Answer:
X(s) = 2/[s³(s + 9)]
Step-by-step explanation:
Here is the complete question
Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions.
dx/dt + 9x = 16t² x(0) = 0 and dx(0)/dt = 5
Solution
dx/dt + 9x = 16t²
Taking the Laplace transform of the differential equation, we have
L{dx/dt + 9x} = L{16t²}
L{dx/dt} + L{9x} = L{16t²}
L{dx/dt} + 9L{x} = 16L{t²}
sL{x} - x(0) + 9L{x} = 16L{t²}
L{x} = X(s)
L{t²} = 2!/s³
Substituting X(s) and L{t²} into the equation above, we have
sX(s) - x(0) + 9X(s) = 2!/s³
Substituting x(0) = 0 into the equation above, we have
sX(s) - x(0) + 9X(s) = 2!/s³
sX(s) - 0 + 9X(s) = 2!/s³
sX(s) + 9X(s) = 2!/s³
Factorizing X(s), we have
(s + 9)X(s) = 2!/s³
X(s) = 2/[s³(s + 9)]
So X(s) in the Laplace domain is
X(s) = 2/[s³(s + 9)]
help with a and describe
Answer:
1
Step-by-step explanation:
Simply plug in 0 for x:
g(0) = 5x + 1
g(0) = 5(0) + 1
g(0) = 1
The formula V = IR shows the relationship between voltage, current, and resistance. Solve this formula for R.
Answer:
R=V/I
Step-by-step explanation:
Divide V by I to isolate R on one side.
Answer:
R=V/I
Step-by-step explanation:
Because resistance formula is v/i
5. Solve: 16 * 22 / 2
Answer:
176
Step-by-step explanation:
Usually you'll follow PEMDAS & the left->right rule, however, as you are only multiplying and dividing, it does not matter.
22/2 = 11
11 * 16 = 176
176 is your answer.
~
Answer:
176
Step-by-step explanation:
PEMDAS : first Multiply 16 & 22 which equals 352. Then Divide 352 by 2 which equals 176.
What is 3.4 x 10-6 in standard notation?
O A. 0.0000034
OB.
1
3.40
C. 3,400,000
D. 0.000034
Answer: Choice A) 0.0000034
[tex]3.4 \times 10^{-6} = 0.0000034[/tex]
There are five zeros between the decimal point and the '3'
To get this answer, you start with 3.4 and then move the decimal point 6 places to the left due to the exponent of -6. If the exponent was positive, then we'd move 6 places to the right.
Calculus 2 Master needed, evaluate the indefinite integral of: [tex]\int\( (lnx)^2} \, dx[/tex] So far I had applied the integration by parts and got: [tex](ln x )^2*x - \int\ x*((lnx)^2/2)}[/tex] do we do integration by parts again? also, do we simplify the x at my current stage? steps shown would be appreciated
Answer:
[tex]\displaystyle \int (\ln(x))^2\, dx=x(\ln(x)^2-2\ln(x)+2)+C[/tex]
Step-by-step explanation:
We want to evaluate the integral:
[tex]\displaystyle \int\left(\ln x\right)^2 \, dx[/tex]
We can use Integration by Parts. Rewriting the integral yields:
[tex]\displaystyle =\int 1\cdot (\ln(x))^2\, dx[/tex]
Recall that IBP is given by:
[tex]\displaystyle \int u\, dv = uv - \int v \, du[/tex]
Let u be (ln(x))². And let dv be (1) dx. Therefore:
[tex]\displaystyle du = 2\ln x \cdot \frac{1}{x}\, dx[/tex]
Simplify:
[tex]\displaystyle du=\frac{2\ln(x)}{x}\, dx[/tex]
And:
[tex]dv=(1)dx\Rightarrow v = x[/tex]
Therefore:
[tex]\displaystyle \int (\ln(x))^2\, dx=\underbrace{\ln(x)^2}_{u}\underbrace{x}_{v}-\int\underbrace{x}_{v}\cdot \underbrace{\frac{2\ln(x)}{x}\, dx}_{du}[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2 \int\ln(x)\, dx[/tex]
We can perform IBP again. Let u = ln(x) and v = 1. Hence:
[tex]\displaystyle du = \frac{1}{x} \, dx[/tex]
And:
[tex]dv=(1)dx\Rightarrow v = x[/tex]
Thus:
[tex]\displaystyle =x\ln(x)^2-2\left(x\ln(x)-\int (x)\frac{1}{x}\, dx\right)[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2\left(x\ln(x)-\int (1)\, dx\right)[/tex]
Evaluate:
[tex]=x\ln(x)^2-2(x\ln(x)-x)+C[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2x\ln(x)+2x[/tex]
Factor:
[tex]=x(\ln(x)^2-2\ln(x)+2)[/tex]
Therefore:
[tex]\displaystyle \int (\ln(x))^2\, dx=x(\ln(x)^2-2\ln(x)+2)+C[/tex]
Rewrite 4/10 : 1/25 as unit rate
Answer: 10
Explanation:
remember that when you have a divided fraction, you can change de numerator and denominator so your fractions be like this:
4/10 * 25/1 = 100/10
10*1
100/10= 10
this happens because when you have a fraction that is being divided, it's also like you are cross multiplying, just like the resolution upwards, then you get 100 divided by 10, which is 10.
