Question 1a:
Compute the Laplace Transforms of
f(x) = { x² +2x +1 , x < 3
{ e⁻⁵ˣ , x ≥ 3
Answers
This is made easy if you know the Laplace transform pair
[tex]u(t - c) y(t - c) \mapsto e^{-cs} Y(s)[/tex]
where u(t) is the Heaviside step function and Y(s) is the Laplace transform of y(t).
We rewrite f, g, and h in terms of u :
[tex]f(x) = (x^2+2x+1) (u(x) - u(x-3)) + e^{-5x} u(x-3)[/tex]
[tex]g(x) = \sin(3x) (u(x-5) - u(x-10))[/tex]
[tex]h(x) = (u(x) - u(x-4)) + 2(u(x-4)-u(x-8)) + 3 (u(x-8)-u(x-16))[/tex]
and we also rearrange terms to get the right shift in argument:
[tex]f(x) = (x^2+2x+1) u(x) - ((x-3)^2+8(x-3)+16) u(x-3) + e^{-15} e^{-5(x-3)} u(x-3)[/tex]
[tex]g(x) = [\cos(15) \sin(3(x-5)) + \sin(15) \cos(3(x-5))] u(x-5) \\\\ ~~~~~~~~~~- [\cos(30) \sin(3(x-10)) + \sin(30) \cos(3(x-10))] u(x - 10)[/tex]
[tex]h(x) = u(x) + u(x-4) + u(x-8) - 3 u(x - 16)[/tex]
Now we can apply the known transform pair, along with
[tex]x^n \mapsto \dfrac{n!}{s^{n+1}}[/tex]
[tex]e^{ax} \mapsto \dfrac1{s-a}[/tex]
[tex]\sin(ax) \mapsto \dfrac{a}{s^2+a^2}[/tex]
[tex]\cos(ax) \mapsto \dfrac{s}{s^2+a^2}[/tex]
The transforms of f, g, and h are then
[tex]F(s) = e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-15} e^{-3s}}{s + 5} \\\\ = \boxed{e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-3(s+5)}}{s + 5}}[/tex]
[tex]G(s) = \dfrac{3\cos(15) e^{-5s}}{s^2+9} + \dfrac{s \sin(15) e^{-5s}}{s^2+9} - \dfrac{3\cos(30)e^{-10s}}{s^2+9} - \dfrac{s \sin(30) e^{-10s}}{s^2+9} \\\\ ~~~~~~~ = \dfrac{3(\cos(15)-\cos(30)) + s(\sin(15) - \sin(30))}{s^2+9} \\\\ ~~~~~~~ = \boxed{\dfrac{6\sin\left(\frac{45}2\right)\sin\left(\frac{15}2\right) - 2s \cos\left(\frac{45}2\right)\sin\left(\frac{15}2\right)}{s^2+9}}[/tex]
[tex]H(s) = \boxed{\dfrac{e^{-s} + e^{-4s} + e^{-8s} - 3 e^{-16s}}s}[/tex]
Related Questions
For problems 11-14, identify the property shown. 11. 16×p=16.
Answers
Answer:
Step-by-step explanation:
11. identity property
12. associative property
13. commutative property
14. zero property
PLS ANSWER THIS FAST
WILL MARK BRAINLIEST
Answers
The actual measurement of the length of the colored face of the aquarium is D. 36 inches by 14 inches.
What is a scale drawing?Generally, a scale drawing is described as a drawing that has been reduced or enlarged from its original size to a specified scale.
For instance, the scale of the drawing of the original aquarium is ¹/16. This implies that the length, width, and height have been scaled down to one-sixteenth of the original size.
Data and Calculations:Scale drawing = ¹/16 of the original aquarium
Length of the colored face = 2¹/₄ inches
The actual length of the colored face = 36 inches (2¹/₄ inches x 16)
Thus, the actual measurement of the length of the colored face of the aquarium is D. 36 inches by 14 inches.
Learn more about measurements at https://brainly.com/question/24842282
Please solve this for me
Answers
anyone help pls??
Find the perimeter and the area of the regular polygon with the given apothem a and side length s.
