1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
xxTIMURxx [149]
3 years ago
15

Check whether the function yequalsStartFraction cosine 2 x Over x EndFraction is a solution of x y prime plus yequalsnegative 2

sine 2 x with the initial condition y (StartFraction pi Over 4 EndFraction )equals0.
Mathematics
1 answer:
Jobisdone [24]3 years ago
6 0

The question is:

Check whether the function:

y = [cos(2x)]/x

is a solution of

xy' + y = -2sin(2x)

with the initial condition y(π/4) = 0

Answer:

To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.

Let us do that.

y = [cos(2x)]/x

y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]

Now,

xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x

= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)

= -2sin(2x)

Which is the right hand side of the differential equation.

Hence, y is a solution to the differential equation.

You might be interested in
How does the exponential function f(x) = 2 · 3^x + 4 appear as a graph?
Ilya [14]
I believe this is how that exponential function would look as a graph (if you need a better pic let me know)

3 0
2 years ago
Consider the vector add = a + b = [13 12 11 10 10] and sub = a - b = [-11 - 6 - 14 8]. Find the vector a and b.
prisoha [69]

Answer:

a = [1   3   5   7   9] and b = [12   9   6   3   1]

Step-by-step explanation:

The addition of two vectors a and b is defined as

a + b = [13   12   11   10   10]                .... (1)

The subtraction of two vectors a and b is defined as

a - b = [-11   - 6   - 1   4    8]                 .... (2)

After adding (1) and (2), we get

(a + b) + (a - b)= [13   12   11   10   10] + [-11   - 6   - 1   4    8]

On simplification we get

2a = [13-11   12-6   11-1   10+4   10+8]

2a = [2   6   10   14   18]

Divide both sides by 2.

a = [1   3   5   7   9]

Substitute the value of vector a in equation (1).

[1   3   5   7   9] + b = [13   12   11   10   10]

Subtract vector a from both sides.

b = [13   12   11   10   10] - [1   3   5   7   9]

On simplification we get

b = [13-1   12-3   11-5   10-7   10-9]

b = [12   9   6   3   1]

Therefore the vectors a and b are defined as a = [1   3   5   7   9] and b = [12   9   6   3   1].

4 0
2 years ago
Help me plz I need it fast
e-lub [12.9K]
1524096 CM is the answer
8 0
2 years ago
Jack wants to find out which can of pineapples is the best buy. He has a choice of four different-sized cans. Which can has the
OLga [1]

Answer:

C

Step-by-step explanation:

Here is the complete question

ack wants to fined out which can pineapples is the best buy. He has a choice of four different -sized cans. Which can has the lowest unit price per ounce?

A. 8 ounce for $ 1.44

B. 6 ounce for $ 1. 14

C. 18 ounce for $ 2.88

D. 10 ounce for $ 1.62

unit price = price / total ounces

$1.44 / 8 = $0.18

$1.14 / 6 = $0.19

$2.88 / 18 = $0.16

$1.62 / 10 = 0.162

the lowest is 18 ounce for $ 2.88

5 0
3 years ago
Double g, then subtract f from the result
Maurinko [17]

Answer:

2g - f

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • X is at most 30 represent as an algebraic inequality
    13·1 answer
  • Help!!! I don't know this ​
    13·2 answers
  • If the measure of angle 1 is 110° and the measure of angle 3 is (2x+10)º, what is the value of x?
    8·1 answer
  • "A grain silo is shown below.
    12·1 answer
  • Some public goods and services are provided by the federal government, others by state governments, and still others by local ci
    13·1 answer
  • Points P and Q ∈ MN , MP = 2, QN = 5 and MN = 12. The distance from M to the midpoint of PQ is: (A) 5.5 (B) 3 (C) 4.5 (D) 6
    11·2 answers
  • How can I draw it please ​
    15·1 answer
  • What percentage of a dollar is the value of 5 quarters and 1 dime
    6·1 answer
  • Will give brainlest if right! Two plus two?
    10·2 answers
  • “If a population is growing at a rate of 3% per year, how long will it take to double? Show work.”
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!