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2 years ago

(09.04 LC)

Mathematics

1 answer:

azamat2 years ago

4 0

Answer:

(x-7)^2+(y-8)^2=121

Step-by-step explanation:

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Square root of 5, 0.6, 4/9, 0.7, square root of 2

ella [17]

1: 2.23
2: 0.77
3: 2/3 or 0.6
4: 0.83
5: 1.41

8 0

3 years ago

Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linea

Aleks [24]

Recall that variation of parameters is used to solve second-order ODEs of the form

y''(t) + p(t) y'(t) + q(t) y(t) = f(t)

so the first thing you need to do is divide both sides of your equation by t :

y'' + (2t - 1)/t y' - 2/t y = 7t

You're looking for a solution of the form

$y=y_1u_1+y_2u_2$

where

$u_1(t)=\displaystyle-\int\frac{y_2(t)f(t)}{W(y_1,y_2)}\,\mathrm dt$

$u_2(t)=\displaystyle\int\frac{y_1(t)f(t)}{W(y_1,y_2)}\,\mathrm dt$

and W denotes the Wronskian determinant.

Compute the Wronskian:

$W(y_1,y_2) = W\left(2t-1,e^{-2t}\right) = \begin{vmatrix}2t-1&e^{-2t}\\2&-2e^{-2t}\end{vmatrix} = -4te^{-2t}$

Then

$u_1=\displaystyle-\int\frac{7te^{-2t}}{-4te^{-2t}}\,\mathrm dt=\frac74\int\mathrm dt = \frac74t$

$u_2=\displaystyle\int\frac{7t(2t-1)}{-4te^{-2t}}\,\mathrm dt=-\frac74\int(2t-1)e^{2t}\,\mathrm dt=-\frac74(t-1)e^{2t}$

The general solution to the ODE is

$y = C_1(2t-1) + C_2e^{-2t} + \dfrac74t(2t-1) - \dfrac74(t-1)e^{2t}e^{-2t}$

which simplifies somewhat to

$\boxed{y = C_1(2t-1) + C_2e^{-2t} + \dfrac74(2t^2-2t+1)}$

4 0

2 years ago

A salesperson earns $300 per week, plus a 25% commission on each sale made. How much would the salesperson earn if he sold $650

Montano1993 [528]

Answer:

$800 = $300 +.05(x), x being the amount that must be sold

Subtract 300 from both sides

$500= .05(x)

Divide by .05

x=$10000

Step-by-step explanation:

5 0

3 years ago

twenty seven out of forty dentists recommended a certain whitener for teeth. if 1080 dentists recommended the whitener in the su

Anestetic [448]

Answer:

1,600 dentists were surveyed in total.

Step-by-step explanation:

We can set up a proportion for this problem:

$\frac{27}{40} = \frac{1080}{x}\\\\\\$

Now we can cross multiply:

$27*x = 1080*40\\\\27x = 43,200\\\\27x/27 = 43,200/27\\\\x = 1,600$

1,600 dentists were surveyed in total.

3 0

2 years ago

|5x|+5=45 can you explain this absloute value equation i have a midterm

Ymorist [56]

So first, you get the absolute value to one side:
$|5x|+5=45\\
|5x|=40$

Next, set up two equations; One where the value inside the absolute value lines is positive, and another where it is negative, and solve both for the variable:
$|5x|=40\\5x=40\\x=\frac{40}{5}=8\\\\-5x=40\\x=\frac{40}{-5}=-8$

Your answers are 8 and -8, or +-8.

8 0

3 years ago

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