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3 years ago

Find the product: ( x-1/x ) ( x+1/x ) ( x2+1/x2 ) ( x4+1/x4 )

Mathematics

1 answer:

erma4kov [3.2K]3 years ago

3 0

Use the difference of 2 squares (a - b)(a + b) = a^2 - b^2:-

(x - 1/x)(x + 1/x) = x^2 - (1/x)^2

= x^2 - 1/x^2

(x ^2 - 1/x^2)(x^2 + 1 /x^2)

= x^4 - 1/x^4

(x^4 - 1/x^4)(x^4 + 1/x^4)

= x^8 - 1 /x^8 Answer

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The snack shop makes 3 mixes of nuts in the following proportions.

Julli [10]

Answer:

$A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}$

$B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

Step-by-step explanation:

It is given that the snack shop makes 3 mixes of nuts in the following proportions.

Mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.

Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.

Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.

they received an order for 25 of mix I, 18 of mix II, and 35 of mix III.

We need to find the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order.

Mix I Mix II Mix III

peanuts 6 5 3

cashews 2 3 4

pecans 2 2 2

$A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}$

$B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

The product of both matrices is

$AB=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

$AB=\begin{bmatrix}6\cdot \:25+5\cdot \:18+3\cdot \:35\\ 2\cdot \:25+3\cdot \:18+4\cdot \:35\\ 2\cdot \:25+2\cdot \:18+3\cdot \:35\end{bmatrix}$

$AB=\begin{bmatrix}345\\ 244\\ 191\end{bmatrix}$

Therefore matrix AB gives the total number of lbs of each nut required to fill the order.

8 0

4 years ago

Can you help me pretty please

Elanso [62]

Answer:

A= 13 B=13.1

Step-by-step explanation:

A-B= -0.1

B-A= 0.1

7 0

3 years ago

Rationalize the denominator in each expression. That is, rewrite the expression so that there is a rational expression in the de

ad-work [718]

Answer:

explanations: we multiply with a rational surd

(x-9)*√(x+9)/(√(x-9)*√(x+9)

=(x-9)√(x+9)/

$x {}^{2} - 9$

B.( x-9)/√x+3 =( x-9)*(√x-3)/(√x+3)*(√x-3)

= (x-9)*(√x-3)/x-9

=√x-3

7 0

4 years ago

Tommy has a piece of toast that has butter on one side, and he dropped it twice. Both times, it landed with the butter side up.

Kryger [21]

Its a one over two chance that the piece of toast won't land on the side with butter

6 0

3 years ago

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aliina [53]

Step-by-step explanation:

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3 years ago