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:
She has 28 pennies
Step-by-step explanation:
Janae has 280 dimes in her piggy bank she has 10 times as many pennies .
If she has 280 dimes in piggy bank
And has 10 times as many pennies
Let dimes= x
Let pennies= y
X= 10y
But x= 280
280= 10y
280/10 = y
28 = y
She has 28 pennies
Answer:
cost of one medium drink = $3.80
cost of one large popcorn = $6.25
Step-by-step explanation:
Let D = cost of one medium drink
Let P = cost of one large popcorn
If a couple bought 2 medium drinks and a large popcorn for $13.85:
⇒ 2D + P = 13.85
If a family bought 3 medium drinks and 2 large popcorn for a total of $23.90:
⇒ 3D + 2P = 23.90
Rewrite 2D + P = 13.85 to make P the subject:
⇒ P = 13.85 - 2D
Substitute into 3D + 2P = 23.90 and solve for D:
⇒ 3D + 2(13.85 - 2D) = 23.90
⇒ 3D + 27.7 - 4D = 23.90
⇒ D = 3.8
Substitute found value of D into P = 13.85 - 2D to find P:
⇒ P = 13.85 - (2 x 3.8) = 6.25
Therefore,
cost of one medium drink = $3.80
cost of one large popcorn = $6.25
V(18-1811) también eres el mejor en la vida y tú me ganas de comer
