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1 year ago

a rectangular lawn has an area of a^3 - 125. use the difference of cubes to find out the dimensions of the rectangle.

Mathematics

1 answer:

ANEK [815]1 year ago

6 0

The area of a rectangle is the product of its dimensions

The dimensions of the rectangle are: $\mathbf{Length = a -5}$ and $\mathbf{Width = a^2 + 5a + 25}$

The area is given as:

$\mathbf{Area = a^3 - 125}$

Express 125 as 5^3

$\mathbf{Area = a^3 - 5^3}$

Apply difference of cubes

$\mathbf{Area = (a - 5)(a^2 + 5a + 5^2)}$

$\mathbf{Area = (a - 5)(a^2 + 5a + 25)}$

The area of a rectangle is:

$\mathbf{Area = Length \times Width}$

So, by comparison:

$\mathbf{Length = a -5}$

$\mathbf{Width = a^2 + 5a + 25}$

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Prove the following using a proof by contradiction:The average of four real numbers is greater than or equal to at least one of

skelet666 [1.2K]

Answer:

By contradiction it can be proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

Step-by-step explanation:

Method of contradiction means we assume opposite to the facts to be proved and then we contradict our assumption.

As a result, we prove the fact.

Here, let the four number be:

$p, q, r, s$

The average will be Sum of all numbers divided by count of numbers.

$\dfrac{p+ q+ r+ s}4$

Now, let us assume the opposite that the average is less than all the numbers.

i.e.

$\dfrac{p+ q+ r+ s}4$

Now, let us add all of them:

$\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 < p+q+r+s\\\Rightarrow \dfrac{4(p+q+r+s)}4$

Which can never be possible hence, our assumption is contradicted.

our assumption is wrong.

Therefore, by contradiction it is proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

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2 years ago

A property tax rate of 16.3 mills is equal to

Westkost [7]

It is approximately 1.000

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2 years ago

Al Johnson is a word processor. He is paid $2.95 a page. A normal job has 600 pages and requires about 225 words per page. About

mezya [45]

$2.95 * 600 pages= $1,770

D is the answer

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2 years ago

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We can calculate eee, the amount of euros that has the same value as ddd u.S. Dollars, using the equation e=\dfrac{17}{20}de= 20

Cloud [144]

We are given eqaution: $e=\frac{17}{20}d$ , where e the amount of euros and d is the value as U.S. Dollars.

We need to find number of euros for 1 U.S. Dollar.

Plugging d=1 in the given equation

We get

$e=\frac{17}{20}(1)$

On simplfying , we get

$e=\frac{17}{20}$

Dividing 17 by 20, we get 0.85.

Therefore, there would be 0.85 euro have the same value as 1 U.S. Dollar.

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2 years ago

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Tanmay had some chocolates with him. He gave one-third of them to Akash and one-fifth of them to Sharad. Tanmay could do so with

Stels [109]

Answer:

The possible value of X are;

15, 30, 45, 60 etc

Step-by-step explanation:

The parameters given are

Number of chocolates Tanmay had = X

Number of chocolates Tanmay gave to Akash = 1/3 × X

Number of chocolates Tanmay gave to Sharad = 1/5 × X

Whereby 3 and 5 are factors of X, therefore;

3 × 5 = 15 is the lowest single factor of X

The possible values of X starting from the lowest factor are given as follows;

15 × 1 = 15

15 × 2 = 30

15 × 3 = 45

15 × 4 = 60

Hence, the possible value of X are the arithmetic progression a + (n - 1)×d

Where:

a = 15

n = 1, 2, 3, 4, ...

d = 15

Which includes;

15, 30, 45, 60

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2 years ago