How many solutions does the following system of equations have?

Use differentiation to show that the given function is a solution of the equation for all values of the constants. (Enter your a

Katena32 [7]

Answer with Step-by-step explanation:

We are given that

DE

$x''+x=2e^t$

Function: $x=C_1sint+C_2cost+e^t$

We have to show that given function is a solution of the equation for all values of the constants.

If given function is solution of DE then it satisfied the given DE.

Differentiate function w.r.t.t

$x'=C_1cost-C_2sint+e^t$

Again differentiate w.r.t. t

$x''=-C_1sint-C_2cost+e^t$

Substitute the values in the given DE

$-C_1sint-C_2cost+e^t+C_1sint+C_2cost+e^t=2e^t$

LHS=RHS

Given function satisfied the given DE.Therefore, it is solution of given DE for all values of the constants.

8 0

3 years ago

As the value of x increases, which of the following functions would eventually exceed to the other three?

MariettaO [177]

$x\ \ \ \ \ \ \ \ |\ \ \ \ \ 0\ \ \ \ |\ \ \ \ \ 1\ \ \ \ \ \ |\ \ \ \ \ 10 \ \ \ \ \ |\ \ \ \ \ \ 100\ \ \ \ \ \ |\\-----------------------\\1000x\ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ 1000\ \ \ | \ \ \ 10000 \ \ \ |\ \ \ \ 100000\ \ \ \ |\\-----------------------\\100x^2\ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ \ 100\ \ \ \ | \ \ \ 10000 \ \ \ |\ \ 1000000\ \ \ \ |\\-----------------------\\50x^3\ \ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ \ \ 50\ \ \ \ \ | \ \ \ 50000 \ \ \ |\ \ 50000000\ \ \ |\\-----------------------$
$2^x\ \ \ \ \ \ |\ \ \ \ 1\ \ \ \ \ |\ \ \ \ \ \ 2\ \ \ \ \ \ | \ \ \ \ 1024 \ \ \ |\ \ \ \ 1024^{10}\ \ \ \ \ |\\$

$if\ x\ \rightarrow\ +\infty\ \ \ then$

$f_1(x)\$

6 0

4 years ago

What is the product?<br> (4y - 3)(2x + 3y – 5)

ahrayia [7]

Answer:

8y3+6y2-29y+15

Step-by-step explanation:

Expand

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by multiplying each term in the first expression by each term in the second expression.

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8 0

4 years ago

A bike rental company charges a fee per hour. The charge, in dollars, is the same each hour. The ordered pairs (3, 13.50) and (5

olchik [2.2K]

If the function is y = 4.5x. Then the rate of change of the function expressed as a unit rate will be 4.5.

<h3>What is the linear system?</h3>

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A bike rental company charges a fee per hour.

The charge, in dollars, is the same each hour.

The ordered pairs (3, 13.50) and (5, 22.50) represent the corresponding hours, x, and cost, y.

Then the linear equation is given as

$\begin{aligned} \rm y - 22.5 &= \rm \dfrac{22.5 - 13.5}{5 - 3} (x- 5)\\\\\rm y - 22.5 &= \rm 4.5x - 22.5\\\\\rm y &= \rm 4.5x \end$

Then the rate of change of the function expressed as a unit rate will be

$\rm \dfrac{dy}{dx} = \dfrac{d}{dx} (4.5x )\\\\\dfrac{dy}{dx} = 4.5$

More about the linear system link is given below.

brainly.com/question/20379472

#SPJ1

7 0

2 years ago

3.) Write the equation of a quadratic function that is shifted down 4 and horizontally compressed by 1/5

sashaice [31]

Answer:

$5x^2 - 4$

Step-by-step explanation:

For shifted down a function you have to follow the next structured:

$f(x) - c$

In our case is:

$x^2 - 4$

Now for compressed or shrink a graph you have to multiply by a factor in the input something like this:

$f(cx)$

In our case is:

$5x^2$

Maybe you can think, why 5 and not $\frac{1}{5}$ instead?. Well, when you multiply by $\frac{1}{5}$ this dilate or stretch the graft because the output of each value is smaller, example:

$f(x) = x^2\\g(x) = \frac{1}{5} x^2$

Then evaluate for a number, for example 5:

$f(5) = 25\\g(5) = 5$

the output of $g(x)$ is 5 steps a far from the answer of $f(x)$ this in a graph is illustrate as a stretching.

So the opposite happen when you multiply by a integer number, the graph is compressed because the output take the "faster steps".

So combine the two transformation and get $5x^2 - 4$

8 0

2 years ago