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2 years ago

Find the solution set (x,y,z) of the system: 3x-2y+4z=6 2y-3z=20 6z=12

Mathematics

1 answer:

gizmo_the_mogwai [7]2 years ago

4 0

Answer:

The solution is x = 8, y = 13 and z = 2.

Step-by-step explanation:

We are given a system of equations with the variables x, y, and z from which we have to solve for x, y, and z.

The equations are

3x - 2y + 4z = 6 ........ (1)

2y - 3z = 20 .......... (2)

6z = 12 ......... (3)

Now, from equation (3), we get z = 2.

Now, putting z = 2 in equation (2) we get

2y = 20 + 6 = 26

⇒ y = 13

Now, from equation (1), putting y = 13 and z = 2, we get

3x = 6 - (4 × 2) + (2 × 13) = 24

⇒ x = 8

So the solution is x = 8, y = 13 and z = 2. (Answer)

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3 years ago

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Solve the following inequality:

ad-work [718]

Answer:

The answer is option 3.

Step-by-step explanation:

In order to solve the inequality, you have to get rid of -3 by adding 3 to both sides :

$k - 3 \leqslant 9$

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$k \leqslant 12$

4 0

3 years ago

Two fair coins are flipped. Given that at least one coin lands on a head, calculate the probability of one head and one tail. Wr

Greeley [361]

The probability of one head and one tail is 2/3.

Step-by-step explanation:

The possibilities for flipping two fair coins are {T,T}, {H,H}, {H,T}, {T,H}
Given the case that at least one coin lands on a head, So the total possibilities are {H,H}, {H,T}, {T,H} = 3 possibilities

Required event is 1 head and 1 tail= {H,T}, {T,H} = 2 possibilities

To calculate the probability of one head and one tail,

Probability = required events / Total events

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8 0

3 years ago

If x = a cosθ and y = b sinθ , find second derivative

Olin [163]

I'm guessing the second derivative is for y with respect to x, i.e.

$\dfrac{\mathrm d^2y}{\mathrm dx^2}$

Compute the first derivative. By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta$

$x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta$

and so

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta$

Now compute the second derivative. Notice that $\frac{\mathrm dy}{\mathrm dx}$ is a function of $\theta$ ; so denote it by $f(\theta)$ . Then

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}$

By the chain rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$f=-\dfrac ba\cot\theta\implies\dfrac{\mathrm df}{\mathrm d\theta}=\dfrac ba\csc^2\theta$

and so the second derivative is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac ba\csc^2\theta}{-a\sin\theta}=-\dfrac b{a^2}\csc^3\theta$

4 0

3 years ago