I hope it helps you. :)
last year ,rita opened an investment account with $400 At the end of the year the amount in the account had decreased by 28.5% how much is this decrease in dollars? how much money way in her account at the end of last year
Answer:
Step-by-step explanation:
decrease=400×0.285=114.000 $
amount at the end=400-114=286 $
what is the differnence between (-2)^2 and -2^2 in math
Answer:
(-2)^2 = 4-2^2 = -4Step-by-step explanation:
The first is (-2)(-2) = 4.
The second is -(2)(2) = -4.
The order of operations says exponents are evaluated first. An exponent signifies repeated multiplication of the base.
_____
If your calculator is working correctly, it will show you the difference.
__
Beware spreadsheet programs. They don't always follow the order of operations when evaluating formulas. Parentheses are often required to keep them honest.
Answer: The one with perinthesis is bigger because you would do the negative first and you would have nothing to take away from
Step-by-step explanation:
D) Solve for k.
4(K + 11) - -2 = 6
K=
Answer: K=23
Step-by-step explanation:
Answer:
k=9
Step-by-step explanation:
4k+44 because you distribute the 4 to the parenthesis
new equation: 4k+44-2=6
add 2 to 6 which would be 8 because you have to get k by itself
4k+44=8 subtract 44 from 8
-36=4k
divide by four
k=-9
if the equation is really 4(k+11)--2=6
do the same first steps so 4k+44
but the -2 would become positive cuz of the double negative
so:
4k+44+2=6
4k+46=6
subtract 46 from 6
4k=-40
divide -40 by 4
k=-10
4x - 3y = 6 ,7x + 3y =27
Answer:
Step-by-step explanation:
4x - 3y = 6
7x + 3y = 27
11x = 33
x = 3
7(3) + 3y = 27
21 + 3y = 27
3y = 6
y = 2
(3,2)
Answer:
x=3 and y=2
Step-by-step explanation:
Let's solve your system by substitution.
4x−3y=6;7x+3y=27
Step: Solve4x−3y=6for x:
4x−3y=6
4x−3y+3y=6+3y(Add 3y to both sides)
4x=3y+6
4x /4 = 3y+6 /4 (Divide both sides by 4)
x= 3 /4 y+ 3 /2
Step: Substitute
3 /4 y+ 3 /2 for x in7x+3y=27:
7x+3y=27
7( 3 /4 y+ 3 /2 )+3y=27
33 /4 y+ 21 /2
=27 (Simplify both sides of the equation)
33 /4 y+ 21 /2 + (−21 /2 )
=27+ (−21 /2) (Add (-21)/2 to both sides)
33 /4 y= 33 2
33/4y=33/2
33 /4 =33/4 (Divide both sides by 33/4)
y=2
Step: Substitute 2 for y in x= 3 /4 y+ 3 /2
x= 3 /4 y+ 3 /2
x= 3 /4 (2)+ 3 /2
x=3 (Simplify both sides of the equation)
Answer:
x=3 and y=2
HOPE THIS HELPS!!!! :)
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Find its inverse, and state the domain and range.