Answers
Step-by-step explanation:
apothem : distance from the center of the object to the side(s).
area : 1/2 × perimeter × apothem
perimeter : 9 x side
perimeter = 9×15 in = 135 in
area = 1/2 × 135 × 20.6 = 1,390.5 in²
The perimeter and area of a nonagon with apothem of 20.6 inches and side of 15 inches are 135 inches and 1390.5 inches² respectively.
What is a nonagon?A nonagon is a polygon with 9 sides. The perimeter and area can be found as follows;
Perimeter = length of the whole sides
side length = 15 inches
P = 9 × 15
p = 135 inches
Area of a nonagon = 1 / 2 pa
where
a = apothemp = perimeterTherefore,
apothem = a = 20.6 inches
area of the nonagon = 1 / 2 × 135 × 20.6
area of the nonagon = 2781 / 2
area of the nonagon = 1390.5 inches²
learn more on nonagon here: https://brainly.com/question/16228968?referrer=searchResults
How do you write 0.92 as a percentage?
Answers
0.92 ×
100
100
= (0.92 × 100) ×
1
100
=
92
100
Write in percentage notation: 92%
PLEASE HELP PLEASE PLEASE HELP
Answers
Answer:
The brightest star in the night sky is Sirius, located 500,000 times further away than the sun. Sirius is also 20 times brighter than the sun, which is why it is so easy to see at night. Our sun is a medium star of average size and brightness.
what is the answer because i dont know
Answers
Answer:
x° = 68°
Step-by-step explanation:
angle EGB = x° = angle AGF = complementary angle of 22°
The complementary angle of 22° is :
[tex]x^{o} =(90-22)^{o} =68^{o}[/tex]
Hope this helps
I need help finding the direction please. 100 points!
Answers
=======================================================
Explanation:
Take note that the x and y coordinate of this vector are the same.
This leads to a 45-45-90 reference triangle. If the vector was in the first quadrant (the northeast), then the answer would be 45 degrees.
However, we need to add on 180 so we get to the third quadrant instead where x and y are both negative. This gets us to 180+45 = 225 degrees
---------------
If you wanted to use a calculator, then you would compute the value of [tex]\tan^{-1}(b/a)[/tex] where <a,b> is the vector in question.
Since a = b in this case, we have b/a = 1 and the arctangent of this is 45 degrees. The adjustment of adding on 180 still applies like from before.
IM STUCK CAN SOMEBODY SOLVE THE EQUATION
Answers
Answer:
m = 4
(0, 1)
y = 4x + 1
Step-by-step explanation:
Slope using first two points (-2, 7) & (-1, -3):
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{-3+7}{-1+2} =\frac{4}{1}[/tex]
m = 4
Y-intercept, b: (0, 1)
Equation:
y = mx + b
y = 4x + 1
A family-size container of trail mix contains 40 ounces. This is 250% of the amount in the regular-size container.
How many ounces are in the regular-size container of trail mix?
Enter your answer in the box
Answers
Answer:
16 should be the correct answer
Help picture below problem 14
Answers
Answer:
value of missing angle is..57°
Step-by-step explanation:
mark me brainliest
54° and 69°
to find:the missing angle of the triangle.
solution:let's consider the missing angle as n.
sum of interior angle of triangle= 180°
n+54°+69°= 180° (adding up to sum of interior angle of triangle)
n+123°= 180°
n= 180°-123°
n= 57°
Sancho paints the new sign for his bike shop. One quart of paint covers 200 square
feet, and Sancho plans on applying three coats of paint. One quart of paint cost
$8.97. What is the square footage of his sign and ow much must Sancho spend to
paint the sign?
Answers
Slit the shape into a rectangle and two triangles:
Rectangle = 9 x 8 = 72 sq. Ft.
Triangle = 1/2 x 8 x 2.5 = 10 sq. Ft x 2 = 20 sq. Ft.
Total area = 72 + 20 = 92 sq. Ft.
3 coats x 92 = 276 sq ft worth of paint.
1 quart covers 200 so he would need to buy 2 quarts:
2 x $8.97 = $17.94 total
solve for x ~
[tex]x {}^{2} - 4x = 0[/tex]
thankyou ~
Answers
Answer:
[tex]x = 0 \\ x = 4[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 4x = 0 \\ x(x - 4) = 0 \\ \\ x = 0 \\ \\ x - 4 = 0 \: - > x = 4[/tex]
Which expression is a factored form of
3n² - 4n - 4
Answer choices.............................
