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3 years ago

For a given input value rrrr, the function hhhh outputs a value qqqq to satisfy the following equation.

Mathematics

1 answer:

trapecia [35]3 years ago

5 0

65fjeiidhdhdsbisjsisbsbsbs

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Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

IgorLugansk [536]

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The product:

$A * B = \frac{1}{2} * \frac{2}{3}$

$A * B = \frac{1}{1} * \frac{1}{3}$

$A * B = 1 * \frac{1}{3}$

$A * B = \frac{1}{3}$

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The quotient:

$A / B = \frac{1}{2} / \frac{2}{3}$

Express as product

$A / B = \frac{1}{2} / \frac{3}{2}$

$A / B = \frac{1*3}{2*2}$

$A / B = \frac{3}{4}$

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

$x = \frac{1}{2}$

$y = \frac{2}{3}$

The sum:

$x + y = \frac{1}{2} + \frac{2}{3}$

Take LCM

$x + y = \frac{3+4}{6}$

$x + y = \frac{7}{6}$

Proved, because 7/6 is rational

<em>The above proof works for all values of A, B, x and y; as long as they are rational values</em>

8 0

3 years ago

A restaurant’s dining room measures 30 ft by 40 ft. If the fire code requires one square meter per guest, what is the seating ca

Mnenie [13.5K]

The restaurant is 30*40= 1200 square feet

1 square meter is 10.76 sq feet

1200/10.76 ~=111.5

Assuming people are integers, the restaurant has a max seating capacity of 111

3 0

3 years ago

Read 2 more answers

Ivan and Tanya share £150 in the ratio 4:1<br> How much more does Ivan get than Tanya

mina [271]

Answer:

Ivan gets £90 more than Tanya

Step-by-step explanation:

Given that

Total amount = £150

Ratio: 4:1

First of all we have to find the sum of ratio: 4+1 = 5

Now,

Ivan's Share:

$= \frac{4}{5} * 150\\= 120$

Tanya's Share:

$=\frac{1}{5} * 150\\= 30$

Ivan gets £120 and Tanya gets £30

The difference between their shares is the answer.

So,

$= 120-30 = 90$

Hence,

Ivan gets £90 more than Tanya

6 0

3 years ago

What is the y-intercept of the exponential function? f(x)=−0.25(6)x+2−1

nadya68 [22]

F(x) is another form of y-intercept

7 0

3 years ago

Read 2 more answers

What comes after 'a thousand trillion' ?

Allushta [10]

One thousand n two trillion

7 0

3 years ago