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3 years ago

2x+3y=-12 2x+t=-16 X=. Y= Help plz

Mathematics

1 answer:

8090 [49]3 years ago

8 0

To make this problem solvable, I have replaced the 't' in the second equation for a 'y'.

Answer:

x = -9

y = 2

Step-by-step explanation:

Solve the system:

2x + 3y = -12 [1]

2x + y = -16 [2]

Subtracting [1] and [2]:

3y - y = -12 + 16

2y = 4

y = 4/2 = 2

From [1]:

2x + 3(2) = -12

2x + 6 = -12

2x = -18

x = -18/2 = -9

Solution:

x = -9

y = 2

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3 years ago

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Answer:

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

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 $p(x)=\frac{-2}{x}\,\,,\,\,q(x)=x^2\cos x$

I.F = $e^{\int p(x)\,dx}=e^{\int \frac{-2}{x}\,dx}=e^{-2\ln x}=e^{\ln x^{-2}}=\frac{1}{x^2}$ { formula used: $\ln a^b=b\ln a$ }

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 :

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

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3 years ago

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Step-by-step explanation:

Probability of obtaining at least one tail on a toss of coin 5 times ;

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Using the binomial distribution formula :

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P( 0 tails) = 5C0 * 0.5^0 * 0.5^(5-0)

= 1 * 1 * 0.03125

= 0.03125

P(at leat 1 tail) = 1 - 0.03125

P(atleast 1 tail) = 0.96875

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