................................................
ANSWER
for reference of other who need it. cuz I needed it and it wasn't on here
A: (n+2) (3n +1)
Answers
Answer:
The answer is (n – 2) (3n + 2)
Step-by-step explanation:
3n² – 4n – 4
3n² – 6n + 2n – 4
3n(n – 2) + 2(n – 2)
(n – 2) (3n + 2)
Thus, (n – 2) (3n + 2) is a factored of
3n² - 4n - 4
(2x > 10) list some values for x that would make this inequality true
Answers
Answer:
6 , 7 , 8 , 9...
Step-by-step explanation:
2x > 10
x > 5
then
x = 6 , 7 , 8, 9...
I think that I am right and also think this will helpful to you.....
Which of the following is equivalent to 3(y + 4) – 7? (А) Зу — 5 - В Зу – 3 С Зу + 5 D Зу +6
Answers
Use the Distributive Property, which states the following:-
a(b+c)[tex]\rightarrow[/tex]ab+ac
Simplify:-
3(y+4)-7
3y+12-7
Combine Like terms:-
[tex]\sf{3y+5}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
is 2/100 equivalent to 2/10
Answers
Answer:
no, because 2/10 is actually bigger than 2/100
Step-by-step explanation:
because if you think about a fraction as a part of a circle, and each of the denominators standed for one piece of the circle, then there would be way more pieces on the 100 circle and they would be smaller, thus, making 2 of them worth less than 2 of the circle with only 10 pieces.
can anyone help with this?
Answers
Answer:
It's a 270 degree rotation or -90 degree rotation there the same thing all the other answer choices are wrong besides 270 degree rotation.
Step-by-step explanation:
Traveling in a fried-out Kombi
On a hippie trail, head full of zombie
I met a strange lady, she made me nervous
She took me in and gave me breakfast
And she said
Do you come from a land down under?
Where women glow and men plunder?
Can't you hear, can't you hear the thunder?
You better run, you better take cover
Buying bread from a man in Brussels
He was six-foot-four and full of muscle
I said, "Do you speak-a my language?"
He just smiled and gave me a Vegemite sandwich
And he said
I come from a land down under
Where beer does flow and men chunder
Can't you hear, can't you hear the thunder?
You better run, you better take cover, yeah
Lyin' in a den in Bombay
With a slack jaw, and not much to say
I said to the man, "Are you trying to tempt me
Because I come from the land of plenty?"
And he said
Oh, you come from a land down under? (Ooh, yeah, yeah)
Where women glow and men plunder?
Can't you hear, can't you hear the thunder?
You better run, you better take cover ('cause we are)
Living in a land down under
Where women glow and men plunder
(Can't you hear thunder) can't you hear, can't you hear the thunder?
You better run, you better take cover
Living in a land down under
Where women glow and men plunder
Can't you hear, can't you hear the thunder? (Ooh yeah)
Better run, you better take cover (we are)
Living in a land down under (ooh yeah)
Where women glow and men plunder
Can't you, can't you hear the thunder?
Better run, you better take cover
Living in a land down under (living in a land down under)
Where women glow and men plunder
Can't you, can't you hear the thunder?
Alexander is a stockbroker. He earns 14% commission each week. Last week, he sold $5,400 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
Answers
Answer:
In that one week, his commision was $896, over all 52 weeks, he made $46592
Step-by-step explanation:
So, he makes 14% commision on any stock he sells. This week, he sold $6,400 worth of stocks, and, hes going to make 14% on it. So, take 6400 and divide that by 14%, and what do you get? $896! So, he made $896 that week. Now, say he made that amount EVERY WEEK. so, all you have to do is know how many weeks are in a year (52) and multiply that by 896, which gives you 46592.
Please help I'll mark brainliest
Answers
Answer:
The final answer is 16.
Gd luck with your work! :)
Answer:
Step-by-step explanation:
The equation c= 0.20t +3.50 shows the relationship between the charge, c in dollars, for renting a kayak for t minutes.
