price.
A shopkeeper marks the price of his her goods 40 % above the cost price and
allows 20% discount. If his her purchase price of an item is Rs 6.000. how much
should a customer pay for it levying 13 % VAT!
e 990 the honorariter​

Answers

Answer 1

Answer:

73%

Step-by-step explanation:


Related Questions

NEED HELP ASAP!!!!!!!!!!

Answers

Answer:

Hey there!

A is correct. The +2 means shifted up two units, 1/2 means compressed by a factor of 1/2, and the -3 means to the left of three units.

Let me know if this helps :)

On a coordinate plane, a line goes through (negative 3, 3) and (negative 2, 1). A point is at (4, 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)? y − 1 = −2(x − 4) y – 1 = Negative one-half(x – 4) y – 1 = One-half(x – 4) y − 1 = 2(x − 4)

Answers

Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

Find out more at: https://brainly.com/question/18880408

micah drove 4 1/4 miles on Monday and 2 2/3 miles on Tuesday. On Wednesday, he drove 1 1/3 fewer miles than he had driven on Monday. How many miles did they drive in total

Answers

Answer:

9.5

Step-by-step explanation:

Monday: [tex]4\frac{1}{4}[/tex]

Tuesday: [tex]2\frac{2}{3}[/tex]

Wednesday: [tex]4\frac{1}{4} - 1\frac{1}{3}[/tex]

Total: [tex]4\frac{1}{4} + 2\frac{2}{3} + (4\frac{1}{4} - 1\frac{1}{3})[/tex]

                                               

Start by subtracting [tex]4\frac{1}{4} and[/tex] [tex]1\frac{1}{3}:[/tex] [tex]\frac{35}{12}[/tex]

Now, add them all up: [tex]4\frac{1}{4} + 2\frac{2}{3} + \frac{35}{12} = 9.5[/tex]

Therefore, Micah drove 9.5 miles in total.


Two basketball players average the same number of points per game. What information would be most helpful in
determining which player's game performances show the least variability?
the most and least points each player has scored in a game
the number of games each player has played
the average number of points each player's team scores per game
O the total number of points each player has scored

Answers

Answer:

number of games each player has played

the average number of points each player's team scores per

Step-by-step explanation:

number of games each player has played

the average number of points each player's team scores per

Please help me answer the question

Answers

Answer:

fourth option

Step-by-step explanation:

Common difference is given by difference of two consecutive term

d = nth term - (n-1)th term

______________________________________

for all the  series lets take second term as nth term

and first term as (n-1)th term

_________________________________________

for first series

n th term = -3 1/2 = -3.5

(n-1)th term = -5

therefore

d= -3.5 -(-5) = -3.5 +5 = 1.5

______________________________________

for second series

n th term = 4 1/2 = 4.5

(n-1)th term = 2 1/2 = 2.5

therefore

d= 4.5 -(2.5) =2

_________________________

for third series

n th term = 3

(n-1)th term =1.5

therefore

d= 3 - 1.5 = 1.5

__________________________________

for fourth series

n th term = -1.5

(n-1)th term = -4

therefore

d= -1.5 -(-4) = -1.5 + 4 = 2.5 = 2 1/2

___________________________________

Thus, based on above solution option four has common difference of 2 1/2

Starting at point​ A, a ship sails 18.9 km on a bearing of 190 degrees and ​then turns and sails 47.2km on a bearing of 318 degrees. Find the distance of the ship from point A. (Use trigonometry)

Answers

Answer:

Approximately 38.56 kilometers

Step-by-step explanation:

So, from the picture, we want to find x.

To do this, we can use the Law of Cosines. We simply need to find the angle between the two sides and then plug them into the Law of Cosines. First, the Law of Cosines is:

[tex]c^2=a^2+b^2-2ab\cos(C)\\[/tex]

The c in this equation is our x, and the C is the angle we need to find.

From the picture, you can see that angle C is the sum of the red and blue angles.

From a bearing of 190 degrees, we can determine that the red angle measures 10 degrees. Then by alternate interior angles, the other red angle must also measure 10 degrees.

