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Lana71 [14]
3 years ago
11

The Laplace Transform of a function f(t), which is defined for all t > 0, is denoted by L{f(t)} and is defined by the imprope

r integral L{f(t)}(s) = infinity 0 e-st.f(t)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of as a fixed constant)
1. Find L{t}. (hint: remember integration by parts)
A. 1
B. -1/s2
C. 0
D. 1/s2
E. -s2
F. None of these
2. Find L{1}.
a.1/s
b. 1
c. 0
d. -s
e. -1/s
f. none of these
Mathematics
1 answer:
lesya692 [45]3 years ago
7 0

(1) D

L_s\left\{t\right\} = \displaystyle\int_0^\infty te^{-st}\,\mathrm dt

Integrate by parts, taking

u = t \implies \mathrm du=\mathrm dt

\mathrm dv = e^{-st}\,\mathrm dt \implies v=-\dfrac1se^{-st}

Then

L_s\left\{t\right\} = \displaystyle \left[-\frac1ste^{-st}\right]\bigg|_{t=0}^{t\to\infty}+\frac1s\int_0^\infty e^{-st}\,\mathrm dt

L_s\left\{t\right\} = \displaystyle \frac1s\int_0^\infty e^{-st}\,\mathrm dt

L_s\left\{t\right\} = \displaystyle -\frac1{s^2}e^{-st}\bigg|_{t=0}^{t\to\infty}

L_s\left\{t\right\} = \displaystyle \boxed{\frac1{s^2}}

(2) A

L_s\left\{1\right\} = \displaystyle\int_0^\infty e^{-st}\,\mathrm dt

L_s\left\{1\right\} = \displaystyle\left[-\frac1se^{-st}\right]\bigg|_{t=0}^{t\to\infty}

L_s\left\{1\right\} = \displaystyle\boxed{\frac1s}

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MaRussiya [10]

Answer:

A) H0:  mean of A= mean of B= mean of C

   H1: all means are unequal

B) 3.48194

C) 0.04515

D) H0 is accepted. There is significant difference among mean hours after which visibile abrasion is observed for each type of paint

Step-by-step explanation:

A) Here Anova test will be used as we are comparing three groups

B) mean of A= 229.6, SD of A= 158.1962, SE of A= 50.026

   mean of B= 309.9 , SD of B= 147.8742, SE of B= 46.7619

   mean of C= 427.8, SD of C= 196.8179, SE of C= 62.2393

overall mean= 322.43

degrees of freedom between groups= 3-1=2

degrees of freeddom of error= total number of observations - number of groups= 30-3= 27

total degrees of freedom= total number of samples-1= 30-1 =29

Sum of squares between groups=∑ sample size of group×(individual group mean- over all mean)²

=198772.4667

mean of sum of squares between groups= sum of squares between groups/ (number of groups -1)

  = 198772.4667/2

sum of squares of error=∑∑ (individual observation of group- group mean)²

                                            = 770670.9223

mean sum of squares of erros= sum of squares of error/(total number of samples-number of groups)

                                                       = 770670.92/27

                                                         = 28543.38

F- stat= mean sum of squares between groups/ mean sum of squares of error

     F stat= 3.48194

C) p- value= 0.04515

D) since F-stat is greater than p- value, null hypothesis is rejected

from F distribution table

F(2,27)=

3 0
3 years ago
A translation is applied to the triangle formed by the points A(−1, 4) , B(−1, 10) , and C(3, 6) . The image is the triangle tha
Dvinal [7]
X(A')=X(A)+4= -1+4=3
X(B')=X(B)+4= -1+4=3
X(C')=X(C)+4= 3+4=7
4 points to the right
7 0
3 years ago
Read 2 more answers
QRS contains the points: Q(4, 2) R(5, 1) S(3, 7). If the triangle is reflected across the y-axis, what will S' be? ANDWER ASAP W
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Answer:

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Step-by-step explanation:

7 0
3 years ago
Select all the equations below that have a slope of -5.
Zanzabum

Answer:

B and C

Step-by-step explanation:

they have -5x,   it doesn't really matter on their order

7 0
3 years ago
Geometry :))), please help me
amm1812

Answer:

x = -5

Step-by-step explanation:

Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.

This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).

So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.

On the right side we are given 9 for AD, and 18 for DC.

9/18 = 0.5

This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:

If AD/DC = 0.5, then BE/EC will also = 0.5

BE = x+23

EC = x+41

Therefore:

\frac{x+23}{x+41} = 0.5

Now we can solve by multiplying both sides by x+41 to eliminate the fraction:

x+23=0.5(x+41)

Now we multiply out the brackets and move the terms to different sides:

x+23=0.5x+20.5

0.5x = -2.5

x = -5

And if we substitute the -5 into the equations:

-5+23 = 18

-5 + 41 = 36

We will see that -5 does indeed give us the same ratio between the lengths:

18/36 = 0.5

Hope this helped!

4 0
3 years ago
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