Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
The base is 5 because the base = 2 Area/Height
One way in which to approach this problem would be to treat it as an equation of ratios and to cross multiply:
<span>[(4x + 15) / 5x)] = 1/2 could be written as:
4x + 15 1
----------- = ---
5x 2
Then 8x + 30 = 5x
3x = -30, and so x = -10 (answer). Be certain to check this answer through substitution!
</span>
Answer:
98.88
Step-by-step explanation:
Given: They cheered 12 rounds. Each round = 8.24
To find the total number, multiply how much one round is with the total number of rounds.
8.24
× 12
-----------
1648
+ 8240
----------
98.88
Each girl cheered 98.88 minutes. If you need this estimated, the answer would be 99 minutes.
Y - x = 154
let z = xy = x(154 + x) = x^2 + 154x
we need to find the minimum value of z
z' = 2x + 154 which = zero for minm or maxm value
x = -77 and y = 154 -77 = 77
so the 2 numbers are -77 and 77