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:
(y + 7i)(y - 7i)
Step-by-step explanation:
It cannot be factored using real numbers, but consider
7i × - 7i
= -49i² and i² = - 1
= 49
The factoring as a difference of squares to obtain
y² + 49 = (y + 7i)(y - 7i)
I think this problem is 3
Consecutive numbers mean in order from smallest to largest, therefore, 7, 8, 9, would be the answer. 7+8+9=24.
Well, you would divide 4.20/6 to find the price of just 1 muffin. 4.20/6 is 0.7, meaning that the price for one muffin is 70 cents.
