Step-by-step explanation:
radius of sphere, rs
radius of cylinder, rc
height of cylinder, h
given: h = rs = rc =r..eq1
volume of cylinder, vc = 27pi ft...eq2
volume of cylinder, vc = pi × rc^2 × h...eq3
volume of sphere, vs = 4/3(pi×rs^3)...eq4
subst for h & rs from eqn 1 in eqn 3...
vc = pi x r^2 x r= pi x r^3...eqn 5
subst for vc from eqn 2 in eqn 5...
=> 27 pi ft = pi x r^3
=> 27 = r^3
=> r = 3ft...eqn 6
subst for rs from eqn 1 in eqn 4
vs = 4/3 (pi x r^3)...eqn7
subst for pi x r^3 from eqn 5 in eqn 7
vs = 4/3 vc = 4/3 (27pi ft) = 36 pi ft
n=2
8+8(8-n)=40+8n (distribute 8 through the parenthesis)
8+64-8n=40-8n (add the numbers)
<em>72-</em>8n=40+8n (move the variable to the left side and change its sign)
<em>72</em><em>-</em>8n+8n=40
-8n+8n=40<em>-72</em> (connect like terms)
-16n = -32 (divide both sides by -16)
<u><em>n=2</em></u>
Answer:
The base is decreasing at 2 cm/min.
Step-by-step explanation:
The area (A) of a triangle is given by:
(1)
Where:
b: is the base
h: is the altitude = 10 cm
If we take the derivative of equation (1) as a function of time we have:
We can find the base by solving equation (1) for b:
Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:
Therefore, the base is decreasing at 2 cm/min.
I hope it helps you!
Answer: B
just make the included side equal