From a bearing of 318 degrees, the remaining 48 degrees is outside the triangle. However, we have a complementary angle, so we can find the angle inside the triangle by subtracting in into 90. Therefore, the blue angle inside is 90-48=42 degrees.

Therefore, angle C is 42+10 which equals 52 degrees. Now we can plug this into our formula:

[tex]x^2=a^2+b^2-2ab\cos(C)\\\\x^2=(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)\\x=\sqrt{(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)}\\\text{Use a Calculator}\\x\approx38.5566 \text{ km}[/tex]

write a thirdthird-degree polynomial expression that has only two terms with a leading term that has a coefficient of five and a constant of negative two ​

Answers

Answer:

5x^3-2

[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]

Answer: [tex]5x^3 - 2[/tex]

Explanation:

The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.

We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.

The coefficient is the number to the left of the variable.

The degree is the largest exponent, which helps form the leading term.

The third degree polynomial written above is considered a cubic binomial. "Cubic"  refers to the third degree, while "binomial" means there are 2 terms.

We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.



Type the missing number in this sequence:
1,
4,
,64, 256,
1,024

Answers

Answer:

16

Step-by-step explanation:

The sequence is 1, 4,...,64, 256, 1024

Notice that:

● 1 = 2^0

● 4 = 2^2

● 64 = 2^6

● 256 = 2^8

● 1024 = 2^10

Notice that we add 2 each time to the exponent so the missing number is:

● 2^(2+2) = 2^4 = 16

Solve the system by graphing y=-4x-2 -2x+y=-2 Plot both lines and point of intersection by moving the dots to the correct location

Answers

Answer:

The point of intersection is (0,-2).

Step-by-step explanation:

Equation 1: [tex]y=-4x-2[/tex]

Equation 2 : [tex]-2x+y=-2[/tex]

Plot the lines on the graph

Refer the attached figure

Equation 1: [tex]y=-4x-2 ---- Red[/tex]

Equation 2 : [tex]-2x+y=-2 ---- Blue[/tex]

Point of intersection : A point where both the lines intersect is called point of intersection.

So, Both lines intersect at point (0,-2)

So, Point of intersection is (0,-2)

Hence The point of intersection is (0,-2).

A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix. A number line goes from 65 to 115. Crackers's whiskers range from 70 to 100, and the box ranges from 75 to 85. A line divides the box at 80. Cookies's whiskers range from 70 to 115, and the box ranges from 90 to 105. A line divides the box at 100. Which statement is true about the box plots

Answers

OPTIONS:

A. The interquartile range of the trail mix data is greater than the range of the cracker data.

B. The value 70 is an outlier in the trail mix data.

C. The upper quartile of the trail mix data is equal to the maximum value of the cracker data.

D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer:

D.

Step-by-step explanation:

With the given information about how the box plot looks like, let's examine each option to see if they are true or not.

Option A: "The interquartile range of the trail mix data is greater than the range of the cracker data."

The interquartile range of trail mix data = 105 - 90 = 15

Range of cracker data = 100 - 70 = 30

Option A is NOT TRUE.

Option B: "The value 70 is an outlier in the trail mix data."

This is NOT TRUE. There are not outliers as 70 is the minimum value if the ranges of the data set for the trail mix.

Option C: "The upper quartile of the trail mix data is equal to the maximum value of the cracker data."

Upper quartile of the trail mix data = 105

Max value of cracker data = 100

This statement is NOT TRUE.

Option D: "The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers."

The greater the range value, the greater the variation. Thus,

Range value of the trail mix data = 115 - 70 = 45

Range value of the cracker data = 100 - 70 = 30

This is statement is correct because trail mix data have a greater range value, hence, it has a greater variation in the number of calories.

Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

3. Solve 6 + 5 √ 2 4 9 − 2 x = 7

Answers

Answer:

please mark my answer brainliest

Step-by-step explanation:

question is unclear to give u correct answer

The lengths of two sides of a triangle are 6cm and 8cm.Between what two measures should the length of the third side fall? PLEASE HELP !!!!!!!!

