1) Graph f(x) = |x|
Observe that y = 2|x - 2| + 5 = 2f(x) + 5
So, these are the transformation rules that you can use:
2) shift the graph 2 units to the rigth: because |x - 2| is f(x - 2)
3) dilate the function (stretch vertically) multiplying by 2
4) shift the graph 5 units upward: because adding a constant to the function moves the graph upward the same amount of units as the value of the constant.
Answer:
228 cm²
Step-by-step explanation:
The volume of a cylinder of radius r and height h is given by ...
V = πr²·h
Filling in the given information, we can solve for r:
235.5 = π·r²·12
√(235.5/(12π)) = r ≈ 2.49937 . . . . cm
The area of a cylinder is given by ...
A = 2πr² + 2πrh = 2πr(r +h)
Filling in the radius and height, we can find the area to be ...
A = 2π·2.49937·(2.49937 +12) ≈ 227.698 . . . . cm²
About 228 cm² of aluminum are required to make a typical soda can.
Answer:
4/5
Step-by-step explanation:
Short and Sweet Have a good day :D
Answer:
125/6(In(x-25)) - 5/6(In(x+5))+C
Step-by-step explanation:
∫x2/x1−20x2−125dx
Should be
∫x²/(x²−20x−125)dx
First of all let's factorize the denominator.
x²−20x−125= x²+5x-25x-125
x²−20x−125= x(x+5) -25(x+5)
x²−20x−125= (x-25)(x+5)
∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx
x²/(x²−20x−125) =x²/((x-25)(x+5))
x²/((x-25)(x+5))= a/(x-25) +b/(x+5)
x²/= a(x+5) + b(x-25)
Let x=25
625 = a30
a= 625/30
a= 125/6
Let x= -5
25 = -30b
b= 25/-30
b= -5/6
x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)
∫x²/(x²−20x−125)dx
=∫125/6(x-25) -∫5/6(x+5) Dx
= 125/6(In(x-25)) - 5/6(In(x+5))+C
