PLEAASSEE HELP 15 POINTS!!!!

Mathematics

2 answers:

S_A_V [24]3 years ago

8 0

Answer:

Step-by-step explanation:

Remark

The purple lines cross but once. A solution to a set of functions counts how many times the functions cross. Since these two lines cross but once, there is only 1 solution.

If the lines are parallel, they never cross. That means there are no solutions.

If you are given 2 equations and one is the same line as the second one, then there are an infinite number of solutions.

storchak [24]3 years ago

5 0

Hi!

Solutions to systems of equations are only where the lines intersect at a point.

That means that if the lines cross over at any point, they have a solution. Lines that don't have a solution -- parallel lines -- do not cross over.

In this graph, we can see that it crosses over at only one point.

That means that this system of equations has exactly one solution.

For a similar problem, see:

brainly.com/question/13956905

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Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply)

DiKsa [7]

Answer:

Step-by-step explanation:

We must compute the derivatives and check if the equation is satisfied.

A. $y'=(3\sin x)'=3\cos x$ . Differentiate again to get $y''=(3\cos x)'=-3\sin x$ , then $y''+y=-3\sin x+3\sin x=0\neq 3\sin x$ so this choice of y doesn't solve the equation.

B. $y'=3\sin x+3x\cos x-5\cosx +5x\sin x=(5x+3)\sin x+(3x-5)\cos x$ and $y''=5\sin x+(5x+3)\cos x+3\cos x-(3x-5)\sin x=(10-3x)\sin x+(5x+6)\cos x$ , then $y''+y=10\sin x+6\cos x\neq 3\sin x$ so y is not a solution

C. $y'=\frac{-3}{2}\cos x+\frac{3}{2}x\sin x$ hence $y''=\frac{3}{2}\sin x+\frac{3}{2}\sin x+\frac{3}{2}x\cos x=3\sin x+\frac{3}{2}x\cos x$ . Then $y''+y=3\sin x+\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\sin x$ so y is a solution.

D. $y'=-3\sin x$ and $y''=-3\cos x$ , then $y''+y=0$ thus y isn't a solution

E. $y'=\frac{3}{2}\sin x+\frac{3}{2}x\cos x$ hence $y''=\frac{3}{2}\cos x+\frac{3}{2}\cos x-\frac{3}{2}x\sin x=3\cos x-\frac{3}{2}x\cos x$ . Then $y''+y=3\cos x-\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\cos x\neq 3\sin x$ then y is not a solution.