Answers

Answer: Search Results

Featured snippet from the web

In triangle sum of 2 sides must be greater than the 3rd side. So, the third > 8 - 6 = 2 and also the third < 8 + 6 = 14. So, the answer is 2 < third side < 14. The third side lies between(2,14).

Step-by-step explanation: Brainlyest please

A box contains 30 widgets, 4 of which are defective. If 4 are sold at random, find the probability that (a) all are defective (b) none are defective.

Answers

Answer:

a. The probability that all are defective is 0.0003160493827

b. Probability that none are defective is 0.99968395

Step-by-step explanation:

Given that 4 of the 30 widgets contained on the box are defective, n = 4. The probability of picking a defective widget is p = 4/30 = 2/15.

Now, P(X = a) = (nCa)P^n(1 - P)^(n - a).

a. To find the probability that all are defective, we want to find P(X = 4)

= (4C4) × (2/15)^4 × (1 - 2/15)^(4 - 4)

= 1 × (2/15)^4 × 1

= 0.0003160493827

b. Probability that none are defective.

This is the same as saying (1 minus the probability that all are defective).

P = 1 - 0.0003160493827

= 0.99968395

A student says that a coordinate grid under a dilation with the center at the origin and scale factor 2 does not change the grid. The image is still a coordinate grid. How do you​ respond?

Answers

Answer:

Dilation changes (x,y) values not the grid or coordinate plane. Basically, dilating a graph or a coordinate grid means the original coordinates you may have had will be changed with the dilation.  For example, a triangle plotted had its original area of 26 dilated to an area of 58.

Please answer this correctly without making mistakes

Answers

Answer:

Put 1/10 in the box.

Step-by-step explanation:

Since, Bluepoint and Milford are at same distance from Weston, the distance further than this to Oakdale is 1/10 miles.

Best Regards!

Answer:

To Oakdale to Milford:

2/5 mi

Step-by-step explanation:

1/10 + 3/20 + 3/20

1/10 = 2/20

then;

2/20 + 3/20 + 3/20 = (2+3+3)/20 = 8/20

8/20 = 2/5

which expression shows a way to find 2813×7

Answers

Answer:

19,691

Step-by-step explanation:

Answer:

2813 x 7 = 19691

Hope this helps!

Let REPEAT TM = { | M is a TM, and for all s ∈ L(M), s = uv where u = v }. Show that REPEATTM is undecidable. Do not use Rice’s Theorem.

Answers

Answer:

Step-by-step explanation:

Let REPEAT [tex]_{TM[/tex]= { | M is a TM, and for all s ∈ L(M), s = uv where u = v }

To prove that REPEAT [tex]_{TM[/tex]  is undecidable.

Let  REPEAT [tex]_{TM[/tex] {| M is a TM that does not accept M}

Then, we form a TM  u for L by applying TM v as a subroutine.

Assume Repeat   is decidable

Let M be the algorithm that  TM which decides the REPEATU = on input "s" simulate the M

Accept; if M ever enters the accept state

Reject; if M ever enters the reject state

U does not decide the REPEAT as it may loop over s

so REPEAT is undecidable

the temp fell 3 degrees every hour for 5 hours what's the change in temperature​

Answers

Answer:

-15

Step-by-step explanation:

If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees

Help me solve this!!!

Answers

Answer:

54°

Step-by-step explanation:

Let ∠CYX=x

AB║CD

∠AXE=∠CYX  (corresponding angles)

∠AXE=3∠CYX-108

x=3x-108

3x-x=108

2x=108

x=108/2=54°

∠AXE=∠CYX=x=54°

∠BXY=∠AXE=54° (Vertically opposite angles)

16.72911 liters rounded to the nearest whole is
liters

Answers

17 is the answer

(Mark me brainliest)

Su Jean is driving from phoenix to houston. A distance of 1185 miles. After driving for 4 hours she calculates that she has driven 237 miles. What portion of the distance does she have left to drive?

