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rodikova [14]
3 years ago
7

8.1.3 Determine the first three nonzero terms in the Taylor polynomial approximation for the given initial value problem. y' = 8

sin y +2e5Xy(0) = 0 The Taylor approximation to three nonzero terms is y(x) = +..
Mathematics
1 answer:
Deffense [45]3 years ago
8 0

Answer:

P(x)=2x+13x^{2}+43x^{3}

Step-by-step explanation:

We follow the procedure to find each term of the Taylor series:

y'=8sin(y)+2e^{5x}\\y'(0)=8sin(0)+2e^{5(0)}\\y'(0)=2\\y''=y'8cos(y)+10e^{5x}\\y''(0)=2*8cos(0)+10e^{5(0)}\\y''(0)=26\\y'''=y''8cos(y)-(y')^{2}8sin(y)+50e^{5x}\\y'''(0)=26*8cos(0)-(2)^{2}8sin(0)+50e^{5(0)}\\y'''(0)=258

Now that we have the first three non-zero terms, we proceed to set the Taylor series:

P(x)=0+\frac{2}{1!} x+\frac{26}{2!} x^{2}+\frac{258}{3!} x^{3}

Then we proceed to solve the polynomial:

P(x)=2x+13x^{2}+43x^{3}

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P + 5 = 15 help meeeeeeeeeeeeee
Viktor [21]

Answer:

p=10

Step-by-step explanation:

subtract 5 on both sides and you'll get p=10 :]

8 0
3 years ago
Consider the quadratic equation x2 = 4x - 5. How many solutions does the equation have?
JulijaS [17]

Answer:

  • no real solutions
  • 2 complex solutions

Step-by-step explanation:

The equation can be rearranged to vertex form:

  x^2 -4x = -5 . . . . . . . . . subtract 4x

  x^2 -4x +4 = -5 +4 . . . . add 4

  (x -2)^2 = -1 . . . . . . . . . show the left side as a square

  x -2 = ±√-1 = ±i . . . . . . take the square root; the right side is imaginary

  x = 2 ± i . . . . . . . . . . . . . add 2. These are the complex solutions.

_____

<em>Comment on the question</em>

Every 2nd degree polynomial equation has two solutions. They may be real, complex, or (real and) identical. That is, there may be 0, 1, or 2 real solutions. This equation has 0 real solutions, because they are both complex.

3 0
3 years ago
Explain why it works to break apart a number by place values to multiply
Scrat [10]
It helps because seeing a number broken up helps your brain undertsand more clearly as to what exactly you are multiplying.
3 0
3 years ago
The product or three and a number n is less than or equal to 15.
koban [17]

Answer:

Step-by-step explanation:

4 0
3 years ago
Assuming x and the number below are measured in degrees find re value of x and find the unknown angle measure in each triangle.
lorasvet [3.4K]

Answer:

x = 16°

4x-7 = 57°

3x+4 = 52°

5x-9 = 71°

Step-by-step explanation:

All angles of any triangle add up to 180°, so if we add up each equation and set it equal to 180 we can find x.

4x-7 + 3x+4 + 5x-9 = 180

Simplify by combining like terms.

12x-12 = 180

Then, do inverse operations to find x.

12x=192

x=16

Now that we found x, we can substitute 16 for x in each angle equation in the triangle.

4(16)-7 = 57

3(16)+4 = 52

5(16)-9 = 71

8 0
2 years ago
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