Find the total surface area of this triangular prism. 10cm 6 cm 4cm 8 cm

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains liters of a dye solution with a

Alja [10]

Answer:

t = 460.52 min

Step-by-step explanation:

Here is the complete question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution

Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.

inflow = 0 (since the incoming water contains no dye)

outflow = concentration × rate of water inflow

Concentration = Quantity/volume = Q/200

outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.

So, Q' = inflow - outflow = 0 - Q/100

Q' = -Q/100 This is our differential equation. We solve it as follows

Q'/Q = -1/100

∫Q'/Q = ∫-1/100

㏑Q = -t/100 + c

$Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c} = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}$

when t = 0, Q = 200 L × 1 g/L = 200 g

$Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}$

We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2

$2 = 200e^{(-t/100)}\\\frac{2}{200} = e^{(-t/100)}$

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

6 0

2 years ago

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere. Wh

viktelen [127]

Answer:

Radius of sphere is 3 units.

Step-by-step explanation:

Volume of sphere is given by $4/3 \pi r^3$

surface area of sphere is given by $4 \pi r^2$

where r is the radius of the sphere.

Given that

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.

we equate formula of Volume of sphere and surface area of sphere

assuming r as the radius.

thus,

$4/3 \pi r^3 = 4 \pi r^2\\\\4/3 \pi r^3/ 4 \pi r^2 = 1\\=>r/3 = 1\\=> r = 3$

Thus, radius of sphere is 3 units.

5 0

2 years ago

Write each situation as a ratio in simplest form. 10 apples and 6 bananas to 3 oranges and 5 grapes.

mojhsa [17]

You only gave 1 situation

5 0

2 years ago

3. Before tax, Louise spent a total of $38 on the items below at Starbucks

soldier1979 [14.2K]

Answer:

47.4%

Step-by-step explanation:

The total amount Louise spent on Frappuccinos was 4×$4.50 = $18. The fraction that is of the total is ...

Fraps/Total = $18/$38 = 9/19

That can be converted to a percentage by multiplying by 100%:

9/19 = (9/19)×100% ≈ 47.4%

Louise spent 47.4% of the $38 on Frappuccinos.

_____

Additional comment

The decimal equivalent of 9/19 is a repeating decimal with an 18-digit repeat.

8 0

1 year ago

Read 2 more answers

Write the equation of the line passing through the points (44,6) and (-4,-6)

Verizon [17]

Answer:

Y = 1/4x - 5

Step-by-step explanation:

Slope (m = y2-y1 / x2-x1) is 1/4 and using one point substituting it instead of x and y you get y - intercept of -5.

Hope this helps. Pls give brainliest.

4 0

2 years ago