Answers

Answer:

4/5

Step-by-step explanation:

237/1185 = .2 = 1/5

meaning there's 4/5 left

Tony rounded each of the numbers 1, 143 and 1, 149 to the nearest hundred which word correctly compares the rounding numbers

Answers

Full Question:

Tony rounded each of the numbers 1,143 and 1,149 to the nearest hundred. Which choice correctly compares the rounded numbers?

[tex]1,000 = 1,000[/tex]

[tex]1,140< 1,150[/tex]

[tex]1,100 = 1.100[/tex]

[tex]1,140>1,150[/tex]

Answer:

[tex]1,100 = 1,100[/tex]

Step-by-step explanation:

Given

1,143 and 1,149

Required

Which of the option is correct

We start by approximating both numbers to nearest digit

1,143; when approximated to nearest hundred is 1,100

1,149; when approximated to nearest hundred is also 1,100

Hence;

1,143 ≅ 1,100

1,149 ≅ 1,100

Comparing both results, we have that

[tex]1,100 = 1,100[/tex]

From the list of given options, option C is correct;

Urgent!!! Please simplify

Answers

Answer:

The answer is

3x² - 2x³

Step-by-step explanation:

First factor (x+1)² out of the expression

That's

[tex] \frac{ ({x + 1})^{2} (6 \cos( \frac{\pi}{3} )) {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) }{ ({x + 1})^{2} } [/tex]

Reduce the expression by (x + 1)²

We have

[tex]6 \cos( \frac{\pi}{3} ) \times {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) [/tex]

Using trigonometric values table

[tex] \cos( \frac{\pi}{3} ) = \frac{1}{2} [/tex]

[tex] \sin( \frac{\pi}{2} ) = 1[/tex]

So we have

[tex]6 \times \frac{1}{2} \times {x}^{2} - {x}^{3} \times 2 \times 1[/tex]

Simplify

We have the final answer as

[tex] {3x}^{2} - 2 {x}^{3} [/tex]

Hope this helps you

A caplet contains 325 mg of medication. How many caplets contain 975 mg of medication?

Answers

Answer:

3 caplets

Step-by-step explanation:

Given  1 caplet = 325 mg of medication, to calculate the number of caplet 975mg of medication will contain, we will follow the steps below;

Let  1 caplet = 325 mg of medication

x caplet = 975 mg of medication

Cross multiply

325 * x = 1 * 975

325x = 975

Divide both sides by 325

325x/325 = 975/325

x = 3

Hence 3 caplets contains 975 mg of medication.

What is the area of a parallelogram if the coordinates of its vertices are (0, -2), (3,2), (8,2), and (5, -2)?

Answers

Answer: 20 sq. units .

Step-by-step explanation:

Let A(0, -2), B(3,2), C(8,2), and D(5, -2) are the points for the parallelogram.

First we plot these points on coordinate plane, we get parallelogram ABCD.

By comparing the y-coordinate of B and C with A and D , we get

height = 2+2 = 4 units

Also by comparing the x coordinates of A and D, we get base = 5-0= 5 units  

Area of parallelogram = Base x height

= 5 x 4 = 20 sq. units

Hence, the area of a parallelogram ABCD is 20 sq. units .

1. Hypothesis Test. Gender bias researchers compared the promotion rate of 412 women in manufacturing management positions to the national average which was known to be 75 months for a mostly male population. They measured the number of months each woman worked in middle management. Given a 0.01 level of significance, the correct statistical conclusion is to reject the null.
A. True
B. False
2. Hypothesis Test. Gender bias researchers compared the promotion rate of 412 women in manufacturing management positions to the national average which was known to be 75 months for a mostly male population. They measured the number of months each woman worked in middle management before being promoted to senior management, and found an average 79 months (s.d. = 19). Researchers want to know if women are promoted more slowly (i.e. after a larger number of months). What is the correct research conclusion?
A. Evidence suggests there is no difference in promotion rates.
B. Evidence suggests a small difference in promotion rates favoring males.
C. Evidence suggests a large difference in promotion rates favoring males.
D. No way to tell.

