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4 years ago

What is -2+2/3w=10 100 pts for this one

Mathematics

2 answers:

Oliga [24]4 years ago

5 0

Answer:

$w=18$

Step-by-step explanation:

we have

$-2+\frac{2}{3}w=10$

solve for w

That means ----> Isolate the variable w

Multiply both sides by 3 to remove the fraction in the left side

$-2(3)+\frac{2}{3}w(3)=10(3)$

$-6+2w=30$

Adds 6 both sides

$-6+2w+6=30+6$

$2w=36$

Divide by 2 both sides

$2w/2=36/2$

$w=18$

DedPeter [7]4 years ago

4 0

Answer:

w=18

Step-by-step explanation:

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Butoxors [25]

Answer:

a. 24.12 ft³/hr b. 0.0768 ft/hr

Step-by-step explanation:

a. Find the rate at which the volume of water in the pool is increasing at time t=6 hours.

The net rate of change of volume of the cylinder dV/dt = volume flow rate in - volume flow rate out

Since volume flow rate in = P(t) and volume flow rate out = R(t),

dV/dt = P(t) - R(t)

$\frac{dV}{dt} = P(t) - 18e^{0.04t}$

We need to find the rate of change of volume when t = 6.

From the table when t = 6, P(6) = 47 ft³/hr

Also, substituting t = 6 into R(t), we have R(6)

$\frac{dV}{dt} = P(t) - 18e^{0.04t}$

$\frac{dV}{dt} = 47 - 18e^{0.04X6}\\\frac{dV}{dt} = 47 - 18e^{0.24}\\\frac{dV}{dt} = 47 - 18 X 1.27125\\\frac{dV}{dt} = 47 - 22.882\\\frac{dV}{dt} = 24.118 ft^{3}/hr$

dV/dt ≅ 24.12 ft³/hr

So, the rate at which the water level in the pool is increasing at t = 6 hours is 24.12 ft³/hr

b. How fast is the water level in the pool rising at t=6 hours?

Since the a rate at which the water level is rising is dV/dt and the volume of the cylinder is V = πr²h where r = radius of cylinder = 10 ft and h = height of cylinder = 5 feet

dV/dt = d(πr²h)/dt = πr²dh/dt since the radius is constant and dh/dt is the rate at which the water level is rising.

So, dV/dt = πr²dh/dt

dh/dt = dV/dt ÷ πr²

Since dV/dt = 24.12 ft³/hr and r = 10 ft,

Substituting the values of the variables into the equation, we have that

dh/dt = dV/dt ÷ πr²

dh/dt = 24.12 ft³/hr ÷ π(10 ft)²

dh/dt = 24.12 ft³/hr ÷ 100π ft²

dh/dt = 0.2412 ft³/hr ÷ π ft²

dh/dt = 0.2412 ft³/hr

dh/dt = 0.0768 ft/hr

So, the arate at which the water level is rising at t = 6 hours is 0.0768 ft/hr

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