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4 years ago

Will give Brainliest to whoever can help me

Mathematics

1 answer:

Murrr4er [49]4 years ago

7 0

Answer:

-4/3, -0.4, 0.8, $\sqrt 2$ , $\sqrt 11$

Step-by-step explanation:

-4/3 equals -1.333(repeating)

\sqrt 2 = 1.4

\sqrt 11 = 3.3

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x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco

igomit [66]

Answer:

$x=-cos(t)+2sin(t)$

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

$a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

Will have a characteristic equation of the form:

$a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Where solutions $r_1,r_2...,r_n$ are the roots from which the general solution can be found.

For real roots the solution is given by:

$y(t)=c_1e^{r_1t} +c_2e^{r_2t}$

For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

$y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)$

Where:

$r_1_,_2=\lambda \pm \mu i$

Let's find the solution for $x''+x=0$ using the previous information:

The characteristic equation is:

$r^{2} +1=0$

So, the roots are given by:

$r_1_,_2=0\pm \sqrt{-1} =\pm i$

Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of $x(t)$ in order to find the constants $c_1$ and $c_2$ :

$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

$x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1$

And

$x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2$

Now we have found the value of the constants, the solution of the second-order IVP is:

$x=-cos(t)+2sin(t)$

3 0

3 years ago

How to solve linear equations using graphs

Artemon [7]

Explanation:

We usually use graphs to solve two linear equations in two unknowns.

The basic idea is that a graph of an equation is the pictorial representation of all of the points that satisfy the equation. So, where the graph of one equation crosses the graph of another, the point where they cross will satisfy both equations.

Finding a solution means finding values of the variables that satisfy all of the equations. Hence, the point of intersection is the solution of the equations.

To solve linear equations by graphing, graph each of the equations. Then find the coordinates of the point where the lines intersect. Those coordinates are the solution to the equations.

If the solution is not at a grid point on the graph, determining its exact value may not be easy. This can often be aided by a graphing calculator, which can often tell you the point of intersection to calculator accuracy.

If the lines don't intersect, there are no solutions. If they are the same line (intersect everywhere), then there are an infinite number of solutions.

3 0

3 years ago

CAN SOMEONE HELP WITH THIS??????????????

svetoff [14.1K]

Answer:

8963.46

Step-by-step explanation:

84*66 for the rectangle and since there is two semi circles you could just calculate it as one so it would be 84*66+33*33*3.14 because formula for area of circle is A= pi*raduis with exponant of 2

3 0

3 years ago

17. Add - 16 + (-27)

Akimi4 [234]

just add the whole numbers and add negative infront -16+-27= -43

4 0

3 years ago

Point C is the center of dilation. Line segment B A is dilated to create line segment B prime A prime. The length of C A is 4. T

saw5 [17]

Answer:

Step-by-step explanation:

Given