Miguel places an 18-foot ladder 8 feet from the base of his house and leans it up

A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he

mina [271]

Answer:

x=4.8473 cups

Step-by-step explanation:

Concentration of Liquids

It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by

$\displaystyle C=\frac{x}{y}$

It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.

Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is

x-1 cups of juice.

The new concentration is

$\displaystyle \frac{x-1}{x}$

The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is

$\displaystyle x-1-\frac{x-1}{x}$ cups of juice.

Simplifying, the cups of juice are

$\displaystyle \frac{\left (x-1\right)^2}{x}$

The new concentration is

$\displaystyle \frac{\left (x-1\right)^2}{x^2}$

For the third time, we now have

$\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2}$ cups of juice.

Simplifying, the final amount of juice is

$\displaystyle \frac{\left (x-1\right)^3}{x^2}$

And the final concentration is

$\displaystyle \frac{\left (x-1\right)^3}{x^3}$

According to the conditions of the question, this must be equal to 50% (0.5)

$\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5$

Taking cubic roots

$\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}$

$\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}$

Operating and joining like terms

$\displaystyle x-\sqrt[3]{0.5}\ x=1$

Solving for x

$\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}$

$x=4.8473\ cups$

Let's test our result

Final concentration:

$\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5$

6 0

3 years ago

What is 3x1/4 please help

IceJOKER [234]

Answer:

3/4

Step-by-step explanation:

3 1/4 is 3/4 i don't know how to explain just multiply

4 0

3 years ago

If a body moves in a straight line according to the law s = 24t + 3t2 - t3 , where s is the distance measured in meters from the

Aneli [31]

Remember that the velocity as a function of time is the derivative of the position as a function of time.
To solve this we are going to take the derivative of our position function $s=24t+3t^2-t^3$ . To do that er are going to apply the power rule of calculus: $\frac{dy}{dx} x^n=nx^{n-1}$

$\frac{dy}{dx} 24t+\frac{dy}{dx}3t^2-\frac{dy}{dx}t^3$
$24+2(3)t-3t^2$
$v=24+6t-3t^2$

We can conclude that the correct answer is: B. V = 24 + 6t - 3t2

6 0

3 years ago

Pls help me I’m struggling

artcher [175]

Answer:

The first one is the answer.

Step-by-step explanation:

T.R.U.S.T. M.E

8 0

3 years ago

Read 2 more answers

Sean tried to drink a slushy as fast as he could. He drank the slushy at a constant rate. There were originally 275 milliliters