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lakkis [162]
3 years ago
6

How do you do this question?

Mathematics
1 answer:
ElenaW [278]3 years ago
6 0

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

where C is a constant. In this case, C = -5 leads to a solution

y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.

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Which is true of an adjustable rate mortgage?
stealth61 [152]

Answer:

The rate of interest may vary , totally depends on the market value of that agency or company or the financial agency which is providing the mortgage money at certain rate. So, option (B) the interest rate may change depending on the condition of the economy is true statement regarding adjustable rate mortgage.Step-by-step explanation: hope it helps

5 0
3 years ago
Island A is 150 miles from island B. A ship captain travels 240 miles from island A and then finds that he is off course and 200
Stells [14]
We know that
Applying the law of cosines: 

<span>c</span>²<span> = a</span>²<span> + b</span>²<span> - 2abcos(C) </span>
<span>where: </span>
<span>a,b and c are sides of the triangle and C is the angle opposite side c </span>

<span>that is </span>
<span>150</span>²<span> = 240</span>²<span> + 200</span>²<span> - 2(240)(200)cos(C) </span>

<span>solve for C </span>

<span>22,500 = 57,600 + 40,000 - 96,000cos(C) </span>
<span>22,500-57,600-40,000 = -96,000cos(C) 
</span>-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)--------> C=38.53°°

<span>hence, </span>
<span>he should turn in the direction of island b by
180 - 38.53 </span><span>= 141.47 degrees</span>
4 0
3 years ago
What is the standard form equation for y=2x-4?
Oksanka [162]
Isn't it already in standard form?
4 0
3 years ago
I need help with this please !! I have to use the tabular method which is using like the boxes. Thank you!!
NikAS [45]

Answer:

a. 12 - 8x - x² + x³

b. 275 - 375x - 351x² + 240x³ + 112x⁴

c. 30 + 37m - m² - 25m³ - 14m⁴ + 3m⁵

d. 81 + 9x² + x⁴

Step-by-step explanation:

Tabular method is what I hear people call "Partial Products". Alright. All you have to do is look at how many terms are in each factor, break them up separately into columns and rows, then do your multiplication. This is the best example you will get, and just so you know, it is NOT drawn to scale [IMPERFECT]:

d.

9 | -3x | x²

------|-------|-----

9 | 81 | -27x | 9x²

____________________

3x | 27x| -9x² | 3x³

| | |

____________________

x² |9x² | -3x³ | x⁴

| | |

Add up all the boldfaced terms inside the box, and you will get the above answer.

I am joyous to assist you anytime.

3 0
3 years ago
What are 3 math equations for x=-3
harina [27]

Multiply both sides by any number you want. I'll pick 2

x = -3 turns into 2x = -6 after doing so

--------------------------

Add anything you want to both sides. I'll pick 7

x = -3 turns into x+7 = 4 after doing so

---------------------------

you can do a combination of both multiplication and addition, as long as you do the same thing to both sides. First I'll do multiplication. I'm going to multiply both sides by 2 first

x = -3 turns into 2x = -6

then I'm going to add 7 to both sides

2x = -6 turns into 2x+7 = 1

If you were to solve 2x+7 = -1, then you'd get to x = -3 again

As a check, replace x with -3 and we have...

2x+7 = 1

2(-3)+7 = 1

-6+7 = 1

1 = 1

we get a true statement, which helps confirm we have the right equation.

5 0
3 years ago
Read 2 more answers
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