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2 years ago

If (n+1)!=90×(n-1)!,find n.

1 answer:

4 0

$\displaystyle\bf\\(n+1)!=90\times (n-1)!\\\\(n-1)!\times n\times(n+1)=90\times (n-1)!~~~\Big|~:(n-1)!\\\\n(n+1)=90\\\\n(n+1)=9\times10\\\\n(n+1)=9(9+1)\\\\\implies~~\boxed{\bf n=9}$

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Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

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

Multiply both sides by -1

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

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

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3 years ago

Henry has 4 more cards than Doug. Doug has 12 cards. How many cards does Henry have?

PIT_PIT [208]

Answer: doug has 16 cards

Step-by-step explanation: 12+4=16

Give brainliest if it help :)

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2 years ago

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Clara has less than $75. She wants to buy 3 pairs of shoes. What price shoes can Clara afford if all the shoes are the same pric

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Answer:$25

Step-by-step explanation:

Take 75 and divide it by 3 to get 25 dollars.

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3 years ago

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The $199.99 digital camera Anne purchased was on sale for 15% off. What amount did Anne get off the price?

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Answer:

Step-by-step explanation:

200x.15=30

200-30=170

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2 years ago

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A company has to buy computers and printers. Each computer, x, costs $525 and each printer, y, costs $315. If the company spends

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I think it is the answer b because I think it the right choice I think you should choose B ok have a great day.

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2 years ago

If (n+1)!=90×(n-1)!,find n.​

If (n+1)!=90×(n-1)!,find n.