Find the Laplace transform F(s) = L {f(t)} of the function f(t) = et-³h(t – 3), defined on the interval t > 0. F(s) = L {et ³h(t - 3)}
The Laplace transform of f(t) = et-³h(t – 3) is F(s) = 1/3 * 1/(s + 3) - 1/3 * 1/s, or F(s) = (s - 1)/(3s(s + 3)).
To find the Laplace transform F(s) = L{f(t)} of the function f(t) = et-³h(t – 3), we can use the properties and formulas of Laplace transforms. Let's break down the function and compute its transform step by step.
et-³: This term represents the exponential function with a power of t-³. The Laplace transform of et is given by 1/(s - a), where a is the exponent in the exponential function. Therefore, the Laplace transform of et-³ is 1/(s + 3).
h(t - 3): This term represents the Heaviside step function, h(t), shifted by 3 units to the right. The Laplace transform of the Heaviside step function h(t) is 1/s. When the function is shifted by a constant, the Laplace transform remains the same.
Combining these results, we have F(s) = L{f(t)} = 1/(s + 3) * 1/s.
To simplify the expression, we can use partial fraction decomposition:
1/(s + 3) * 1/s = A/(s + 3) + B/s.
Solving for A and B by equating numerators, we find A = 1/3 and B = -1/3.
Therefore, the Laplace transform of f(t) = et-³h(t – 3) is F(s) = 1/3 * 1/(s + 3) - 1/3 * 1/s, or F(s) = (s - 1)/(3s(s + 3)).
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Plz help me we are almost done
Answer: 1. A 2. 1/5 3. 5/12 4. Not sure
Step-by-step explanation:
She spent 1hr 15min washing her car and she spent 1hr 50min cleaning her house, how long did it take
Answer:
3 hours 5 minutes
Step-by-step explanation:
1 hour + 1 hour = 2hrs
15 minutes + 50 minutes = 65 minutes
65 minutes to 1 hr = 1 hr 5 minutes
2 hours + 1 hr 5 minutes = 3 hours 5 minutes
Answer:
3 hours and 5 minutes
Step-by-step explanation:
1 hour=60 minutes
1 hour +1 hour =2 hours
50 minutes +15 minutes = 1 hour and 5 minutes
1 hour and 5 minutes +2 hours=
3 hours and 5 minutes
A Bow-Wow chew toy costs $20. 10% of the purchase price is
donated to an animal shelter. How much is donated for each
chew toy?
Answer:
2 dollars donated.
Step-by-step explanation:
Answer:
18.18
Step-by-step explanation:
Solve for the given time.
You buy a car for $15,000 and it depreciates at a rate of 4.3% per month. How much is the car worth after a year?
Answer:
8851.86
Step-by-step explanation:
100-4.3= 95.7%
15000(.957)^12
what is the area of the smaller figure, in square centimeters?
a. 4
b. 8
c. 20
d. 40
A composite figure consists of two smaller figures - a rectangle and a Triangle. Therefore, the answer is 4 cm² (option a).
A composite figure that consists of two smaller figures - a rectangle and a triangle.
To find the area of the composite figure, we need to find the area of each smaller figure and add them up .Areaof rectangle to find the area of the rectangle, we need to multiply its length and width :Area of rectangle = 2 cm × 4 cm = 8 cm²Areaof triangle too find the area of the triangle, we need to use the formula :
Area of triangle = 1/2 × base ×heightT
he base of the triangle is 4 cm and the height is 2 cm, so:
Area of triangle = 1/2 × 4 cm × 2 cm = 4 cm²Area of composite figure To find the area of the composite figure, we need to add up the area of the rectangle and the area of the triangle: Area of composite figure = 8 cm² + 4 cm² = 12 cm². Therefore, the answer is 4 cm² (option a).
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You have been offered a unique investment opportunity. If you invest $10,000 today, you will receive $500 one year from now, $1,500 two years from now, and $10,000 ten years from now a. What is the NPV of the investment opportunity if the interest rate is 6% por year? Should you take the opportunity? b. What is the NPV of the investment opportunity if the interest rate is 2% per year? Should you take the opportunity? a. What is the NPV of the investment opportunity if the interest rate is 6% per year? The NPV of the investment opportunity at the interest rate is 0% per year is $(Round to the nearest dollar)
The NPV of the investment opportunity at a 6% interest rate is approximately $6,374. Taking into account the timing and value of the cash flows, it is advisable to take the opportunity.
The Net Present Value (NPV) of an investment opportunity calculates the present value of future cash flows discounted at a specific interest rate. Let's calculate the NPV at a 6% interest rate:
Year 1: Receive $500.
Year 2: Receive $1,500.
Year 10: Receive $10,000.
