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:
88.02 ft/s
Step-by-step explanation:
Angle with the horizontal, θ =25°
Initial velocity, v = 60 mph
1 mph = 1.467 ft/s
60 mph = 60 × 1.467 ft/s = 88.02 ft/s
Vertical component, v sin θ = 88.02 sin 25° = 37.2 ft/s
Horizontal component, v cos θ = 88.02 cos 25°= 79.8 ft/s
Answer:
Step-by-step explanation:no you should not
-9x+27=-13
-9x-27=13
-9x=18
-2=x
The function represents exponential growth (since the exponent is positive).
The percentage increase is, if I'm not mistaken, 181.3% (since 710 is just a constant, we don't need to worry about that - it won't affect the growth rate of the function)
Assuming your equation is: -2/5n = -30
-2/5n = -30 <- We get rid of the "/5n" by multiplying each side by 5n
-2 = -30 * 5n
-2 = -150n
-1 = -75n
75n = 1
But this doesn't match up with any of your answers, so if you wouldn't mind giving me the equation again, i'll work it out
