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maw [93]
3 years ago
15

Solve the initial value problem: 9y′′−6y′+8y=0, y(π/2)=−2, y′(π/2)=−1. Give your answer as y=... . Use x as the independent vari

able.

Mathematics
1 answer:
8_murik_8 [283]3 years ago
5 0

Answer:

y = e^(x/3)[0.0016cos(x√7/3) - 1.2056sin(x√7/3)]

Step-by-step explanation:

The problem is solved by first writing an auxiliary equation

9m² - 6m + 8 = 0

of the differential equation

9y'' - 6y' + 8y = 0.

The auxiliary equation is the solved to obtain the values (1/3 ± i√7/3) of m. These values are then used to obtain the complementary equation

y = e^(x/3)[Acos(x√7/3) + Bsin(x√7/3)]

of the differential equation.

The conditions given are then applied.

1. y(π/2) = -2

Put y = -2 and x = π/2.

This gives an equation in terms of A and B.

2. y'(π/2) = -1

Differentiate y to obtain y', and put y' = -1 and x = π/2.

This gives another equation in terms of A and B.

The two equations obtained here are then solved simultaneously to obtain values for A (0.0016), and B (-1.2056).

These values of A and B are substituted into the complimentary solution obtained earlier to have the desired particular solution.

The step-by-step explanation is shown in the attachment.

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Please help!! i will help you back!!
NeX [460]

Answer:

c = 50

Step-by-step explanation:

Using the Pythagorean Theorem:

Plug in the values of a = 14, and b = 48

a^{2} +b^{2} =c^{2}\\14^{2} +48^{2} =c^{2}  \\c^{2} = 2500\\c = \sqrt{2500} \\c = 50

7 0
3 years ago
What the answer to this it pre algebra Order operation
olga55 [171]

PEMDAS

parenthesis

exponents

multiplication

division

addition

subtraction

9-7-6/6

first 6/6=1

9-7-1

9-7=2

2-1=1

answer is 1

5 0
3 years ago
Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Dhs.4000, find the marked pric
vekshin1
B dhs.3200

because 10% of 4000=400
20%=800
4000-800=3200
4 0
2 years ago
672,591 is closer to 700,000 than
GaryK [48]
That number is closer to 700,000 than 185,505 for example, because it is a bigger number. Hope that makes sense.
7 0
2 years ago
Read 2 more answers
What is an equation for the line with slope 2/3 and 7-intercept 9? 30 points to whoever answers this correctly and gets brainlie
Annette [7]

The equation of the line is y = \frac{2}{3} x + 9

Step-by-step explanation:

The equation of a line in slope-intercept form is y = m x + b, where

  • m is the slope of the line
  • b is the y-intercept ⇒ the value of y when x = 0

∵ The line has a slope \frac{2}{3}

∴ m = \frac{2}{3}

∵ The y-intercept is 9

∴ b = 9

- Substitute the values of m and b in the form of the equation below

∵ y = m x + b

∴ y = \frac{2}{3} x + 9

The equation of the line is y = \frac{2}{3} x + 9

Learn more:

You can learn more about the linear equations in brainly.com/question/12941985

#LearnwithBrainly

4 0
3 years ago
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