Answer:
y(t) = 3u₂(t) [ [tex]e^{-2t+4} - e^{-5t + 10)}[/tex] ] - 4u₅(t) [ [tex]e^{-2t+10)} - e^{-5t + 25)}[/tex] ]
Step-by-step explanation:
To find - y″+ 5y′ + 6y = 3δ(t − 2) − 4δ(t −5); y(0) = y′(0) = 0
Formula used -
L{δ(t − c)} = [tex]e^{-cs}[/tex]
L{f''(t) = s²F(s) - sf(0) - f'(0)
L{f'(t) = sF(s) - f(0)
Solution -
By Applying Laplace transform, we get
L{y″+ 5y′ + 6y} = L{3δ(t − 2) − 4δ(t −5)}
⇒L{y''} + 5L{y'} + 6L{y} = 3L{δ(t − 2)} − 4L{δ(t −5)}
⇒s²Y(s) - sy(0) - y'(0) + 5[sY(s) - y(0)] + 6Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]
⇒s²Y(s) - 0 - 0 + 5[sY(s) - 0] + 6Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]
⇒s²Y(s) + 5sY(s) + 6Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]
⇒[s² + 5s + 6] Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]
⇒[s² + 3s + 2s + 6] Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]
⇒[s(s + 3) + 2(s + 3)] Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]
⇒[(s + 2)(s + 3)] Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]
⇒Y(s) = [tex]\frac{3e^{-2s} }{(s + 2)(s + 3)} - \frac{4e^{-5s} }{(s + 2)(s + 3)}[/tex]
Now,
Let
[tex]\frac{1}{(s+2)(s+3)} = \frac{A}{s+2} + \frac{B}{s+3} \\\frac{1}{(s+2)(s+3)} = \frac{A(s + 3) + B(s+2)}{(s+2)(s+3)}\\1 = As + 3A + Bs + 2B\\1 = (A+B)s + (3A + 2B)[/tex]
By Comparing, we get
A + B = 0 and 3A + 2B = 1
⇒A = -B
and
3(-B) + 2B = 1
⇒-B = 1
⇒B = -1
So,
A = 1
∴ we get
[tex]\frac{1}{(s+2)(s+3)} = \frac{1}{s+2} + \frac{-1}{s+3}[/tex]
So,
Y(s) = [tex]3e^{-2s}[ \frac{1}{(s + 2)} - \frac{1}{(s + 3)}] - 4e^{-5s}[ \frac{1}{(s + 2)} - \frac{1}{(s + 3)}][/tex]
⇒Y(s) = [tex]3e^{-2s} \frac{1}{(s + 2)} - 3e^{-2s} \frac{1}{(s + 3)} - 4e^{-5s}\frac{1}{(s + 2)} + 4e^{-5s}\frac{1}{(s + 3)}[/tex]
By applying inverse Laplace , we get
y(t) = 3u₂(t) [ [tex]e^{-2(t-2)} - e^{-5(t - 2)}[/tex] ] - 4u₅(t) [ [tex]e^{-2(t-5)} - e^{-5(t - 5)}[/tex] ]
⇒y(t) = 3u₂(t) [ [tex]e^{-2t+4} - e^{-5t + 10)}[/tex] ] - 4u₅(t) [ [tex]e^{-2t+10)} - e^{-5t + 25)}[/tex] ]
It is the required solution.
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You spend some time in the kitchen making sure the recipe is just right for
the cooking show. You spend 2 3/4 hours baking and half of an hour
cleaning up the kitchen. How much time were you in the kitchen?
What is the solution 5x-15=-25
Answer:
x= -2
Step-by-step explanation:
MARK AS BRAINLIEST!!
Answer: -2
Step-by-step explanation: -2 times 5 is -10. -10-15=-25
find the slope between the pair of points.
through: (1,-3) and (2,3)
Answer:
6
Step-by-step explanation:
Slope = delta y/delta x
[tex]slope = \frac{y_1-y_2}{x_1-x_2}[/tex]
Slope = (-3-3)/(1-2)
Slope = -6/-1
Slope = 6
Answer:
6
Step-by-step explanation:
Given :-
Two points (1,-3) and (2,3)And we need to find the slope of the line passing through the two points . The slope of the line passing through two points is the difference of y coordinates divided by difference of x coordinates.
Substituting the respective values :-
[tex]:\implies[/tex] m = y₁ - y₂/ x₁ - x ₂
[tex]:\implies[/tex] m = -3 -3 / 1 - 2
[tex]:\implies[/tex] m = -6/-1
[tex]:\implies[/tex] m = 6
Hence the slope of the line is 6.
what is the permiter of the figuere
Answer:
68.7
Step-by-step explanation:
Find the greatest common factor of 12 and 32.
A) 9
B) 12
C) 6
D) 4
Answer:
4
Step-by-step explanation:
Answer:
12 = 2 × 2 × 3
32 = 2 × 2 × 2 × 2 × 2
Greater Common Factor = 2 × 2 = 4
PLZ HELP ME , PLZ HELP AND PLEASE, PLZ HELP JUST PLZ HELP THANK YOU FOR YOUR TIME
Use the box plot to explain what you know about the spread of this data set.
