MATHEMATICS COLLEGE

Dy/dx=2xy/x²+y² solve​

Answers

Answer 1
Answer:

Answer:

y=(-1)/(2) \sqrt[]{4x^2+4c_(1)^2} -c_(1)\ or \ (1)/(2) \sqrt[]{4x^2+4c_(1)^2} -c_(1)

Step-by-step explanation:

As it is first order nonlinear ordinary differential equation

Let y(x) = x v(x)

2xy/(x²+y²)=2v/(v^2+1)

dy=xdv+vdx

dy/dx=d(dv/dx)+v

x(dv/dx)+v=(2v)/(v^2+1)

dv/dx=[(2v)/(v^2+1)-v]/x

(dv)/(dx)=(-(v^2-1)v)/(x(v^2+1))

(v^2+1)/((v^2-1)v)dv=(-1)/(x)dx

∫(v^2+1)/((v^2-1)v)dv = ∫(-1)/(x)dx

u=v^2

du=2vdv

Left hand side:

∫(v^2+1)/(v(v^2-1))dv

=∫(u+1)/(2u(u-1))du

=(1)/(2)∫((2)/(u-1) -(1)/(u) )du

=ln(u-1)-(ln(u))/(2) +c

=ln(v^2-1)-(ln(v^2))/(2)+c

Right hand side:

=-ln(x)

Solve for v:

v=-\frac{-c_(1)+\sqrt{c_(2)+4x^2 } }{2x} \ or \ \frac{-c_(1)+\sqrt{c_(2)+4x^2 } }{2x}\n

y=(-1)/(2) \sqrt[]{4x^2+4c_(1)^2} -c_(1)\ or \ (1)/(2) \sqrt[]{4x^2+4c_(1)^2} -c_(1)

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A cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus s0.05 per text. Plan B costs $10 per month plus $0.10 per text. For how many text messages per month are the plans the same cost? O20 O30 O 200 O 300​
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Explain how to write 2 dividid 5 as a fraction
A city council is deciding whether or not to spend additional money to reduce the amount of traffic. The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 18 minutes. A sample of 26 main roads results in a mean waiting time of 21.1 minutes with a sample standard deviation of 5.4 minutes. Conduct a hypothesis test at the 5% significance level.

Hello, there are three questions and pictures of them in the links If you could solve them that would be awesome, thank you!

Answers

Answer:

1.  1 * x^(3/6) = x^(3/6) (it will be equal to the sixth root of x cube)

2.  No, the expression x^(3) X x^(3) X x^(3) will be equal to x^(3 + 3 + 3 ) since the powers of      numbers with the same base are added

3. B and D   1/x^(-1) is the same as 'x'

as mentioned in the last answer, powers of numbers with same base are added. hence, option D will be x^(3/3) which will be equal to x

The 3rd degree Taylor polynomial for cos(x) centered at a = π 2 is given by, cos(x) = − (x − π/2) + 1/6 (x − π/2)3 + R3(x). Using this, estimate cos(86°) correct to five decimal places.

Answers

Answer:

The cosine of 86º is approximately 0.06976.

Step-by-step explanation:

The third degree Taylor polynomial for the cosine function centered at a = (\pi)/(2) is:

\cos x \approx -\left(x-(\pi)/(2) \right)+(1)/(6)\cdot \left(x-(\pi)/(2) \right)^(3)

The value of 86º in radians is:

86^(\circ) = (86^(\circ))/(180^(\circ))* \pi

86^(\circ) = (43)/(90)\pi\,rad

Then, the cosine of 86º is:

\cos 86^(\circ) \approx -\left((43)/(90)\pi-(\pi)/(2)\right)+(1)/(6)\cdot \left((43)/(90)\pi-(\pi)/(2)\right)^(3)

\cos 86^(\circ) \approx 0.06976

The cosine of 86º is approximately 0.06976.

Final answer:

We estimate the cosine of 86 degrees by first converting 86 degrees to radians (approximately 1.50098) and substituting this into the Taylor polynomial. The result is -0.08716

Explanation:

To calculate the cosine of 86 degrees using the Taylor polynomial, we first have to convert the degrees to radians, as the Taylor polynomial is based on the radian definition. The conversion yields approximately 1.50098 radians.

Then, we substitute this value into the Taylor polynomial. We ignore R3(x) as it represents the remainder and tends to zero as x approaches π/2. So, cos(86°) ≈ - (1.50098 - π/2) + 1/6 * (1.50098 - π/2)³. Computing this gives us an estimate of cos(86°) = -0.08716 to five decimal places.

Learn more about Taylor Polynomial here:

brainly.com/question/31419648

#SPJ3

ABCD is a trapezoid.
What is the area of trapezoid?

Answers

Let h represent the height of the trapezoid, the perpendicular distance between AB and DC. Then the area of the trapezoid is
  Area = (1/2)(AB + DC)·h
We are given a relationship between AB and DC, so we can write
  Area = (1/2)(AB + AB/4)·h = (5/8)AB·h

The given dimensions let us determine the area of ∆BCE to be
  Area ∆BCE = (1/2)(5 cm)(12 cm) = 30 cm²

The total area of the trapezoid is also the sum of the areas ...
  Area = Area ∆BCE + Area ∆ABE + Area ∆DCE
Since AE = 1/3(AD), the perpendicular distance from E to AB will be h/3. The areas of the two smaller triangles can be computed as
  Area ∆ABE = (1/2)(AB)·h/3 = (1/6)AB·h
  Area ∆DCE = (1/2)(DC)·(2/3)h = (1/2)(AB/4)·(2/3)h = (1/12)AB·h

Putting all of the above into the equation for the total area of the trapezoid, we have
  Area = (5/8)AB·h = 30 cm² + (1/6)AB·h + (1/12)AB·h
  (5/8 -1/6 -1/12)AB·h = 30 cm²
  AB·h = (30 cm²)/(3/8) = 80 cm²

Then the area of the trapezoid is
  Area = (5/8)AB·h = (5/8)·80 cm² = 50 cm²

Find the value of X Need help ASAP.

Answers

1. 4 inside angles must sum to 360:

X = 360-45-65-95 = 155

2. All the outside angles must sum

To 360:

2x + 70+ 86 + 9 = 2x + 248

2x = 360-248

2x = 112

X = 112/2 = 56

3. Sum of interior angles for 6 sides figure = 720.

X = 720 - 90-120-130-140-150

X = 90

4. Exterior angles sum to 360

4x +x + 98 + 162 = 360

5x + 260 = 360

5x = 100

X = 100/5

X = 20

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog.If the veterinarian gives a 30-pound dog 5 milligram of the medicine, which equation relates the weight, w, and the
dosage, o?

Answers

Question: The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog 3/5 milligram of the medicine, which equation relates the weight,w, and the dosage, d?

Answer: d= 1/50w

Explanation: I took the test in Edgenuity.

Hope this helps!

Which figures demonstrate a single reflection?

Select each correct answer.

Answers

Answer:

Please see the attached image below, to find more information about the graph

The figures that are obtained by a single reflection are shown in the image inside a red rectangle.

The axis of reflection is shown with a black line.

- The figure from the left shows horizontal reflection

- The figure from the right shows vertical reflection
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