PLEASE HELPPPP Which value is equivalent to cos10∘?

Plz use Differential equation method to solve this:

Oduvanchick [21]

Answer:

Step-by-step explanation:

We have the differential equation $y' = y + \frac{x}{y}$ with initial conditions $y(0)=1$ .

First, notice that the equation can be rewritten as

$y'-y =xy^{-1}$ ,

which is a Bernoulli equation. Once we have recognized the type of the equation we know how to continue. Recall that a Bernoulli equation has the general form

$y'+p(x)y=q(x)y^n$ .

In this particular case we have $n=-1$ . This kind of equation is solved by the change of variable $z=y^{1-n}$ . In our exercise we get $z=y^{1-(-1)}=y^2$ . Now we take derivatives and get

$z'=2yy'$ which es equivalent to $\frac{z'}{2y}=y'$ .

Then, we substitute the value of $y'$ we have obtained in the original equation:

$\frac{z'}{2y}-y = xy^{-1}$ .

The next step is to multiply the whole equation by $2y$ , in order to eliminate the denominator of $z'$ . Thus,

$z' -2y^2=2x$ .

Recall that $y^2=z$ , then

$z' -2z=2x$ .

This last equation is a linear equation, which has general solution

$z(x) = \exp\left(-\int(-2)dx\right)\left(\int 2x \exp\left(\int(-2)dx + C\right)\right)$ .

So, let us calculate the integral that appear in the formula:

$\int(-2)dx = -2x$

$\int 2x e^{-2x}dx = -\frac{\left(2x+1\right)e^{-2x}}{2}$ .

Then, the solution for $z$ is

$z(x) = e^{2x}\left(-\frac{\left(2x+1\right)e^{-2x}}{2} + C\right) = -\frac{\left(2x+1\right)}{2} + Ce^{2x}$ .

Now, we return the change of variable:

$(y(x))^2 =-\frac{\left(2x+1\right)}{2} + Ce^{2x}$ .

The last step is to find the value of the constant $C$ . In order to do this, substitute the initial value:

$(y(0))^2 = 1 =\frac{\left(2\cdot 0+1\right)}{2} + Ce^{2\cdot 0} = -\frac{1}{2} + C$ .

Thus, we have the equation

$1=-\frac{1}{2} + C$ that gives $C=\frac{3}{2}$ .

Therefore,

$(y(x))^2 = -\frac{\left(2x+1\right)}{2} + \frac{3}{2}e^{2x}$ .

8 0

4 years ago

Diego is asked to solve 3x−8=4(x+5). What do you recommend he does to each side first?

vodomira [7]

Answer:

He would factor out 4(x+5)

Step-by-step explanation:

You can't do much until the 4(x+5) is factored out.

Once it is then it'd be 3x-8=4x+20

Then you subtract 3x on both sides and subtract 20 on both sides.

You'd be left with -28=x

Hope this helps

8 0

3 years ago

write two division problems related to the multiplication problem below. 8×(-2)=-16

Mrac [35]

We can write two division problems related the given equation as follows.

Division problem one :

Here 8 is in multiplication with -2 on the left side.

so when we bring this 8 on the right side, we will have to apply opposite operation of multiplication which is division.

so dividing (-16) by 8 on the right side, we have:

$-2=\frac{-16}{8}$

Division problem two :

Here -2 is in multiplication with 8 on the left side.

so when we bring this (-2) on the right side, we will have to apply opposite operation of multiplication which is division.

so dividing (-16) by (-2) on the right side, we have:

$8=\frac{-16}{-2}$

7 0

3 years ago

Score Frequency

RUDIKE [14]

Scores on an AP Exam at a local high school are recorded in the table. What was the average score?

Answer: D) 4.266 is correct

Explanation:

We are given the below frequency table:

Score Frequency

1 | 0

2 | 3

3 | 4

4 | 16

5 | 22

Let's denote the score by $x$ and frequency by $f$ .

The average formula is:

$Average=\frac{\sum fx}{\sum f}$

$=\frac{(1\times0) + (2\times3)+(3\times4) +(4\times16) + (5\times22)}{0+3+4+16+22}$

$=\frac{0+6+12+64+110}{45}$

$=\frac{192}{45}=4.267$

Therefore, the average score was 4.267

Hence the option D) 4.266

7 0

4 years ago

A light bulb filament is one-hundredth of an inch thick, with an allowable error of 2 percent. What is the least allowable thick

Andreyy89

Answer:

0.00998 Inches

Step-by-step explanation:

Thickness of the light bulb filament = 0.01 Inch

Allowable error = 2%.

2% of 0.01 = 0.02 X 0.01 =0.0002 Inch

Therefore, the allowable thickness of the bulb filament

$=0.01 \pm 0.0002 $ Inches$

We can then calculate the least allowable thickness of the filament as:

$=0.01 - 0.0002 \\=0.00998$ Inches$

The least allowable thickness of the filament is 0.00998 Inches.

3 0

4 years ago