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2 years ago

when a natural number is decreased by 20,the result is 96 times the reciprocal of the number.find the number

Mathematics

1 answer:

olga2289 [7]2 years ago

5 0

Answer:

let natural no be x

(x-20)=96/x

x²-20x-96=0

x²-24x+4x-96=0

x(x-24)+4(x-24)=0

(x-24)(x+4)=0

either

x=24

x=-4

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2 years ago

According to the rational root theorem, which number is a potential root of

11Alexandr11 [23.1K]

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2 years ago

Find the general solution to 1/x dy/dx - 2y/x^2 = x cos x, y(pi) = pi^2

Finger [1]

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$\frac{y}{x^2}=\sin x+\pi$

Step-by-step explanation:

Consider linear differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$

It's solution is of form $y\,I.F=\int I.F\,q(x)\,dx$ where I.F is integrating factor given by $I.F=e^{\int p(x)\,dx}$ .

Given: $\frac{1}{x}\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x^2}=x\cos x$

We can write this equation as $\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x}=x^2\cos x$

On comparing this equation with $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$ , we get $p(x)=\frac{-2}{x}\,\,,\,\,q(x)=x^2\cos x$

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we get solution as follows:

$\frac{y}{x^2}=\int \frac{1}{x^2}x^2\cos x\,dx\\\frac{y}{x^2}=\int \cos x\,dx\\\\\frac{y}{x^2}=\sin x+C$

{ formula used: $\int \cos x\,dx=\sin x$ }

Applying condition: $y(\pi)=\pi^2$

$\frac{y}{x^2}=\sin x+C\\\frac{\pi^2}{\pi}=\sin\pi+C\\\pi=C$

So, we get solution as :

$\frac{y}{x^2}=\sin x+\pi$

4 0

2 years ago

I need help with this two questions.

mezya [45]

Always get rid of denominators first. Multiply both right and left side by 6
-7 (6) = -c (6)/6 + 12(6)
-42 = -c + 72
c = 72 +42
c = 114

rearrange like terms together
42 = 18 - 4x
4x = 18 -42
4x = -24
divide both sides by 4
x = -6

8 0

2 years ago

when a natural number is decreased by 20,the result is 96 times the reciprocal of the number.find the number​

when a natural number is decreased by 20,the result is 96 times the reciprocal of the number.find the number