Answers

Answer:

1. B. False

2. B. Evidence suggests a small difference in promotion rates favoring males.

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

pls what is the nearest 100 of 49​

Answers

Answer:

the nearest hundred is 50

Prove for
mathematical
induction is the statement
is true
3+7+11+... (4n-1) = n(2n+1)

Answers

Answer:

Step-by-step explanation:

Hello, we want to prove that a proposition depending on n, that we can note P(n), is true for any n positive integer greater than 1. We need to follow several steps.

Step 1 - prove P(1)

For n = 1, n(2n+1)=1*3 =3 so we have

3 = 3, which is obviously true.

First step done!

Step 2 - for [tex]k\geq 1[/tex] we assume P(k) and we need to prove P(k+1)

We assume that 3+7+11+...+(4k-1)=k(2k+1)

so we can write that

3+7+11+...+(4k-1)+(4(k+1)-1)=k(2k+1)+(4k+4-1)=k(2k+1)+4k+3

[tex]=2k^2+k+4k+3\\\\=2k^2+5k+3[/tex]

and

(k+1)(2(k+1)+1)=(k+1)(2k+3)

[tex]=k(2k+3)+2k+3\\\\=2k^2+3k+2k+3\\\\=2k^3+5k+3[/tex]

These two expressions are the same so it means that P(k+1) is true, meaning that

3+7+11+...+(4k-1)+(4(k+1)-1)=(k+1)(2(k+1)+1)

Step 3 - The conclusion

Finally, we have just proved that

3+7+11+...+(4n-1)=n(2n+1) for any n positive integer > 0

Thank you

The given sum of arithmetic progression series 3+7+11+... (4n-1) = n(2n+1) is true.

What is Arithmetic progression?

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2.

The Sum of n terms of an AP is given by,

S= n/2[2a + (n-1)d ] where a is first term and d is common difference.

In our series 3+7+11+... (4n-1)

First term (a) = 3

Common difference (d) = 7 - 3 = 4

So the sum will be

S = n/2[2(3) + (n-1)4]

S = n[3 + 2(n - 1)]

S = n (2n + 1 ) = Right hand side.

Hence "The given sum of arithmetic progression series 3+7+11+... (4n-1) = n(2n+1) is true".

For more about Arithmetic progression,

https://brainly.com/question/20385181

#SPJ2

Find 0.01 more than 9.154

Answers

Answer:

Hey!

Your answer is 9.164!!

Step-by-step explanation:

Adding 0.01 means just adding 1 to THE DIGIT IN THE HUNDRETH PLACE...2 SPACES RIGHT OF DECIMAL POINT!

5+1=6

SUB IN:

9.164

find the response of the function at * (t=4) using Laplace transform (y() + 2y" + y = sint) y(0)=1, y (0)=-2, y"(0)=3 , y"(0)=0

Answers

Considering you have four initial conditions (the last of which should probably read [tex]y'''(0)=0[/tex]), I'm assuming the ODE is

[tex]y^{(4)}(t)+2y''(t)+y(t)=\sin t[/tex]

with [tex]y(0)=1[/tex], [tex]y'(0)=-2[/tex], [tex]y''(0)=3[/tex], and [tex]y'''(0)=0[/tex].

Take the Laplace transform of both sides, denoting the transform of [tex]y(t)[/tex] by [tex]Y(s)[/tex]:

[tex](s^4Y(s)-s^3y(0)-s^2y'(0)-sy''(0)-y'''(0))+2(s^2Y(s)-sy(0)-y'(0))+Y(s)=\dfrac1{s^2+1}[/tex]

Solve for [tex]Y(s)[/tex]:

[tex](s^4+2s^2+1)Y(s)-s^3+2s^2-5s+4=\dfrac1{s^2+1}[/tex]

[tex]Y(s)=\dfrac{1+(s^3-2s^2+5s-4)(s^2+1)}{(s^2+1)(s^4+2s^2+1)}[/tex]

Notice that

[tex]s^4+2s^2+1=(s^2+1)^2[/tex]

[tex]\implies Y(s)=\dfrac{1+(s^3-2s^2+5-4)(s^2+1)}{(s^2+1)^3}[/tex]

and simplify a bit to get

[tex]Y(s)=\dfrac{s^5-2s^4+6s^3-6s^2+5s-3}{(s^2+1)^3}[/tex]

