Answer:
a) shown
b) h = [sqrt(17) - (5/2)t]²
c) t = 2sqrt(17)/5 seconds
Step-by-step explanation:
V = pi × r² × h
V = pi × 5² × h
V = 25pi × h
a) dV/dt = dV/dh × dh/dt
-5pi × sqrt(h) = 25pi × dh/dt
dh/dt = -sqrt(h)/5
b) 1/sqrt(h) .dh = -5. dt
2sqrt(h) = -5t + c
t = 0, h = 17
2sqrt(17) = 0 + c
c = 2sqrt(17)
2sqrt(h) = -5t + 2sqrt(17)
sqrt(h) = [2sqrt(17) - 5t] ÷ 2
sqrt(h) = sqrt(17) - (5/2)t
Square both sides
h = [sqrt(17) - (5/2)t]²
c) empty: h = 0
0 = [sqrt(17) - (5/2)t]²
sqrt(17) - (5/2)t = 0
(5/2)t = sqrt(17)
t = 2sqrt(17)/5
t = 1.64924225 seconds
sqrt: square root
It'd be easier to do #18 if y ou were to break it up:
14* (first term + 14th term)
Sum from n=1 to 14 of n = S = ---------------------------------
14 2
14(1+14)
= ---------------- = 7(15) = 105
2
The sum of twice that is 210. The sum of "1 from n=1 to n=14" is just 14.
The final sum is 210 + 14 = 224 (answer)
It's the zero in the tenth place
1:4 because both numbers can be divided by 64.
