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3 years ago

Which of the following is the function f(x) if f'(x) = *#4?

Mathematics

1 answer:

TEA [102]3 years ago

8 0

Answer:

Step-by-step explanation:

To find a function's inverse, you first switch the x and y coordinates, and then solve for the new y. The same goes for finding an inverse's function. We have:

$y=\frac{x+4}{11}$ We will switch the x and y variables and then solve for the new y:

$x=\frac{y+4}{11}$ and

11x = y + 4 so

11x - 4 = y and

11x - 4 = f(x) which is choice C.

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Find the general solution to 1/x dy/dx - 2y/x^2 = x cos x, y(pi) = pi^2

Finger [1]

Answer:

$\frac{y}{x^2}=\sin x+\pi$

Step-by-step explanation:

Consider linear differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$

It's solution is of form $y\,I.F=\int I.F\,q(x)\,dx$ where I.F is integrating factor given by $I.F=e^{\int p(x)\,dx}$ .

Given: $\frac{1}{x}\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x^2}=x\cos x$

We can write this equation as $\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x}=x^2\cos x$

On comparing this equation with $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$ , we get $p(x)=\frac{-2}{x}\,\,,\,\,q(x)=x^2\cos x$

I.F = $e^{\int p(x)\,dx}=e^{\int \frac{-2}{x}\,dx}=e^{-2\ln x}=e^{\ln x^{-2}}=\frac{1}{x^2}$ { formula used: $\ln a^b=b\ln a$ }

we get solution as follows:

$\frac{y}{x^2}=\int \frac{1}{x^2}x^2\cos x\,dx\\\frac{y}{x^2}=\int \cos x\,dx\\\\\frac{y}{x^2}=\sin x+C$

{ formula used: $\int \cos x\,dx=\sin x$ }

Applying condition: $y(\pi)=\pi^2$

$\frac{y}{x^2}=\sin x+C\\\frac{\pi^2}{\pi}=\sin\pi+C\\\pi=C$

So, we get solution as :

$\frac{y}{x^2}=\sin x+\pi$

4 0

3 years ago

jar contains 51 coins which are either quarters or nickels. total value of jar is 5.15. how many of each type of coin do they ha

docker41 [41]

I believe there are 20 quarters and 3 nickels.....

Total value of the jar is $5.15.....

Quarters are worth 25 cents
And nickels are worth 5 cents.

First you know that there are 4 quarters in a dollar.
You have 5 dollars so you do 4 x 5 = 20

So five dollars ($5.00) is 20 quarters.
And you still have 15 cents left.

Because quarters are 25 cents the rest are nickels.

Nickels are worth 5 cents so you'd do 5 x 3 = 15.

15 cents!

Add all this together and get $5.15.

So your answer is

There are 20 quarters and 3 nickels in the jar.

8 0

3 years ago

Please help me answer this!

STatiana [176]

Sorry I don’t know ): hopefully someone answeres

5 0

3 years ago

Read 2 more answers

Write the prime factorization of 36. Use Exponents when appropriate and order the factors from least to greatest

Setler [38]

Answer:

2 x 2 x 3 x 3

Step-by-step explanation:

6 x 6

3 x 2 x 3 x 2

7 0

3 years ago

Here a easy one tooooooooooooo

Leviafan [203]

Remember:
A triangle is always 180 degrees and so is a straight line so 360 degrees in total:

1) Add 92 and 123 which equals 215
Then 360 subtracted by 215 is 145

Answer: 145

2) add 100 and 25= 125
360-125= 235
Answer: 235 degrees

8 0

3 years ago

Read 2 more answers