! The first thing to do is to find the amount of change by subtracting both numbers. 2.60 - 0.25 is 2.35. Now, we set up a proportion by doing change/original = x/100. With the values plugged in, it would be written like this: 2.35/0.25 = x/100. Cross multiply the values in the proportion. When you do, you get 235 = 0.25x. Now, divide each side by 0.25 to isolate the "x". When you do that, x = 940. The price of gas has gone up 940% since 1930.
Answer:
244.965
Step-by-step explanation:
it is what it is
Answer: A. 1993
Step-by-step explanation: A P E X
I find it best to switch everything exponents when taking derivatives.
F(x) = 7/x
Same as..
F(x) = 7x^-1
Take derivative..
F'(x) = -7x^-2
Plug in x = 1
F'(1) = -7(1)^-2
F'(1) = -7
