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2 years ago

1. Find the volume of a rectangular block 15 cm long, 5 cm wide and 10 cm length

Mathematics

1 answer:

xxMikexx [17]2 years ago

7 0

9514 1404 393

Answer:

750 cm³

Step-by-step explanation:

The volume is given by the formula ...

V = LWH . . . . where L, W, H represent length, width, height

The volume is the product of the dimensions.

V = (15 cm)(5 cm)(10 cm) = 750 cm³

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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:

Step-by-step explanation:

<u>Concentration of Liquids </u>

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

Johanna is selling cheese at the farmers’ market. One wheel of cheese has a diameter of 9 inches.

AleksAgata [21]

Answer:

The area of the wheel cheese is 63.62 inches²

The cost per square inch is $0.29

Step-by-step explanation:

* Lets explain how to solve the problem

- One wheel of cheese has a diameter of 9 inches

∵ The wheel is shaped a circle

∵ The diameter of the wheel is 9 inches

- The radius of the circle is half its diameter

∵ The radius of the wheel = 1/2 its diameter

∴ The radius of the wheel = 1/2 (9) = 4.5 inches

- The area of a circle = πr²

∴ The area of the wheel cheese = π(4.5)² = 63.61725124 inches²

* The area of the wheel cheese is 63.62 inches²

- The 9-inch wheel of cheese costs $18.60

∵ The area of the wheel cheese is 63.62 inches²

∵ It cost is $18.60

- To find the cost per square inch divide the cost of the wheel

by its area

∴ The cost per square inch = 18.60 ÷ 63.62 = 0.29

∴ The cost per square inch is $0.29

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3 years ago

Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution. u = x 4(x +1) x +1 (x + 1)2

marta [7]

no substituion only rea numbersStep-by-stion:

4 0

2 years ago

simplify 4 (5c ÷4d)-16 show me how you figure it out to put the numbers in this and I'll be asking two more questions for the ni

Darya [45]

$4(5c + 4d) - 16 \\ 20c + 16d - 16$
This is your final answer none of the terms are "like terms".

7 0

3 years ago

What is the factored form of x^2-x-2

lisov135 [29]

Answer:

(x-2),(x+1)

Step-by-step explanation:

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2 years ago

1. Find the volume of a rectangular block 15 cm long, 5 cm wide and 10 cm length​

1. Find the volume of a rectangular block 15 cm long, 5 cm wide and 10 cm length