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: 6700 meters
Step-by-step explanation:
From the question given, we are informed that Gephart is traveling from his house to the history museum and that the distance from home to the history museum is six and seven-tenths kilometers.
In order to know the distance in meters
that he will travel to the museum, we have to multiply the convert the distance given in kilometers to meters. This will be:
1000 meters = 1 kilometer
Therefore, 6 7/10km = (6 7/10 × 1000m)
= 6 7/10 × 1000
= 67/10 × 1000
= 67 × 100
= 6700 meters
He'll travel 6700 meters to the museum.
If you need any steps explained lmk
Answer:
Step-by-step explanation:
Since the two triangles are similar, you can use proportions to solve for the value of 
Now, just multiply 4 and 12.
Then divide that by 3.
Therefore, 
.
