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3 years ago

Which of the following is an example of a system of three linear equations in theee variables

Mathematics

2 answers:

harkovskaia [24]3 years ago

6 0

Answer:

I think option D is correct

Gnom [1K]3 years ago

5 0

Answer:

1) no, because a solution must be an ordered triple pair (x,y,z)

2) { x+y+z=5

{ 2x-3y+z=7

{ x+2y-4z=2

3) infinity many solutions

4) use equations (1) and (2) to eliminate y

5) solve one equation for one of its variables

Step-by-step explanation:

should be 100% on the quick check if you put those answers

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3 years ago

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Vinvika [58]

Hello from MrBillDoesMath!

Answer:

Choice A, 18x - 6y = 20

Discussion:

Given line

-9x + 3y = 12 (M)

Choice A:

18x - 6y = 20 => divide both sides by -2

-9x + 3y = -10 (N)

The left hand sides of (M) and (N) are equal implying that right hand sides are equal which further implies 12 = -10. Contradiction! so the system M and N has no solution.

Thank you,

MrB

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3 years ago

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7 0

3 years ago

Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

8 0

3 years ago