What is the meaning of the y-intercept?
O For So you can rent a kayak for 3.5 minutes.
It costs $3.50 per minute to rent a kayak
Every 3.50 minutes you have to pay $1.00
O You have to pay $3.50 up front before using the kayak.
Answers
Answer:
You have to pay $3.50 up front before using the kayak
True or False?
(–3)^22 is greater than (–2)^33
Answers
Answer:
true
Step-by-step explanation:
(-3)^22 -> to the power of an even number -> answer is positive
(-2)^33 -> to the power of an odd number -> answer is negative
positive # > negative #
Answer:
True
Step-by-step explanation:
First let's compare them.
(-3)²² (-2)³³-3 raised to an even power will give a positive number.
-2 raised to an odd power will give a negative number.
Therefore, (-3)²² > (-2)³³ is a true statement.
solve the system of equations:
-3x + 7y = -15
3x + 5y = 15
what do X and Y equal?
Answers
Answer:
x=5
y=0
Step-by-step explanation:
Let's solve the system of equations through elimination
Solving by elimination is when you add or subtract one equation by the other to eliminate one variable
In this case, adding 3x and -3x would cancel each other out so we should add the equations
[tex]-3x + 7y = -15\\+(3x + 5y = 15)\\0+12y=0\\12y=0[/tex]
Now solve for y
Divide both sides by 12 to isolate y
[tex]12y=0\\\\\frac{12y}{12} =\frac{0}{12} \\\\y=0[/tex]
Now sub in the value of y into one of the original equations and solve for x
[tex]3x+5y=15\\3x+5(0)=15\\3x=15\\[/tex]
Divide both sides by 3 to isolate x
[tex]\frac{3x}{3} =\frac{15}{3} \\x=5[/tex]
If John had four pizzas and shared them equally to his three friends, how many slices will he have?
Answers
Answer:
Is this really college math?
He would have 8 slices of pizza
Step-by-step explanation:
8 * 4 = 32
32 / 4 = 8...
the number of slices John would have after distributing it among his friends.
solution8×4=32
32/4
= 8
John would have 8 slices of pizza.
could anyone give me some quick help with this?
Answers
Answer:
a) 8xy = (4)(2xy)
b) 15x⁴z = (5x²)(3x²z)
c) -12x³y³ = (3y³)(-4x³)
d) 8x-2y = (2)(4x-y)
Step-by-step explanation:
a) 8xy = (4)(2xy) for the right side to equal the left 2xy needs to be multiplied by 4 to equal 8xy
b) 15x⁴z = (5x²)(3x²z) you need to multiply 5x² by 3x²z to equal 15x⁴z.
5*3 = 15 and x²*x² = x⁴ so 15x⁴*z = 15x⁴z
c) -12x³y³ = (3y³)(-4x³) becuase -4*3 = -12 and x³*y³ equal x³y³
d) 8x - 2y = (2)(4x-y) when you multiply 2 by 4x-y it equals 8x-2y
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
What are the last two digits of 7^1867?
Answers
Considering that the powers of 7 follow a pattern, it is found that the last two digits of [tex]7^{1867}[/tex] are 43.
What is the powers of 7 pattern?The last two digits of a power of 7 will always follow the following pattern: {07, 49, 43, 01}, which means that, for [tex]7^n[/tex], we have to look at the remainder of the division by 4:
If the remainder is of 1, the last two digits are 07.If the remainder is of 2, the last two digits are 49.If the remainder is of 3, the last two digits are 43.If the remainder is of 0, the last two digits are 01.In this problem, we have that n = 1867, and the remainder of the division of 1867 by 4 is of 3, hence the last two digits of [tex]7^{1867}[/tex] are 43.
More can be learned about the powers of 7 pattern at https://brainly.com/question/10598663
Si en total tiene 250 monedas que suman $42.50 ,Cuántas monedas de 25 centavos tiene en su alcancía?
Answers
Answer:
65 alojamiento
Step-by-step explanation:
answer quick i’ll give brainliest!! if you send links i’ll report u!
