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:
21 roses
Step-by-step explanation:
49 / 7 = 7
Each friend got 7 roses.
7 x 3 = 21
3 friends combine their roses together, making a bouquet of 21 roses.
Answer:
4p +2
Step-by-step explanation:
(2p + 1)(2)
Distribute
2p * 2 + 1*2
4p +2
Split it into 2 equations
2x-9 = 7
2x = 16
x = 8
And another equation
2x-9 = -7
2x = 2
x = 1
The answer is x =1, x= 8
A. So we know that a 6 foot figure casts a shadow 4 feet long. 4 foot shadow x 5 = a 20 foot shadow. So this means we take 6 x 5 = 30, and the tree is 30 feet tall.
B. 30 - 6 = 24 feet taller than Frank
