Answer:
k = 16
Step-by-step explanation:
To solve this we must isolate k. Let's first simplify this equation by subtracting 8 from both sides:
k/4 = 4
Next, remove the fraction by multiplying both sides by 4:
k = 16
Find the inverse transform by convolution: 4 (s-3)(s-2) C.27.
I suppose you're asking about the inverse Laplace transform of
[tex]F(s)=\dfrac4{(s-3)(s-2)}[/tex]
by way of the convolution theorem.
The theorem itself says that
[tex]\mathscr L^{-1}\{A(s)B(s)\}=(a*b)(t)[/tex]
where [tex]A(s)[/tex] and [tex]B(s)[/tex] are the Laplace transforms of [tex]a(t)[/tex] and [tex]b(t)[/tex], respectively.
Let [tex]A(s)=\frac1{s-3}[/tex] and [tex]B(s)=\frac1{s-2}[/tex]. Then
[tex]a(t)=\mathscr L^{-1}\left\{\dfrac1{s-3}\right\}=e^{3t}[/tex]
[tex]b(t)=\mathscr L^{-1}\left\{\dfrac1{s-2}\right\}=e^{2t}[/tex]
So we have
[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=e^{3t}*e^{2t}[/tex]
Convolution is defined as
[tex](a*b)(t)=\displaystyle\int_0^t a(t-\tau)b(\tau)\,\mathrm d\tau[/tex]
The convolution of [tex]e^{3t}[/tex] and [tex]e^{2t}[/tex] is
[tex]e^{3t}*e^{2t}=\displaystyle\int_0^t e^{3(t-\tau)}e^{2\tau}\,\mathrm d\tau[/tex]
[tex]=\displaystyle e^{3t} \int_0^t e^{-\tau}\,\mathrm d\tau[/tex]
[tex]=e^{3t}(1-e^{-t})=e^{3t}-e^{2t}[/tex]
We end up with
[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=\boxed{4(e^{3t}-e^{2t})}[/tex]
PLEASE HELP!!! URGENT
Answer:
scale factor = ratio of corresponding side= 0p/xy = 4/10= 2/5
∠x = 58
∠y= 180-49-58= 73
Step-by-step explanation:
What is the expanded form for 102,200
Answer: 100,000 + 2000 + 200
Hope this helps!
Please mark Brainliest!
Answer:
100,00+2,000+200
Step-by-step explanation:
simplify to create an equivalent expression -4(z+3)-4(5-4z)
evaluate 7m+2n-8p/n m=4, n=2, and p=1.5
Steps to solve:
7m + 2n - 8p/n
~Substitute
7(4) + 2(2) - 8(1.5)/2
~Simplify
28 + 4 - 12/2
~Simplify
28 + 4 - 6
~Add
32
~Subtract
26
Best of Luck!
scientific notation
Answer:
1.45
Step-by-step explanation:
not sure but trying to help :)
find the first three terms of the sequence with nth term 3n-2
Answer:
To find out the first three terms of 3n - 2 substitute 1 ,2 and 3 into the equation.
so the three terms a
3(1)-2=1
3(2)-2=6-2=4
3(3)-2=9-2=7
As you can see the sequence goes up in 1,4 and 7.To find out the 10th term you also substitute 10 into the equation so 3(9)-2=18-2=16
so 16 is the tenth term
Hope this helped!
Dale made a model of a lighthouse using a 4 inches=50 feet if the lighthouse is 120 feet tall, how tall is his model
Answer:
8 2/5 inches!
Step-by-step explanation:
The lighthouse is 120 feet, and 4 inches of height on the model equals 50 feet of height on the lighthouse. 100 divided by 50 = 2, and 4 multiplied by 2 is 8. 20 divided by 50 = 2/5, so the answer is 8 2/5 inches. :)
A clown uses canisters of helium to make balloons. The graph shows the number of canisters used and the number of balloons created. What does the point (0,0) represent? A It shows the number of balloons created using 1 canister of helium. B It shows that when 0 canisters of helium are used, 0 balloons are created. C It shows that when 0 canisters of helium are used, 5 balloons are created. D It shows the number of canisters needed to create 10 balloons.
Answer:
B It shows that when 0 canisters of helium are used, 0 balloons are created
Step-by-step explanation:
from the graph, we can see that point (0,0) means that when the number of canisters of helium used is 0, then the number of balloons created is also 0
the closest answer to this observation is:
B It shows that when 0 canisters of helium are used, 0 balloons are created
What is 45divided by 9 ?
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Step 1:
45 ÷ 9
Answer:
5
Hope This Helps :)
1/2 + .50 + 1/5 help ):
Answer:
the answer is 1.2 or 1 1/5
Step-by-step explanation:
Answer:
.50 = 1/2 so its 1/2 plus 1/2 plus 1/5 which you turn 1/5 and 1/2 in ten and it now 5/10 plus 5/10 plus 2/10 with equals 1 and 2/10 or otherwise 1 and 1/5
Step-by-step explanation:
Gabriel surveyed 1000 of the students in his school about their favorite color. 55% said their favorite color was purple. How many students' favorite color was purple?
Answer:
550 students
Step-by-step explanation:
Answer:
550 students
Step-by-step explanation:
I need help and it’s due today
Answer: same bruh
Step-by-step explanation:
Integers are ________ whole numbers. braineist for first person to get it right and hurry im on a time limit 20 points for it also
sometimes whole numbers
Step-by-step explanation:
maybe
Perform the operation (7x3)+(- 2x3/8x2)
What is the Domain and range of (3,4)(5,7)(-3,8)(2,0)(1,3)
The domain is all x-values.