To find the NPV, we need to discount each cash flow back to its present value and sum them up:
NPV = (Cash flow at Year 1 / (1 + Interest rate)^1) + (Cash flow at Year 2 / (1 + Interest rate)^2) + (Cash flow at Year 10 / (1 + Interest rate)^10) - Initial investment
Plugging in the values, we get:
NPV = (500 / (1 + 0.06)^1) + (1500 / (1 + 0.06)^2) + (10000 / (1 + 0.06)^10) - 10000
≈ $6,374
Therefore, at a 6% interest rate, the NPV of the investment opportunity is approximately $6,374. Since the NPV is positive, it indicates that the investment is expected to generate a return greater than the cost of capital. Hence, it is advisable to take the opportunity.
(Note: The calculation for the NPV at 0% interest rate requires all future cash flows to be treated at their face value. Therefore, the NPV at a 0% interest rate would be equal to the sum of all future cash flows, which is $11,000 in this case.)
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City 1
New Orleans, Louisiana
New Orleans, Louisiana
New Orleans, Louisiana
New Orleans, Louisiana
City 2
Washington, DC
Nashville, Tennessee
Seattle, Washington
Shreveport, Louisiana
Approximate Distance Between cities
2 x 106 meters
9 x 105 meters
4 X 106 meters
5 x 105 meters
Add
1. What is the combined distance that you would travel if you completed a roundtrip from New Orleans, Louisiana,
to Washington, DC, and a roundtrip from New Orleans, Louisiana, to Seattle, Washington? Write your answer in
scientific notation.
The electronics store is offering 30% off all accessories. If Lisa saves $9.00 buying four charging cords, what was the original price of the cords?
Answer:
Cost of each cord = $7.5
Step-by-step explanation:
Given:
Discount rate = 30% = 0.30
Amount save by Lisa = $9
Number of charger = 4
Find:
Cost of each cord
Computation:
Total cost of 4 charger = Amount save by Lisa[1/Discount rate]
Total cost of 4 charger = 9[1/0.30]
Total cost of 4 charger = $30
Cost of each cord = Total cost of 4 charger / Number of charger
Cost of each cord = $30 / 4
Cost of each cord = $7.5
Each Friday, the school prints 400 copies of the school newsletter. The equation c = 400w models the relationship between the number of weeks and the total number of copies of the newsletters printed. What is true of the graph of this scenario?
A viable point on the graph is
.
The values of w must be
Answer: A viable point on the graph is ✔ (8, 3,200).
The values of w must be✔ any whole number.
Answer:
A viable point on the graph is
✔ (8, 3,200)
.
The values of w must be
✔ any whole number
.Step-by-step explanation:
I did it on Edge and got it right
Which expression is equivalent to 16 + 2 * 36?
Answer: F 2^4+2^3 .3^2
Step-by-step explanation:
16+2*36
2^4+72
2^4+2^3 .3^2
here 2^3=8
and 3^2=9
so 8*9=72
What is the square root of 144
The square root of 144 using the prime factorization method is 12.
When a number is multiplied by itself, the square of the number can be obtained.
The square root of 144 can be determined by the prime factorization method:
The prime factors of 144 are:
[tex]144 = 2 \times 2\times2 \times2 \times3 \times 3[/tex]
Since the square root can be obtained by forming the pair of the given number.
It can be written as:
144 = [tex]2^2 \times 3[/tex]
=[tex]4 \times 3[/tex]
= 12
Thus, the square root of 144 is 12.
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Can I get help with this please I am so stuck in here
Answer:
the correct answer is d
hope it help
Use the order of operations to solve for C when n = 5.
C = 7(4n + 2) - 8
Use order of operations to solve for C when n = 5.
C = 45 - 3n
What is 5 - (-2) =
Plz help I’m thinking it’s 3 but don’t know
Answer:
7
Step-by-step explanation:
just add them
them you get answer
Find the value of x. A 65° B 32.5° C 70° D 147.5°
Answer:
A
Step-by-step explanation:
idek sorry i think its A
3 3/5 X (-8 1/3) = ?
-30 is your answer.
Step by Step pictured below.
OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME WHAT TO DRAW
Answer:
calm down rosie.... it's okay to not be too good at math... take Justin Timberlake. in the show "Friends with Benefits" he's horrible at math but good at life. so don't worry too much. You are still a good person.. even if you're bad at math :P
Step-by-step explanation:
now for the math part
as below
PLEASE HELP:)!!!!!
Which of the following projections is MOST accurate?