Decompose [tex]Y(s)[/tex] into partial fractions:

[tex]\dfrac{s^5-2s^4+6s^3-6s^2+5s-3}{(s^2+1)^3}=\dfrac{a_0+a_1s}{s^2+1}+\dfrac{b_0+b_1s}{(s^2+1)^2}+\dfrac{c_0+c_1s}{(s^2+1)^3}[/tex]

[tex]s^5-2s^4+6s^3-6s^2+5s-3=(a_0+a_1s)(s^2+1)^2+(b_0+b_1s)(s^2+1)+(c_0+c_1s)[/tex]

[tex]s^5-2s^4+6s^3-6s^2+5s-3=a_1s^5+a_0s^4+(2a_1+b_1)s^3+(2a_0+b_0)s^2+(a_1+b_1+c_1)s+(a_0+b_0+c_0)[/tex]

[tex]\implies\begin{cases}a_1=1\\a_0=-2\\2a_1+b_1=6\\2a_0+b_0=-6\\a_1+b_1+c_1=5\\a_0+b_0+c_0=-3\end{cases}[/tex]

[tex]\implies a_0=-2,a_1=1,b_0=-2,b_1=4,c_0=1,c_1=0[/tex]

So we have

[tex]Y(s)=\dfrac{s-2}{s^2+1}+\dfrac{4s-2}{(s^2+1)^2}+\dfrac1{(s^2+1)^3}[/tex]

Split up the first term to get two easy inverse transforms:

[tex]L^{-1}\left[\dfrac s{s^2+1}\right]=\cos t[/tex]

[tex]L^{-1}\left[-\dfrac2{s^2+1}\right]=-2\sin t[/tex]

Also split up the second term, but use the convolution theorem, which says

[tex]L\left[(\alpha \ast \beta)(t)\right]=A(s)\cdot B(s)[/tex]

where [tex]A(s)[/tex] and [tex]B(s)[/tex] are the Laplace transforms of [tex]\alpha(t)[/tex] and [tex]\beta(t)[/tex], respectively, and the convolution is defined by

[tex](\alpha \ast \beta)(t)=\displaystyle\int_0^t\alpha(\tau)\beta(t-\tau)\,\mathrm d\tau[/tex]

Take

[tex]A(s)=\dfrac{4s}{s^2+1}\text{ and }B(s)=\dfrac1{s^2+1}[/tex]

so that

[tex]\alpha(t)=4\cos t\text{ and }\beta(t)=\sin t[/tex]

and their convolution is

[tex]L^{-1}\left[\dfrac{4s}{(s^2+1)^2}\right]=(\alpha \ast \beta)(t)=2t\sin t[/tex]

Next, take

[tex]A(s)=-\dfrac2{s^2+1}\text{ and }B(s)=\dfrac1{s^2+1}[/tex]

[tex]\implies \alpha(t)=-2\sin t\text{ and }\beta(t)=\sin t[/tex]

[tex]\implies L^{-1}\left[-\dfrac2{(s^2+1)^2}\right]=t\cos t-\sin t[/tex]

You can treat the third term similarly, but with an extra step. First compute

[tex]L^{-1}\left[\dfrac1{(s^2+1)^2}\right][/tex]

by taking

[tex]A(s)=B(s)=\dfrac1{s^2+1}[/tex]

[tex]\implies \alpha(t)=\beta(t)=\sin t[/tex]

Then

[tex]L^{-1}\left[\dfrac1{(s^2+1)^2}\right]=\dfrac{\sin t-t\cos t}2[/tex]

Next, take

[tex]A(s)=\dfrac1{(s^2+1)^2}\text{ and }B(s)=\dfrac1{s^2+1}[/tex]

[tex]\implies \alpha(t)=\dfrac{\sin t-t\cos t}2\text{ and }\beta(t)=\sin t[/tex]

[tex]\implies L^{-1}\left[\dfrac1{(s^2+1)^3}\right]=\dfrac{(3-t^2)\sin t-3t\cos t}8[/tex]