939miles * 15gallons / 40miles = x
Answer: 281.7
Step-by-step explanation:
What is the next number 5, -20, 80, -320, 1280 _
1.CONVERT TO SCIENTIFIC NOTATION2.CONVERT TO STANDARD NOTATION
a. 895,000,000,000a. 3.65 x 108
Answer:
Step-by-step explanation:
a. 8.95 x 10^11
b. 3.65 x 10^8= 365,000,000
Answer:
a. 8.95 x 10^11
b. 3.65 x 10^8= 365,000,000
Step-by-step explanation:
31.14
A soap factory randomly inspects 100 bars of soap to better identify problems that occur during the manufacturing
process. The table below displays the possible problems and frequency for each.
Frequency
4
2
Soap Problems
Underweight
Impurities
Broken bar
None
Total
3
91
100
If the soap factory makes 5,000 bars of soap per day, how many of those bars would they expect to be broken?
O They would expect 100 bars to be broken.
They would expect 150 bars to be broken.
They would expect 300 bars to be broken.
They would’ve many bars would they expect to be broken
expect 450 bars to be broken.
Save and Exit
Next
Submar
Mark this and
Answer:
B. 150 bars to be broken
Answer:
They would expect 150 bars to be broken.
Step-by-step explanation:
Correct on Edge2020
The population of a town increased from 3600 in 2006 to 4500 in 2011. Find the absolute and relative (precent) increase.
what grade math is this????????????????????
Which name describe only those numbers highlighted on the number line.
Answer: negative numbers
Explanation: Notice that on the number line, 0 is in the middle, all numbers to the left of 0 are negative, and all numbers to the right of 0 are positive.
Since the numbers highlighted only include numbers
to the left of 0, negative numbers are shown here.
Pregunta 4 (1 punto)
4.) Fill in the blank
2(x+7) = 2x + _
оа
a) 7
b) 14
c
c) 7x
d) 14x
Od
Answer:
7....................
Hi guys, can anyone help me with this? Many thanks:)
Step-by-step explanation:
y = √—16x²+8x—2√8x+1+2The bad debt ratio for a financial institution is defined to the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose that a random sample of 7 Ohio banks is selected and that the bad debt ratios (written as percentages) for these banks are 6%, 8%, 5%, 9%, 7%, 5% and 8%. Banking officials claim that the mean debt ratio for all Midwestern banks is 3.5 percent and the mean bad debt ratio for Ohio banks is higher. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that the mean bad debt ratio for Ohio banks exceed 3.5 percent. (a) H0: μ ≤ [ Select ] % versus Ha: μ > [ Select ] %. (b) Discuss the meanings of a Type I error and a Type II error in this situation. Type I : Conclude that Ohio's mean debt ratio is [ Select ] 3.5 % when it actually is 3.5%. Type II : Conclude that Ohio's mean debt ratio is [ Select ] 3.5 % when it actually is 3.5%.
Answer:
Step-by-step explanation:
From the information given:
Consider X to be the random variable denoting the bad debt ratios for Ohio Bank.
Then, [tex]X \sim N ( \mu, \sigma ^2)[/tex]
Thus the null hypothesis and the alternative can be computed as:
Null hypothesis:
[tex]H_o : \mu \leq3.5\%[/tex]
Alternative hypothesis
[tex]H_1 : \mu > 3.5\%[/tex]
The type I and type II error is as follows:
Type I:
The mean bad debt ratio is > 3.5% when it is not
Type II:
The mean bad debt ratio is ≤ 3.5% when it is not.
The test statistics can be calculated by using the formula:
[tex]t = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
where;
sample size n = 7
mean = 6+8+5+9+7+5+8 = 48
sample mean [tex]\overline x =\dfrac{48}{7}[/tex]
[tex]\overline x[/tex] = 6.86
sample standard deviation is :
[tex]s = \sqrt{\dfrac{\sum( x -\overline x)^2}{n-1}}[/tex]
[tex]s = \sqrt{\dfrac{( 6 -6.86)^2+( 8-6.86)^2+ ( 5 -6.86)^2 + ...+( 7 -6.86)^2+ ( 5 -6.86)^2+( 8 -6.86)^2 }{7-1}}[/tex]
s = 1.573
population mean [tex]\mu = 3.5[/tex]
Therefore, the test statistics is :
[tex]t = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{6.86- 3.5}{\dfrac{1.573}{\sqrt{7}}}[/tex]
[tex]t = \dfrac{3.36}{\dfrac{1.573}{2.65}}[/tex]
[tex]t = \dfrac{3.36\times {2.65}}{{1.573}}[/tex]
t = 5.660
At significance level of 0.01
[tex]t_{0.01} = 3.707[/tex]
P - value = P(T > 5.66)
P - value = 1 - (T < 5.66)
P - value = 1 - 0.9993
P-value = 0.0007
Therefore, since [tex]t_{0.01} < t[/tex] , we reject the null hypothesis and conclude that the claim that the mean bad debt ratio for Ohio banks is higher than the mean for all financial institutions is true.
