A <br> B <br> C <br> D <br> What is the answer?

Write additive and multiplicative inverse of19/-6 and-2/3<br>

Sedbober [7]

<h2>Answer:</h2>

Additive inverse of 19/-6 is 19/6

Additive inverse of -2/3 is 2/3

Multiplicative inverse of 19/-6 is -6/19

Multiplicative inverse of -2/3 is 3/-2 (also written as -3/2)

<h2>Step-by-step explanation:</h2>

(a) The additive inverse of a number is that number that when added to it gives 0.

For example, the additive inverse of x is -x.

This is because adding -x to x gives 0. i.e

x + (-x) = 0

In other words, the additive inverse of a number is the negative of that number.

Given:

(i) 19/-6

The additive inverse of 19/-6 is the <em>negative</em> of 19/-6 which is -(19/-6).

-(19/-6) then gives 19/6

Therefore, the additive inverse of 19/-6 is 19/6

(ii) -2/3

The additive inverse of -2/3 is the <em><u>negative</u></em> of -2/3 which is -(-2/3).

-(-2/3) then gives 2/3

Therefore, the additive inverse of -2/3 is 2/3

(b) The multiplicative inverse of a number is that number that when multiplied by it gives 1.

For example, the multiplicative inverse of y is 1/y.

This is because multiplying y by 1/y gives 1. i.e

y x (1/y) = 1

In other words, the multiplicative inverse of a number is the reciprocal of that number.

Given:

(i) 19/-6

The multiplicative inverse of 19/-6 is the <em>reciprocal</em> of 19/-6 which is 1/(19/-6).

1 / (19/-6) then gives -6/19

This is found by just swapping the numerator(19) and the denominator(-6)

Therefore, the multiplicative inverse of 19/-6 is -6/19

(ii) -2/3

The multiplicative inverse of -2/3 is the <em>reciprocal</em> of -2/3 which is 1/(-2/3).

1 / ( -2/3) then gives 3/-2

This is found by just swapping the numerator(-2) and the denominator(3)

Therefore, the multiplicative inverse of -2/3 is 3/-2 (also written as -3/2).

4 0

3 years ago

A candy box is made from a piece of cardboard that measures 23 by 13 inches. Squares of equal size will be cut out of each corne

wolverine [178]

Answer:

2.67 inches.

Step-by-step explanation:

Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).

The formula for a rectangular box = L × B × W

= (23 -2y)(13-2y) (y)

= (299 - 46y - 26y + 4y²)y

= 299y - 72y² + 4y³

Now for the maximum volume:

dV/dy = 0

This implies that:

299y - 72y² + 4y³ = 299 - 144y + 12y² = 0

By using the quadratic formula; we have :

$= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}$