Answers
Answer:
[tex]\fbox{ Option D ➫ \: 416 \: cm²}[/tex]
Step by step explanation:
Given:
height of prism h = 18 cm
length of base of triangle b = 10cm
height of triangle h' = 2 cm
side A of triangle = 5 cm
side B of triangle = 7 cm
To find:
Surface area of prism = ?
Solution:
[tex]Area \: of \: base \: triangle = \: \frac{1}{2}\cdot{b}{h'} \\ Area \: of \: base \: triangle = \frac{1} {\not2}\cdot{10} \times \not{2} \\ Area \: of \: base \: triangle = 10 \: {cm}^{2} [/tex]
[tex] \fbox{Area \: of \: base \: triangle \: (B) = 10 \: cm²}[/tex]
[tex]Perimeter \: of \: base \: triangle = Side A + Side B + base b \\ Perimeter \: of \: base \: triangle = 5 + 7 + 10 \: cm \\ Perimeter \: of \: base \: triangle = 22 \: cm[/tex]
[tex] \fbox{Perimeter \: of \: base \: triangle (p) \: = 22 \: cm}[/tex]
[tex]Surface \: area \: of \: prism = 2B+ \: ph \\ Surface \: area \: of \: prism = 2 \times 10+ \: 22 \times 18 \\ Surface \: area \: of \: prism = 20 + 396\\ Surface \: area \: of \: prism = 416 \: {cm}^{2} [/tex]
[tex]\fbox{Surface \: area \: of \: prism = 416 \: cm²}[/tex]
Thanks for joining brainly community!
Answer:
D. 416 cm²
Step-by-step explanation:
Let S be the surface area of the prism
B be the area of the base of the prism
A be the lateral area of the prism
_______
formula :
S = 2B + A
__________
The base is a triangle ,then B the area of the base :
[tex]B=\frac{10 \times 2}{2}=10 \mathrm{~cm}^{2}[/tex]
_______
formula :
A = (Perimeter of the base) × (the height of the prism)
__________
then ,
[tex]\begin{aligned}A &=(10+5+7) \times 18 \\&=22 \times 18 \\&=396cm^2\end{aligned}[/tex]
Conclusion:
[tex]\begin{aligned}S &=2 B+A \\&=2 \times(10)+396 \\&=20+396 \\&=416 \mathrm{~cm}^{2}\end{aligned}[/tex]
write an equation of the line in slope-intercept form: A(-1,3) and b(2,-1)
Answers
Answer: y = [tex]\frac{-4}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
First we will find the slope, then we will find the y-intercept.
Slope is change in y over change in x:
[tex]\frac{-1-3}{2--1}=\frac{-4}{3}[/tex]
Now we will solve for the y-intercept:
y = [tex]\frac{-4}{3}[/tex]x + b
(-1) = [tex]\frac{-4}{3}[/tex](2) + b
-1 = [tex]\frac{-8}{3}[/tex] + b
[tex]\frac{5}{3}[/tex] = b
b = [tex]\frac{5}{3}[/tex]
Final equation:
y = [tex]\frac{-4}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
Having trouble with the question!
Answers
Answer:
C) [tex]6r^2-9r-6[/tex]
Step-by-step explanation:
Open the parentheses, you get:
[tex]-3r^2-2r-4+9r^2-7r-2[/tex]
Then combine like terms:
[tex]-3r^2+9r^2=6r^2\\-2r-7r=-9r\\-4-2=-6\\[/tex]
Then right as a polynomial:
[tex]6r^2-9r-6[/tex]
So the answer would be C)
Answer:
6r² - 9r - 6
Step-by-step explanation:
(-3r² - 2r - 4) - (-9r² + 7r + 2)
Multiply to remove the parenthesis:
(-3r² - 2r - 4) - (-9r² + 7r + 2)
1(-3r² - 2r - 4) - 1(-9r² + 7r + 2)
1(-3r²) +1(-2r) + 1(-4) + -1(-9r²) + -1(7r) + -1(2) <== remember that multiplying 2 negatives, makes a positive
-3r² - 2r - 4 + 9r² - 7r - 2
Combine any like terms:
-3r² - 2r - 4 + 9r² - 7r - 2
6r² - 9r - 6 <== make sure that your answer is in Standard form (in decreasing degrees)
Hope this helps!