july00
24.07.2020 •
Mathematics
Please help with this
Solved
Show answers
More tips
- O Other What happens if you get scared half to death twice?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
- S Style and Beauty How to Make Your Lips Fuller? Ideas and Tips for Beautiful Lips...
- S Style and Beauty How are artificial nails removed?...
- F Family and Home How to Sew Curtain Tapes: Best Tips from Professionals...
- H Horoscopes, Magic, Divination How to Cast a Love Spell on a Guy? Guide for Guys...
- F Family and Home How to Properly Use a Water Level?...
- L Legal consultation What Documents Are Required for a Russian Passport?...
- H Health and Medicine How to Treat Styes: Causes, Symptoms, and Home Remedies...
- F Family and Home Protect Your Home or Apartment from Pesky Ants...
Answers on questions: Mathematics
- M Mathematics Pls help! In the figure below, m∠ABC = 57 degrees and m∠DAB =116 degrees. What is m∠ABC?...
- M Mathematics ASAP due in 4 minutes links will be reported. Right answers is brainliest marked and 5 stars and heart thank you...
- M Mathematics A triangle is placed in a semicircle with a radius of 9 ft, as shown below. Find the area of the shaded region. Use the value 3.14 for (pie symbol), and do not round your answer....
- M Mathematics Solve the problem. Suppose a necklace is made from 18-karat gold and weighs 54 grams. Find the weight, in grams, of the pure gold in the necklace....
- M Mathematics Acil yaparmisiniz ıdkdkdjdkkdkz...
- M Mathematics Find the values of x, y, and (a) Find the value of x (b) Find the value of y (C) Find the value of z...
- M Mathematics Please help!! 50% of my grade NO LINKS!this is the rest of my points...
- M Mathematics And what is the permiter of the right triangle A. 21 in sq B. 28 in sq C. 31.5 in sq D. 63 in sq...
- M Mathematics Please answer correctly...
- M Mathematics A box of dried fruit has 39 calories in 3 servings. How many calories are there per serving?...
Ответ:
B) 5
Step-by-step explanation:
Solve by ratios.
10/5x = 8/20
Cross multiply.
5x × 8 = 20 × 10
40x = 200
Divide both sides by 40.
(40x)/40 = 200/40
x = 5
Ответ:
y(t) = (191/102)e^(-3t) + (205/183)e^(6t) + (15/2074)cos(5t) + (43/2074)sin(5t)
Step-by-step explanation:
Given the differential equation:
y'' - 3y' - 18y = sin(5t)(1)
y(0) = 3
y'(0) = 1
To find this, by taking the Laplace transform of the differential equation, we know that
L{y(t)} = Y.
L{y''} = s²Y - sy(0) - y'(0)
L{y'} = sY - y(0)
y(0) = 3
y'(0) = 1
Taking the Laplace transform of both sides (1), we have have the differential equation to be:
[s²Y - sy(0) - y'(0)] - 3[sY - y(0)] - 18[Y] = 5/(s² + 25)
s²Y - 3s - 1 - 3sY + 9 - 18Y = 5/(s² + 25)
(s² - 3s - 18)Y - 3s + 8 = 5/(s² + 25)
(s² - 3s - 18)Y = 3s - 8 + 5/(s² + 25)
(s + 3)(s - 6)Y = 3s - 8 + 5/(s² + 25)
Divide both sides by (s + 3)(s - 6) to have:
Y = 3s/(s + 3)(s - 6) - 8/(s + 3)(s - 6) + 5/(s²+ 25)(s + 3)(s - 6)
Resolving each of the fractions on the right hand side into partial fractions, we have
Y = 1/(s + 3) + 2/(s - 6) - (8/9)[1/(s - 6) - 1/(s + 3)] + (5/2074)[3s/(s² + 25) - 43/(s² + 25)] + (5/549)[1/(s - 6)] - (5/306)[1/(s + 3)]
Next, we take the Inverse Laplace Transform of the last equation to obtain the required solution:
y(t) = e^(-3t) + 2e^(6t) - (8/9)[e^(6t) - e^(-3t)] + (5/2074)[3cos(5t) + (43/5)sin(5t)] + (5/549)e^(6t) - (5/306)e^(-3t)
= (1 + 8/9 - 5/306)e^(-3t) + (2 - 8/9 + 5/549)e^(6t) + (15/2074)cos(5t) + (43/2074)sin(5t)
= (191/102)e^(-3t) + (205/183)e^(6t) + (15/2074)cos(5t) + (43/2074)sin(5t)