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2 years ago

A bicycle wheel is about 26 inches in diameter.find its radius,circumference,and area

2 answers:

7 0

Radius = diameter /2

radius = 13

circumference = pi * diameter
circumference = $26 \pi$

Area = radius^2 * pi
Area = $169 \pi$

PSYCHO15rus [73]2 years ago

3 0

radius=13 area=40.82 circumfrence=8.28025477707

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A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

2 years ago

If g(x)= 4, then g(5x) = ?

Neporo4naja [7]

Answer:

g(5x)= 20

Step-by-step explanation:

g(x)=4 is basically saying that 1 x is equal to 4.

g(5x) wants to know what 5 times 1 x is equal to (5 times 4 (4 is equal to 1 x)

g(5x)= 5(x=4)

g(5x)= 20

4 0

2 years ago

What's the simplest from for 15/72

pychu [463]

Divide them both by three and you will get your answer, which is 5/24

4 0

2 years ago

Mike traveled to Greensboro by car. Going there took 6 hours, and the return trip was four hours. Mike averaged a speed of 81 mi

Marat540 [252]

Answer: 64.8 mph

Step-by-step explanation:

Given

Arriving time is 6 hours

return time is 4 hours

The average speed of returning 81 mph

Distance traveled while returning

$\Rightarrow d=81\times 4=324\ miles$

the average speed of the entire trip is

$\Rightarrow v_{avg}=\dfrac{2\times 324}{6+4}=\dfrac{648}{10}=64.8\ mph$

4 0

2 years ago

What is the equivalent of 243 to the power of (2/5)

nasty-shy [4]

(243)^(2/5) = ?
---
The 5 in the denominator means "take the 5th root".
The 2 in the numerator means "square".

---

Taking the 5th root first you get:
(243)^(2/5) = 3^2
Now squaring gives you
3^2 = 9

So the answer is 9.

Hope this helps :)
~Davinia.

6 0

2 years ago