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3 years ago

The reciprocal of two more than a number is three times the reciprocal of the number. find the number

Mathematics

1 answer:

vichka [17]3 years ago

4 0

Let the number be x
reciprocal=1/x
2 more the reciprocal=1/2+x
but 1/2+x=3(1/x)
1/2+x=3/x
x=6+3x
x=-2

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AveGali [126]

Number one is x=9,-9
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number four is 5i, -5i

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3 years ago

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y=f(x) is odd (f(-x)=-f(x)) and f(x>0) = x^2-5x-12, x is not = to 0. What points does the line f(x)=12 go through.

solmaris [256]

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One number is 4 more than another, and their sum is 60. What is the smaller number? If x = the larger number and y = the smaller

erik [133]

Answer:

a. $x+y=60$ and $-x+y=4$

Step-by-step explanation:

Let x be the larger number and y be the smaller number.

We have been given that one number is 4 more than another. We can represent this information in an equation as:

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We can manipulate this equation as:

$y-x=x-x+4$

$-x+y=4$

We are also told that the sum of both numbers is 60. We can represent this information in an equation as:

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Upon looking at our given choices, we can see that option 'a' is the correct choice.

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Lapatulllka [165]

Some useful relations and identities:

$\tan x=\dfrac{\sin x}{\cos x}$

$\sin^2x=\dfrac{1-\cos2x}2$

$\cos^2x=\dfrac{1+\cos2x}2$

By the first relation, we have

$\tan^2x\sin^3x=\dfrac{\sin^5x}{\cos^2x}=\dfrac{(\sin^2x)^2\sin x}{\cos^2x}$

Applying the two latter identities, we get

$\dfrac{\left(\frac{1-\cos2x}2\right)^2\sin x}{\frac{1+\cos2x}2}=\dfrac{\frac{1-2\cos2x+\cos^22x}4\sin x}{\frac{1+\cos2x}2}=\dfrac{(1-2\cos2x+\cos^22x)\sin x}{2(1+\cos2x)}$

We can apply the third identity again:

$\dfrac{(1-2\cos2x+\cos^22x)\sin x}{2(1+\cos2x)}=\dfrac{\left(1-2\cos2x+\frac{1+\cos4x}2\right)\sin x}{2(1+\cos2x)}=\dfrac{(3-4\cos2x+\cos4x)\sin x}{4(1+\cos2x)}$

and this is probably as far as you have to go, but by no means is it the only possible solution.

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antiseptic1488 [7]

Answer:

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