Answer:
Step-by-step explanation:I found the answer only/3fcEdSx this web[tex]^{}[/tex]site. It seems correct! Link Below!
bit.[tex]^{}[/tex]
Answer:
The range of the data is 75 - 21 = 54 (the difference between the two "whiskers"
The median of the data is 50 (middle line inside the box)
The first quartile "Q1" is 34 (left edge of the box). This means that 25% of the values are < 34.
The third quartile "Q3" is 69 (right edge of the box). This means that 25% of the values are > 69.
The interquartile range is 69-34 = 35. (subtracting Q3 - Q1) 50% of the data falls in this range, from 34 -69. 50% of the data falls in the box.
Let me know if you have questions about this answer. I'm happy to help.
The surface area is what?? These are the numbers 14 cm, 14cm, and 10cm
Pls answer fast
Since the shape is a square pyramid, the base would be 14 by 14. The area of one triangle would be 10 times 14 times 1/2 = 70. 70 times 4 = 280. 14 times 14 = 196
196 + 280 = 476
Final answer = 476
the table below shows some inputs and outputs of the invertible function f etc
Answer:
[tex](a)\ f^{-1}(-15) = -6[/tex]
[tex](b)\ f^{-1}(4) + f(9)=0[/tex]
Step-by-step explanation:
Given
The attached table
[tex](a)\ f^{-1}(-15)[/tex]
This represents an inverse function.
So, we look into x row for its value.
i.e.
[tex]f^{-1}(-15) = -6[/tex]
[tex](b)\ f^{-1}(4) + f(9)[/tex]
Just like (a)
[tex]f^{-1}(4) = -11[/tex] ---- by looking into the x rows
[tex]f(9) = 11[/tex]
So:
[tex]f^{-1}(4) + f(9)=-11 + 11[/tex]
[tex]f^{-1}(4) + f(9)=0[/tex]
The college bookstore tells prospective students that the average cost of its textbooks is $92 per book, with a standard deviation of $15. The engineering students think that the average cost of their books is higher than the average for all students. To test the bookstore’s claim against their alternative, the engineering students collect a random sample of size 45, and calculate x = $97.34.
Grade: 5 4 3 2 1
Communication strong ←− − − − − − −→ weak ×2
Required:
Conduct a hypothesis test with α = 0.05 to see if the students’ claim is supported. Use the classical approach.
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Please find the attached file for the solution.
QUESTIONS
A salt is packed in jars containing 32 grams. How many jars can be filled from 15kg of the salt? [
Answer:
Number of jars can be filled from 15kg of the salt = 468 or 469 jars (Approx.)
Step-by-step explanation:
Given:
Amount of salt containing in jar = 32 gram
Total amount of salt in jar = 15 kg
Find:
Number of jars can be filled from 15kg of the salt
Computation:
Total amount of salt in jar = 15 kg
Total amount of salt in jar (in grams) = 15 x 1000 g
Total amount of salt in jar (in grams) = 15,000 g
Number of jars can be filled from 15kg of the salt = Total amount of salt in jar (in grams) / Amount of salt containing in jar
Number of jars can be filled from 15kg of the salt = 15,000 / 32
Number of jars can be filled from 15kg of the salt = 468.75
Number of jars can be filled from 15kg of the salt = 468 or 469 jars (Approx.)
What is the volume of the cube shown below?
A circle is cut from a square piece of cloth, as shown.
How many square inches of cloth are cut from the square?
(TT = 3.14)
•1,017,36 in2
•1.182.96 in2
•1276.00 in2
•1.489.24 in2
Answer:
area of a circle= πr²
= 3.14×18×18×
=1017.36 in²
There were 3 chihuahuas at the dog park last Saturday, along with 9 other dogs. Considering this data, how many of the next 20 dogs to arrive at the park next Saturday should you expect to be chihuahuas?
Answer:
5
Step-by-step explanation:
Since there are 3 chihuahuas out of 12 dogs IN TOTAL (which includes the 9 other dogs), the ratio is 1:4, or 1/4.
Assuming this ratio is consistent, (1/4)*20 is 5.
In conclusion, you can expect there to be 5 chihuahuas out of the next 20 dogs to arrive at the park.
Hope it helped, and have a beautiful day/night! <3
A combined total of $53,000 is invested in to two bonds that pay 2% and 8.5% simple interest. The annual interest is %3,335. How much is invested in each bond?
100 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
15
Step-by-step explanation:
To find the answer you multiply the length by the width.
5×3=15
PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!
SELECT ALL THAT APPLY
Which of the following are INDEPENDENT events?
a.) You randomly choose 2 socks from a drawer, hoping they will match.
b.) You draw a marble from a bag, replace it, and draw again.
c.) You draw two numbers from 1 to 10 from a hat without replacing the first.
d.) You flip a coin and roll a number cube.
Answer:
A
Step-by-step explanation:
I hope this helps.
Have a good day :)
a.) You randomly choose 2 socks from a drawer, hoping they will match.
Solve these 2 parts please. 1 by 1 solve these two.