Thus we end up with the solution,

[tex]y(t)=(\cos t-2\sin t)+(2t\sin t+t\cos t-\sin t)+\dfrac{(3-t^2)\sin t-3t\cos t}8[/tex]

[tex]\boxed{y(t)=\dfrac{(8+5t)\cos t+(-21+16t-t^2)\sin t}8}[/tex]

Other Questions
Transactions that do not involve the original issue of securities take place in _________. A. primary markets B. secondary markets C. over-the-counter markets D. institutional markets Solve the equation 7b-27=8(6+4b) In which part of Africa were most of France's possessions in 1914. Types of friction in physics help please, last ride guys In telling the details of her fathers bravery, Oona tried to explain why she cannot be the wife of a coward. These details also serve the purpose of A creating a contrast for Negores supposed cowardice B Creating a sense of impatience and delay in the reader C Increasing the curiosity of the reader about Oona D Increasing the time of Kinoos in the narrative adjective of one please answer B MC Qu. 7-200 Krepps Corporation produces ... Krepps Corporation produces a single product. Last year, Krepps manufactured 29,010 units and sold 23,900 units. Production costs for the year were as follows: Direct materials Direct labor Variable manufacturing overhead Fixed manufacturing overhead $214,674 $121,842 $243,684 $319, 110 Sales totaled $1,159,150 for the year, variable selling and administrative expenses totaled $126,670, and fixed selling and administrative expenses totaled $205,971. There was no beginning Inventory. Assume that direct labor is a variable cost. Under absorption costing, the ending Inventory for the year would be valued at:_________ (Round your Intermediate calculations to 2 decimal places.) a) $158.410 b) $228.410 c) $219.910 d) $185.910 Water discharging into a 10-m-wide rectangular horizontal channel from a sluice gate is observed to have undergone a hydraulic jump. The flow depth and velocity before the jump are 0.8m and 7m/s, respectively. Determine (a) the flow depth and the Froude number after the jump (b) the head loss (c) the dissipation ratio. 2. A person's height is 73 inches. Howwould you convert this height to feetusing a conversion factor?a.73in 12 inift1b.73in ift112in how well Helen Keller performed in university Consider various ways of ordering the letters in the word TENNESSEE. TENENESES, EESSENNET, TNNEESSEE, and so on. (a) How many distinguishable orderings are there When a volcano erupts, tiny particles from which of Earth's spheres are released into the air?atmospherebiospheregeospherehydrosphere At the nationally televised Army-McCarthy hearings in 1954, it was revealed that Group of answer choices McCarthy gloated that he was right and the army had been willing to look the other way to save their reputation. neither side was able to prove their point; Congress dropped the charges as there was insufficient evidence. McCarthy was not fit to stand trial; instead he sent his assistant to read the charges, which could not be entered into evidence without McCarthy's physical appearance in the hearings. McCarthy was a bully who browbeat witnesses and made sweeping accusations with no basis in fact. Quando elementos se unem a um radical para formar novas palavras, temos o processo de derivao, nesse processo podem ser acrescidos elementos antes e depois do radical, escreva abaixo quais so esses dois processos e d um exemplo para cada: Based on the graph what are the solutions to ax^2 + bx+c=0 Select all that applyA. X=-2B. X=10C. X=5D. X=8 witch numbers are domain -3 ,-2 ,-3 ,0 ,-1 ,2 ,1 ,2 Seven Manufacturing Corporation uses both standards and budgets. The company estimates that production for the year will be 100,000 units of Product Fast. To produce these units of Product Fast, the company expects to spend $600,000 for materials and $800,000 for labor.Required:Compute the estimates for a standard cost. In response to Fort Sumter President Lincoln asked Congress to initiate plans for military conscription. both North and South witnessed a tremendous outpouring of support. the states of Maryland, Kentucky, and Missouri seceded and joined the Confederacy. Northern authorities began drafting Blacks for military service. Which kingdom of organisms is being described here?1. Cannot move2. Makes it's own food3. Made of more than one cell4. Cells have a nucleus