A) When the peak temperature is 40°C ,35 units of electricity are used on average
B) When the peak temperature is 40°C, 120 units of electricity are used on average
C) When the peak temperature is 40°C, 48 units of electricity are used on average
D) When the peak temperature is 40°C , 72 units of electricity are used on average
Answer:a
Step-by-step explanation:
jsut heklp plkease ive literally beegn sobbing for foirefver
Answer:
A. Side a is 7 inches long and side b is 6 inches long.
Step-by-step explanation:
a = 21/3 = 7
b = 18/3 = 6
2hours at 30km/h 7 hours at 65 km/h 1/2 hours at 46 km/h 45 minutes at 80 km/h 1 1/2 hours at 55km/h fors numbers 1-5, calculate the distance that you would travel if you drove for;
Answer:
60 km
455 km
23 km
60 km
82.5 km
Step-by-step explanation:
Time = t
Speed = s
Distance is given by
[tex]d=s\times t[/tex]
t = 2 hours
s = 30 km/h
[tex]d=30\times 2=60\ \text{km}[/tex]
Distance driven is 60 km.
t = 7 hours
s = 65 km/h
[tex]d=65\times 7=455\ \text{km}[/tex]
Distance driven is 455 km
t = [tex]\dfrac{1}{2}\ \text{hours}=0.5\ \text{hours}[/tex]
s = 46 km/h
[tex]d=46\times 0.5=23\ \text{km}[/tex]
Distance driven is 23 km
t = 45 minutes = [tex]\dfrac{45}{60}=0.75\ \text{hours}[/tex]
s = 80 km/h
[tex]d=80\times 0.75=60\ \text{km}[/tex]
Distance driven is 60 km
t = [tex]1\dfrac{1}{2}\ \text{hours}=1.5\ \text{hours}[/tex]
s = 55 km/h
[tex]d=55\times 1.5=82.5\ \text{km}[/tex]
The distance driven is 82.5 km
Maths
Oder of rotations symmetry and number of lines of symmetry
Answer:
i) a) 4 lines
b) 1 line
c) 3 line
d) 2 line
ii) don't know
Which theorem can you use to show that the quadrilateral on the tile floor is a parallelogram?
Answer:
Parallelogram Theorem #1 Converse
Step-by-step explanation: : If each of the diagonals of a quadrilateral divide the quadrilateral into two congruent triangles, then the quadrilateral is a parallelogram. Parallelogram Theorem #2 Converse: If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Parallelogram opposite sides converse. Therefore, option A is the correct answer.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
Let the diagonals AC and BC intersect at O.
Consider, triangle BOC and triangle AOD
OA=OC (Shown in the figure)
∠AOD=∠BOC (Vertically opposite angles are equal)
BO=DO (Shown in the figure)
By SAS congruence theorem
triangle BOC and triangle AOD are congruent
So, by CPCT AD=BC
Similarly,
From, triangle AOB and triangle DOC
AB=DC
Therefore, option A is the correct answer.
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A student has a rectangular photograph with side lengths of 5 inches and x inches The area of the rectangle is 33 square inches. The student wants to reduce the size of the photograph so that each side length is of its original length. The photograph will be printed on paper that costs $0.16 per square inch. What will be the cost of the paper needed to print the reduced photograph?
Answer:
1.32
Step-by-step explanation:
total area = 33
33/5 1/2 = 6 . X=6
5 1/2 x 1/2 = 2.75 . 6 x 1/2 = 3
2.75 x 3 = 8.25
new area = 8.25
8.25 x .13 = 1.32
Help plz!! 100 points
Answer:
t = 0, 1, 4, 8
h = 0, 12, 0 , 18
Step-by-step explanation:
t = 0 + 1 + 3 + 4
/ x1 - 5 (2) x + 4x + 9
h = 0, 12, 0, 18
After 18 seconds the ball attains...
x/3 = 1/4 - 4x 2(7) = 9/2 - 2 / 4 (0)
Answer:
t = 0, 1, 4, 8
h = 0, 12, 0 , 18
t = 0 + 1 + 3 + 4
Step-by-step explanation:
/ x1 - 5 (2) x + 4x + 9
h = 0, 12, 0, 18
After 18 seconds the ball attains...
x/3 = 1/4 - 4x 2(7) = 9/2 - 2 / 4 (0)
which of the following matrices has an inverse?
Answer: C
Step-by-step explanation:
3x + 2y = 4
X + 2y = -4
Notice the equations are NOT in slope-intercept form.
Rewrite them in slope intercept form y = mx + b.
Find the slope: Will give brainliest if it is correct
Answer:
-3/5 is the slope of the line.
Can someone help me pleaseee
Answer:
d or c more likey d
Step-by-step explanation:
10!!! POINTS AND BRAINLIEST!!!
Answer:
[tex]\boxed {\boxed {\sf 53}}[/tex]
Step-by-step explanation:
This is a stem and leaf plot, so the stem represents the first digit, while the leaf is the last digit.
Stem# Leaf#The first stem is 0, with a leaf of 4. Therefore,
04 = 4The last stem is 5, with 2 leaves: 6 and 7. We want to find the largest number, so we will use 7.
57The range is the difference between the largest and smallest number. The largest number is 57 and the smallest is 4.
Range= largest-smallest Range= 57-4=53The range is 53.