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3 years ago

Find the height of the rectangular prism given the volume, length, and width.

1 answer:

6 0

The answer is 70cm for the height because you would multiply 50cm x 35cm and you would get 1750. Then you would divide that by 122,500 and you will get the height

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when you subtract one negative integer from another, will your answer be greater or less than the integer you started with

vivado [14]

Lets find out...

-5 - (-2) = -5 + 2 = -3....-3 is greater then -5
-1 - (-3) = -1 + 3 = 2.....2 is greater then -1
-4 - (-2) = -4 + 2 = -2...-2 is greater then -4

so it looks like it is going to be greater then the number u started with.

6 0

3 years ago

A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solu

frutty [35]

Answer:

a. $m(t) = 26.67 - 26.67e^{-0.03t}$ b. 7.44 s

Step-by-step explanation:

a. If the concentration of salt in the brine entering the tank is 0.2 kg/L, determine the mass of salt in the tank after t min.

Let m(t) be the mass of salt in the tank at any time, t.

Now, since a brine solution flows in at a rate of 4 L/min and has a concentration of 0.2 kg/L, the mass flowing in per minute is m' = 4 L/min × 0.2 kg/L = 0.8 kg/min

Now, the concentration in the tank of volume 100 L at any time, t is m(t)/100 L. Since water flows out at a rate of 3 L/min, the mass flowing out per minute is

m(t)/100 × 3 L/min = 3m(t)/100 kg/min

Now the net rate of change of mass of salt in the tank per minute dm/dt = mass flowing in -mass flowing out

dm/dt = 0.8 kg/min - 3m(t)/100 kg/min

So, dm/dt = 0.8 - 0.03m(t)

The initial mass of salt entering m(0) = 0 kg

dm/dt = 0.8 - 0.03m(t)

separating the variables, we have

dm/[0.8 - 0.03m(t)] = dt

Integrating, we have

∫dm/[0.8 - 0.03m(t)] = ∫dt

-0.03/-0.03 × ∫dm/[0.8 - 0.03m(t)] = ∫dt

1/(-0.03)∫-0.03dm/[0.8 - 0.03m(t)] = ∫dt

-1/0.03㏑[0.8 - 0.03m(t)] = t + C

㏑[0.8 - 0.03m(t)] = -0.03t - 0.03C

㏑[0.8 - 0.03m(t)] = -0.03t + C' (C'= -0.03C)

taking exponents of both sides, we have

$0.8 - 0.03m(t) = e^{-0.03t + C'} \\0.8 - 0.03m(t) = e^{-0.03t}e^{C'}\\0.8 - 0.03m(t) = Ae^{-0.03t} A = e^{C'}\\0.03m(t) = 0.8 - Ae^{-0.03t}\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\when t = 0 \\m(0) = 0\\m(0) = 26.67 - \frac{A}{0.03} e^{-0.03(0)}\\\\0 = 26.67 - \frac{A}{0.03} e^{0}\\26.67 = \frac{A}{0.03} \\\frac{A}{0.03} = 26.67\\\frac{A}{0.03} = 6.67\\A = 26.67 X 0.03\\A = 0.8\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\\\m(t) = 26.67 - \frac{0.8}{0.03} e^{-0.03t}\\$

So, the mass of the salt after t min is

$m(t) = 26.67 - 26.67e^{-0.03t}$

b. When will the concentration of salt in the tank reach 0.1 kg/L?

When the concentration of the salt reaches 0.1 kg/L, m(t) = 0.1 kg/L

Solving the equation for t,

$m(t) = 26.67 - 6.67e^{-0.03t}\\0.1 = 26.67 - 26.67e^{-0.03t}\\26.67e^{-0.03t} = 26.67 - 0.1\\26.67e^{-0.03t} = 26.57\\e^{-0.03t} = 26.56/26.67\\e^{-0.03t} = 0.9963\\$

taking natural logarithm of both sides, we have

-0.03t = ㏑0.9963

-0.03t = -0.0038

t = -0.0038/-0.03

t = 0.124 min

t = 0.124 × 60 s

t = 7.44 s

5 0

3 years ago

Let f(x) =2x and g(x)= x - 2 the graph of (f.g )(x) is shown below

Vika [28.1K]

Answer:

The domain of the graph is all real number ⇒ the last answer

Step-by-step explanation:

* Remember that our original exponential formula was y = ab^x

- The b value is the growth factor

* Lets revise how to find the domain of this function

- The domain is all values of x that make the function defined

* Lets revise the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted

into another function.

- For example, f(g(x)) is the composite function that is formed when

g(x) is substituted for x in f(x).

∵ f(x) = 2^x

∵ g(x) = x - 2

∴ (f · g)(x) = f(x - 2)

∵ f(x) = 2^x

∴ (f · g)(x) = f(x - 2) = 2^(x - 2)

- For this function there is no values of x make the function undefined

∴ The Domain is all real numbers

- Look to the graph, the values of x go from -∞ to ∞

* The domain of the graph is all real number

6 0

3 years ago

PLEASEEEEE HELPPPP ASAPPPPPP FIND THE SLOPE

NemiM [27]

Answer:

8/7 is the slope of the line

Step-by-step explanation:

Hope this helps

6 0

3 years ago

Identify all factors in the expression 4x2 + 173 - 15 2 3 2+5 4. – 3 4x + 3

sashaice [31]

Answer:

the first answer is 166

Step-by-step explanation:

6 0

3 years ago