(7,-1) and ( 21,-5) what is the slope
Answer:
-2/7
Step-by-step explanation:
Going from (7,-1) to ( 21,-5) we see x (the 'run') increasing by 14 and y (the 'rise') decreasing by 4. Thus, the slope of the line connecting these two points is m = rise/run = -4/14, or -2/7.
Other than itself, what is an angle that is congruent to ∠CFD?
Answer:
CFB or DFE
Step-by-step explanation:
Congruent angles have the same value in degrees.
Knowing that line DB is straight and CE is perpendicular to DB (at 90 degrees to DB), we know CFD is 90 for the sum of CFD and CFB to equal 180 degrees (since they are on a straight line which is 180 degrees). We also know DFE is 90 for the same reason.
Our question is asking what is congruent or the same angle as CFD. In this case, there are 2 congruent angles: CFB and DFE.
CFB is 90 these angles are on the same line DB and are supplementary (add up to 180 degrees)
DFE is also a correct option since this and CFD are on the line CE and are also supplementary
How many quarts of pure antifreeze must be added to 2 quarts of a 10% antifreeze solution to obtain a 30% antifreeze solution
Answer:
x: 1/4=0.25 quarts of 100% antifreeze
Hope this helps
A homeowners association charges a $3.85 fee for each day your payment is late. If a bull is paid 13 days late, then how much will the homeowners association charge in late fees?
Answer:
$50.05
Step-by-step explanation:
Since you have to pay $3.85 per day, and you pay it 13 days late, then you would multiply $3.85 and 13.
3.85*13= 50.05
Total amount of late charges fee is $50.05
Given that;Amount pay for late charges = $3.85
Number of days = 13 days
Find:Total amount of late charges fee
Computation:Total amount of late charges fee = Amount pay for late charges × Number of days
Total amount of late charges fee = 3.85 × 13
Total amount of late charges fee = $50.05
Learn more:https://brainly.com/question/22177923?referrer=searchResults
Which angles are complementary to each other?
Answer:
angle CDA and angle BDC
mark this as brainliest!
Answer:
∠CDA and ∠BDC as their sum equals 90°
Step-by-step explanation:
Why is it important to have all parts of a graph clearly labeled and drawn
Answer:
A graph has to be clearly labelled and drawn for clarity and to aid the correct interpretation of the data shown on the graph.
15. _TYU and ZUYB form a linear pair. The mZTYU = 5x - 4 and mZUYB =
3x + 10. Find the degree measure of each angle. HINT: draw a picture.
Upload your work in canvas assignment.
Answer:
∠TYU = 104.75°∠UYB = 75.25°Step-by-step explanation:
A picture on scratch paper works as well as any.
__
The sum of the two angles is 180°:
(5x -4) +(3x +10) = 180
8x = 174 . . . . . . collect terms, subtract 6
x = 21.75 . . . . . .divide by 8
Then the angle measures are ...
∠TYU = 5(21.75) -4 = 104.75°
∠UYB = 3(21.75) +10 = 75.25°
_____
Check
The total is 104.75 +75.25 = 180, as required.
Answer:
104.75 +75.25 = 180
Step-by-step explanation:
Write the expression in words 5-y
Answer:
five minus y
Step-by-step explanation:
Answer:
y less than five
Step-by-step explanation:
thats your answer, please trust me
On a shelf there are 40 chips. 30 of them are cheddars flavored . What is the percentage of those that are cream cheese flavored?
Answer:
Hey there!
30/40 are cheddar flavored, so 10/40 are cream cheese flavored.
10/40=25, so 25% of the chips are cream cheese flavored (assuming that the rest of the chips are all cream cheese flavored)
Let me know if this helps :)
Your school’s football team scored 49 points. Your team’s score was 19 points more than the opponent’s score s. Write and solve an equation to find the opponent’s score.
Answer:
30
Step-by-step explanation:
Well its pretty simple just take 19-49 unless its for something else all i knew was that its 19-49= 30