Since the two cylinders are congruent, it means that their dimensions are exactly the same thing.
In other words, the radius of cylinder 1 is the same as that of cylinder 2, and the height of cylinder 2 is the same as that of cylinder 1. This is what it means for two solid shapes to be congruent.
Now, to find the volume of cylinder 2, we apply the frmula for the volume of a tyical cylnder:
Now,
radius of cylinder 2 = radius of cylinder 1 = 3
height of cylinder 2 = 8
Thus: r = 3, h= 8
Therefore:
Therefore the volume of cylinder 2 is 72pi cubic units (Option D)
You get the hypothenuse by doing √a²+b² = c
So....
Square both terms
x² + (3x+3)² = 625
x² + 9x² + 18x + 9 - 625 = 0
10x² + 18x - 616 = 0
x₁,₂ = (-b±√Δ)/2a
Δ = b²-4ac
You call a 10, b 18 and c -616
x1,2 = (-18±√18²-4*10*-616)/2*10
x1,2 = (-18±√324+24640)/20
x1,2 = (-18±√24964)/20
x1,2 = (-18<span>±158)/20
x1 = -18+158/20 = 140/20 = 7
x2 = (-18-158)/20 = -176/20 = -44/5
Pick the first solution
So one leg is 7 and the other is 3(7+1) = 3(8) = 24
Let's verify </span>√24²+7² = √576+49 = √625 = 25
The derivative of f(x) at x=3 is 2x=6 approaching from the left side (apply power rule to y=x^2). The derivative of f(x) at x=3 is m approaching from the right side. In order for the function to be differentiable, the limit of derivative at x=3 must be the same approaching from both sides, so m=6. Then, x^2=mx+b at x=3, plug in m=6, 9=18+b, so b=-9.
First, let's reduce our fractions to their simplest forms.
4/5 is already in its simplest form
16/20 = 4/5.
Now that both of por fractions are in their simplest forms, let's compare them.
4/5 is equal to 4/5
D is the correct answer.
25% is the same as a quarter (as a fraction) so you can simply divide 2536 by 4:
2536/4 = 1268/2 = 634