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
vovangra [49]
3 years ago
14

Show that y=2e^(−x) cos(x)−e^(−x) sin(x) is a solution to y''+2y'+2y=0.

Mathematics
1 answer:
Furkat [3]3 years ago
7 0

Answer:

y=2e^(−x)cosx−e^(−x)sinx

Satisfies the equation

Step-by-step explanation:

Answer:

y=2e^(−x)cosx−e^(−x)sinx

y = e^(-x)[2cosx - sinx]

Find y' and y" using product law

y' = -e^(-x)[2cosx - sinx] + e^(-x)[-2sinx - cosx]

y' = -e^(-x)[2cosx - sinx + 2sinx + cosx]

y' = -e^(-x)[3cosx + sinx]

y" = e^(-x)[3cosx + sinx] - e^(-x)[-3sinx + cosx]

y" = e^(-x)[3cosx - cosx + sinx + 3sinx]

y" = e^(-x)[2cosx + 4sinx]

y" + 2y' + 2y

e^(-x)[2cosx + 4sinx] - 2e^(-x)[3cosx + sinx] +2e^(-x)[2cosx - sinx]

e^(-x)[4sinx - 2sinx - 2sinx + 2cosx - 6 cosx + 4cosx]

= e^(-x) × 0

= 0

You might be interested in
One side of triangle is 4cm longer than the shortest side and 2cm shorter than the longest side the perimeter is 38cm what are t
o-na [289]
9.3, 13.3, 15.3
Hope it helps!
7 0
3 years ago
Read 2 more answers
Pls help I’ll give extra pints
Sonja [21]

Answer:

pls help with what brainlics

4 0
3 years ago
Read 2 more answers
What is 3/5(15k+10)=12k-9 in steps
Diano4ka-milaya [45]
<em>multiply both sides by 5  </em>        3(15k+10)=5(12k-9)     
<em>get rid of the brackets</em>             45k+30=60k-45
<em>take away 45k to both sides</em>    30=15k-45
<em>plus 45 to both sides</em>               75=15k
<em>divide both by 15</em>                     k=5
8 0
3 years ago
Use the x-intercept method to find all real solutions of the equation -9^3-72^2-96x+36=3x^3+x^2-3x+8
Vadim26 [7]

Answer:

 x ≈ 0.290640965127

Step-by-step explanation:

y subtracting the right side of the equation, we get a function that is zero at a real solution for x. The only x-intercept is at approximately 0.290640965127.

___

The graph shows the x-intercept to be 0.2906. The value above was obtained by Newton's method iteration. The roots of this cubic will all be irrational.

7 0
3 years ago
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the
Svetlanka [38]

Answer:

The hotel charge in each city before tax was <u>$5125</u> of the first city and <u>$3625</u> of the second city.

Step-by-step explanation:

Given:

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.

The tax of the first city was 6% and the tax of the second city was 10%.

Total hotel tax paid for two cities with $670.

Now, to find the hotel charge in each city before tax.

Let the hotel charge in first city before tax be x.

And the hotel charge in second city before tax be y.

<em>So, as the hotel charge of the second city was 1500 higher than the first.</em>

<em>Thus</em>,

y=x-1500   ........(1)

<em>And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.</em>

6% of x + 10% of y = $670.

\frac{6x}{100} +\frac{10y}{100} =670

0.06x+0.10y=670

Substituting the value of y from equation (1) we get:

0.06x+0.10(x-1500)=670

0.06x+0.10x-150=670

0.16x-150=670

<em>Adding both sides by 150 we get:</em>

0.16x=820

<em>Dividing both sides by 0.16 we get:</em>

x=5125.

<em>The hotel charge in first city before tax = $5125.</em>

Now, substituting the value of x in equation (1) we get:

y=x-1500

y=5125-1500

y=3625.

<em>The hotel charge in second city before tax = $3625.</em>

Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

5 0
3 years ago
Other questions:
  • How do i simplify -√80<br> please explain in depth
    14·1 answer
  • Select from the drop-down menu to correctly compare the numbers.
    10·2 answers
  • A and B share the cost in a ratio of 3:2 the cost is £85 how much does A pay.
    14·1 answer
  • A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC b
    12·1 answer
  • The formula F = ma shows the relationship between force, mass, and acceleration. Solve this formula for a.
    11·1 answer
  • Jillian buys 3.6 meters of fabric. The fabric costs $5.75 for each meter. How much does Jillian spend for the fabric?I need help
    15·1 answer
  • What percent is 23 of 92?
    6·2 answers
  • Help and explain pls and thankyouuu
    14·2 answers
  • What is the value of 6x² when x = 1/3​
    13·1 answer
  • The length of a rectangle is 6 inches longer than its width. The perimeter of the rectangle is 28 inches. If x represents the
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!