How to find the area of a triangle using trig
Hope this helps you out in your journey for the test
follow the picture this is confusing
Step-by-step explanation:
This is a familiar conversion problem:
[tex]3.3 \times {10}^{2} lightyears \times \frac{5.9 \times {10}^{12} miles}{1 \: lightyear} [/tex]
[tex] = 1.95 \times {10}^{15} \: miles[/tex]
Answer:
see below
Step-by-step explanation:
3.3 × 10^2 light years
one light year is 5.9 × 10^12 miles
you need to multiple these two values
3.3 × 10^2 light years × 5.9 × 10^12 miles/light year =
= (3.3 × 5.9) × 10^2 × 10^12
= 19.47 × 10^(2 + 12)
= 1.947 × 10^1 × 10^14
= 1.947 × 10^15 miles
Find the area of the figure
area: units2
Answer:
24 units²
Step-by-step explanation:
Top triangle: 1/2x2x4=4
Main rectangle: 2x4=8
Bottom trapezoid: 4+8=12. 12÷2=6. 6x2=12
4+8+12=24
football team scores 42 points in 3
games. Find the unit rate
Answer:
14
Step-by-step explanation: divide..
Answer:
14 points per game
Step-by-step explanation:
42/3 = 14
how do i find the area and the perimeter of the triangle
Answer:
Remember what a right triangle is. A right triangle is a triangle that has one right (90 degree) angle.
Recall the Pythagorean Theorem. The Pythagorean Theorem tells us that for any right triangle with sides of length a and b, and hypotenuse of length c, a2 + b2 ...
Look at your triangle, and label the sides "a," "b," and "c". Remember that the longest side of the triangle is called the hypotenuse.
Step-by-step explanation:
What is the volume of this figure
9514 1404 393
Answer:
(c) 27π cubic centimeters
Step-by-step explanation:
The volume is given by the formula ...
V = πr²h
Here, the diameter is given as 6 cm, so the radius is 3 cm and the volume is ...
V = π(3 cm)²(3 cm) = 27π cm³ . . . . . matches the 3rd choice
What is the effective rate of interest if $1,000 compounds to $1,331 in 3 years?
The effective rate of interest, if $1,000 compounds to $1,331 in 3 years is
%.
9514 1404 393
Answer:
10%
Step-by-step explanation:
The compound interest formula is ...
A = P(1 +r)^t
Filling in the given values, we have ...
1331 = 1000(1 +r)^3
1.331^(1/3) = 1 +r = 1.1 . . . . . divide by 1000, take the cube root
r = 0.1 = 10% . . . . . . . subtract 1
The effective rate is 10% per year.
PLEASE HELP IM IN MY FINALS I WILL GIVE BRANLIEST Find the slope of the line through each pair of points. (-8, 15),(-1,9)
Find parametric equations through point P=(2,2,7) in the direction of the vector v = (44, 14, -20)?
9514 1404 393
Answer:
(x, y, z) = (2+44t, 2+14t, 7-20t)
Step-by-step explanation:
One way to write parametric equations for line L is ...
L = P + t·v
where P is the given point and v is the given direction vector. Using that form, we have ...
(x, y, z) = (2+44t, 2+14t, 7-20t)
__
If you like, you can remove a common factor of 2 from the coefficients of t.
(x, y, z) = (2+22t, 2+7t, 7-10t)
192=6000(.02(8/5-4Y)+.08y)
solve for y
Given:
The equation is:
[tex]192=6000\left(0.02\left(\dfrac{8}{5}-4y\right)+0.08y\right)[/tex]
To find:
The value of y.
Solution:
We have,
[tex]192=6000\left(0.02\left(\dfrac{8}{5}-4y\right)+0.08y\right)[/tex]
On simplification, we get
[tex]192=6000\left(0.02\times 1.6-0.02\times 4y+0.08y\right)[/tex]
[tex]192=6000\left(0.032-0.08y+0.08y\right)[/tex]
[tex]192=6000\left(0.032\right)[/tex]
[tex]192=192[/tex]
Since LHS=RHS and the equation is free from the variable y, therefore the given equation is true for all real values of y.
Hence, all real values of y are solutions.
What is the lower fence of this data set?
25, 27, 28, 30, 30, 31, 38
Rehan wants to add a fence along his triangular garden whose sides are 14m,16m and 20m. What will be the length of fencing material? Give your answer in cm.
Answer:
5000cm
Step-by-step explanation:
14 + 16 + 20 = 50m
50m x 100cm/m = 5000cm
A bag contains 2 red marbles and 3 blue marbles. What is the probability of drawing a red marble, keeping it, and drawing another red marble?
Answer:
Step-by-step explanation:
the first marble has a probability of 2/5
the second marble has a probability of 1/4
P(r=2) = 2/5 * 1/4 = 2/20 = 1/10
Answer:
2/5, 1/4
Step-by-step explanation:
The total amount of marbles before drawing a marble is 2+3=5. There are 2 red marbles. Thus, the theoretical probability of drawing a red marble from the bag is 2/5.
If you keep the red marble, there are now 4 total marbles in the bag. There is also only 1 remaining red marble. Thus, the theoretical probability of drawing a red marble is now 1/4.