The range is all y-values.
Domain: 3, 5, -3, 2, 1
Range: 4, 7, 8, 0, 3
Best of Luck!
1. You want to purchase a car that costs $25,000. You must pay a 10% down payment. How much is this?
Answer: 2,500
2. What do you still owe?
Answer: 22,500
3. Determine the monthly payment for 60 months with an APR of 5.5%. Round to the nearest cent.
Answer: 22,500(0.055/12)/(1-(1+0.055/12)^(-60)= 429.78 rounded to the nearest cent.
4. How much do you pay all together at the end of the 60 months including the down payment and interest charges?
I need help with number 4. Please.
Answer: If interest is not given, it would be 25,000+ interest as your answer
Step-by-step explanation:
What are the values of the two 3s in 3,435?
Answer:
The first 3 is in the thousandths place. it is worth 3 thousand. The second 3 is in the tenths place. It is worth 30.
Answer: 3,435
Least place value to largest largest place value-
5-ones place
3-tens place
4-hundreds place
3-thousands place
I hope that worked!
74.052 using expanded form with fractions and expanded form with decimals
Answer:
[tex]74.052 = 7 * 10 + 4 * 1 + 0 * 0.1 + 5 * 0.01 + 2 * 0.001[/tex]
[tex]74.052 = 7 * 10 + 4 * 1 + \frac{0}{10} + \frac{5}{100} + \frac{2}{1000}[/tex]
Step-by-step explanation:
Given
74.052
Required
Write in Expanded Form
In Decimals
[tex]7 = 7 * 10[/tex]
[tex]4 = 4 * 1[/tex]
[tex]0 = 0 * 0.1[/tex]
[tex]5 = 5 * 0.01[/tex]
[tex]2 = 2 * 0.001[/tex]
Bring these together,
[tex]74.052 = 7 * 10 + 4 * 1 + 0 * 0.1 + 5 * 0.01 + 2 * 0.001[/tex]
In Fraction
[tex]74.052 = 7 * 10 + 4 * 1 + 0 * 0.1 + 5 * 0.01 + 2 * 0.001[/tex]
Convert decimals to fraction
[tex]74.052 = 7 * 10 + 4 * 1 + 0 * \frac{1}{10} + 5 * \frac{1}{100} + 2 * \frac{1}{1000}[/tex]
[tex]74.052 = 7 * 10 + 4 * 1 + \frac{0}{10} + \frac{5}{100} + \frac{2}{1000}[/tex]
Answer with proper units too!
Answer:
Step-by-step explanation:
1. Area of a parallelogram = base * height
area = 10 * 4 = 40 in squared
perimeter = 2(a + b)
perimeter = 2 * (5 + 10) = 2 * 15 = 30in
2. Area of triangle = 1/2 * base * height
area = 1/2 * 21 * 8 = 84 cm squared
perimeter = sum of outer perimeters
perimeter= 10cm + 17cm + 21cm = 48cm
3. area of trapezium = 1/2 * (a+b) * h
area = 1/2 * (6+12) * 4 = 36ft squared
perimeter = sum of outer perimeters
perimeter = 5ft + 6ft + 12ft + 5ft = 28ft
what is a cumulative gragh
Answer:
Cumulative frequency is the running total of the frequencies. On a graph, it can be represented by a cumulative frequency polygon, where straight lines join up the points, or a cumulative frequency curve.
A standard working day is 8 hours. If you were to work 125% of a normal day, how many total hours would you work?
Answer:
10
Step-by-step explanation:
Whenever we see "of" we know its multiplication
125% x a normal day
125% x 8
[tex]\frac{125}{100}[/tex] x 8
10
:)
I don't understand this
Answer:
tytytytyt
Step-by-step explanation:
Answer:
i don't either
Step-by-step explanation:
2/5 y - 4 + 7 - 9/10 y
Answer:
-1/2y +3
Step-by-step explanation:
2/5y -4 + 7 -9/10y=
combine like terms
-1/2y +3
Find the volume of a cylinder with height 25cm and radius 5cm
Answer:
1963.5
-------------
Answer:
1,932 cm approxmately.
Step-by-step explanation:
Your formula is V= π5²h
V= 3.14 x 5² x 25
V= ≈1932 cm
Find the Slope using the Slope
Answer:
5/5 which simplifies to 1
Step-by-step explanation:
Answer:
m= 5/5
Step-by-step explanation:
y2= 9
y1=4
x2=8
x1=3
9-4 = 5
8-3 = 5
Therefore the slope/rate of change is 5/5
How do you write y − 4 = 2(x − 6) in slope-intercept form?
Sorry answered for more points for more questions I'm so sorry.
An online music company offers 15 downloads for $19.75 and 40 downloads for $43.50. Each price includes the same one-time registration fee. What is the cost of each download and the registration fee?what could be the equation
Answer:
s
Step-by-step explanation:
You will add numbers that are relevant to your life and then find the square root of that sum in simplified radical form. Find the sums of: A. All of the ages of the people in your household. B. All the digits in your telephone number, including the area code. C. All of the letters in your first name if you let a
Step-by-step explanation:
A. Dad = 50, Mum = 47, Sister = 22
me = 19
Total Sum = 50 + 47 + 22 + 19
= 136
√136 = 11.662.
B. + 1435 797 202 = 40
√40 = 6.33
C. BRYAN = 2 + 18 + 25 + 14 = 59
√59 = 7.68.
find the value power of 3^4
Answer:
81
Step-by-step explanation:
3 ^4 =3 ×3 ×3 ×3 =81