Answer:
7 cm
Step-by-step explanation:
SA = 208 cm^2
SA= 2*a*b + 2*a*c + 2*b*c
where:
a= first dimension = 2 cm
b= second dimension = 10 cm
c= third dimension
so we have:
208= 2*2*10 + 2*2*c + 2*10*c
208= 40 + 4c + 20c
208-40= 24c
168=24c
c =168/24
c = 7cm = third dimension
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
y'(t) = k√(y(t)) . . . . for some proportionality constant k
y(0) = 30
y(1) = 29
We observe that a function of the form
y(t) = a(t - b)²
will have a derivative that is proportional to y:
y'(t) = 2a(t -b)
We can find the constants "a" and "b" from the given boundary conditions.
At t=0
30 = a(0 -b)²
a = 30/b²
At t=1
29 = a(1 - b)² . . . . . . . . . substitute for t
29 = 30(1 - b)²/b² . . . . . substitute for a
29/30 = (1/b -1)² . . . . . . divide by 30
1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
b = 30 +√870 . . . . . . . . simplify
The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez
<span><span>x2</span>+<span>y2</span>=25</span>
calculus says
<span>2x<span>x′</span>+2y<span>y′</span>=0</span>
and you are told that
<span><span>y′</span>=2</span>
so you know
<span>2x<span>x′</span>+4y=0</span>
or
<span><span>x′</span>=−<span><span>2y</span>x</span></span>
