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
Answer:
g(z-1)
Step-by-step explanation:
Answer:
There needs to be 300 liters of Drink A and 270 liters of Drink B
Step-by-step explanation:
Let a = the amount of Drink A and b = the amount of Drink B
Multiplying a number by 0.2 is the same as calculating 20% of it and same goes with 15% and 0.15. This makes our equation for the amount of fruit juice:
0.2a + 0.15b = 100.5
We know what the difference between a and b will be 30 liters so:
a - b = 30
Now we have our system of equations
To cancel out a, we can multiply the first equation by -5 so we will now have:
-a - 0.75b = -502.5
a - b = 30
Adding these two equations together, we get:
-1.75b = -472.5
Both sides are negative, so we can take the negative signs away.
1.75b = 472.5
Now divide both sides by 1.75
b = 270
Plugging 270 into b, we have:
a - b = 30
a - 270 = 30
Add 270 to both sides
a = 300
There needs to be 300 liters of Drink A and 270 liters of Drink B
