Answer:
cos 60° = 1/2 because the angles are complements.
Step-by-step explanation:
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
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]
Which expression is equivalent to x+y+x+y+3(y+5)
Answer:
2x + 5y + 15
Step-by-step explanation:
add like terms
(x+x) + (y+y)+3y+15
2x+2y+3y+15
2x + 5y + 15
i hope this helps!
Select the best with the least expensive corn per ounce The choices are in the image
Answer:
B
Step-by-step explanation:
Option A:
1.50÷18≈0.0833
3.00÷36≈0.0833
4.50÷54≈0.0833
Option B:
0.75÷15=0.05
Option C:
2.20÷15=0.146
A population is estimated to have a standard deviation of 9. We want to estimate the population mean within 2, with a 99% level of confidence. How large a sample is required? (Round up your answer to the next whole number.)
Answer:
The sample required is [tex]n = 135[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 9[/tex]
The margin of error is [tex]E = 2[/tex]
Given that the confidence level is 99% then the level of significance is mathematically evaluated as
[tex]\alpha = 100-99[/tex]
[tex]\alpha = 1 \%[/tex]
[tex]\alpha = 0.01[/tex]
Next we will obtain the critical value [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference math dot armstrong dot edu) , the value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58[/tex]
The sample size is mathematically represented as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]
substituting values
[tex]n = [ \frac{ 2.58 * 9 }{2} ]^2[/tex]
[tex]n = 135[/tex]
93/28=15/4n-5+4 4/7 i NEED this answer
Answer:
n=1
Step-by-step explanation:
93/28=15/4n-5+4 4/7
93/28=15/4n-5+32/7
93/28=15/4n-35+32/7
93/28=15/4n-3/7
93/28+3/7=15/4n
15/4n=93*7+28*3/28*7
15/4n= 651+84/196
15/4n=735/196
15/4n*4/15=753/196*4/15
n=49/49
n=1
5/2 divided7 ( please dont report, i just can't figure it out! )
Answer:
5/14
Step-by-step explanation:
You multiply the recripricoal in division problems:
5/2 ÷ 7/1 =
5/2 × 1/7 =
5/14
Answer:
5 / 14
Step-by-step explanation:
will make it simple... the technique is to flip the either 5/2 or 7/1
then multiply.
5/2 x 1/7 = 5 / 14
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.
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
How is the following decimal written using bar notation? 3.126666666666...
3. 126
3.126
0 3.126
03.126
Answer:
_
3.126
Step-by-step explanation:
Bar notation is a way in Mathematics to write decimal number that are repetiting or infinite.
Bar notation symbol is – is placed above the first decimal number that repeats itself. It is easier than writing the same repeating number and over again. It tells us that this particular number with the bar over it, is repeated continuously till infinity
From the above question, we were asked to write 3.126666666666... using Bar notation
_
3.126666666666... = 3.126
The bar is placed over the digit 6
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?
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.
2(2^3+7)^3+2(7^2+5)2
average person lives for about 78 years. Does the average person live for at least 1,000,000 hours? (Hint: There are 365 days in each year and 24 hours in each day.)
Answer:
683,280 hours is what I caculated. Is that right?
Step-by-step explanation:
Answer:
There are (365 x 24) hours for each year.
and 365 x 24 are 8760.
and 8760 x 78 are 683,280.
so, the average person does not live at least 1 Million hours, but they live more than 500 thousand hours, or 5 x 10^5 hours.
Hope it helps!
Bye!
P.S. Please give me Brainliest...
I desperately need one more Brainliest...
Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30? 30n + 60 > 150 30n + 60 150
Answer:
150<60+30n
Step-by-step explanation:
150 is the maximum amount that she can spend on gas. (which is the total)
she already spend $60
each fill up (n) costs 30
Answer:
the answer is B)
Step-by-step explanation:
What is the difference? Complete the equation. -1 2/5 - (-4/5) = ?
Answer:
First convert them which will be
-7/5 - (-4/5)
so when you subtract a negative number from negative number they actually subtract ex = -4-(-2) = -2
so its simply 7/5-4/5 then add a negative sign
so
3/5
now add negative sign so
-3/5
Please answer this correctly without making mistakes
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
Answer:
19,691
Step-by-step explanation:
Answer:
2813 x 7 = 19691
Hope this helps!
What is the slope of the line that goes through the points (-2, 4) and (5, -1)
Answer:
-5/7
Step-by-step explanation:
The slope of a line is given by
m = (y2-y1)/(x2-x1)
= ( -1 -4)/(5 - -2)
= (-1-4)/(5+2)
-5/7
Slope formula: y2-y1/x2-x1
= -1-4/5-(-2)
= -5/7
Best of Luck!
Is the square root of 65 a rational number
Answer:
No
Step-by-step explanation:
The square root of 65 is irrational.
It is not a rational number because 65 is not a perfect square.
The square root of 65 is 8.06225775...
The square root of 65 is not a rational number.
65 is not a perfect square which means it's impossible to
find a whole number times itself to give us 65.
On a calculator if you type in the square root of 65,
you will get an infinite decimal number.
The decimal values never end and never have same repeated pattern.
Help me please answer this, this will be my first grade for freshman year. The picture of the question is down below.
Answer:
D
Step-by-step explanation:
-0.81 is a high negative correlation, which means the y is decreasing with x increasing, which means y(the number of broken glass) decreases when x(amount of paper used) increased. So we can say that the toilet paper is surely helping.
make me brainly if you find it correct
Find 0.01 more than 9.154
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
On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0). Which statement best explains the relationship between lines AB and CD? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
Answer:
A. they are parallel because their slopes are equal.
Step-by-step explanation:
edge 2020
Answer:
its A in egde
Step-by-step explanation:
A bus averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle to travel 155 miles, then what is the speed of each?
Answer:
The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour
Step-by-step explanation:
Represent the bus average speed with x and the motorcycle average speed with y
Given
[tex]x = y + 2[/tex]
Distance covered by bus = 165 miles
Distance covered by motorcycle in same time = 155 miles
Required
Determine the speed of each
Average Speed is calculated as;
[tex]Average\ Speed = \frac{Distance}{Time}[/tex]
Since the two are measured with the same time, represent time with T
For the bus
[tex]Average\ Speed = \frac{Distance}{Time}[/tex] becomes
[tex]x = \frac{165}{T}[/tex]
Make T the subject of formula
[tex]T = \frac{165}{x}[/tex]
For the motorcycle
[tex]y = \frac{155}{T}[/tex]
Make T the subject of formula
[tex]T = \frac{155}{y}[/tex]
Since, T = T; we have that
[tex]\frac{165}{x} = \frac{155}{y}[/tex]
Cross Multiply
[tex]165y = 155x[/tex]
Substitute [tex]x = y + 2[/tex]
[tex]165y = 155(y+2)[/tex]
Open Bracket
[tex]165y = 155y - 310[/tex]
Collect Like Terms
[tex]165y - 155y = 310[/tex]
[tex]10y = 310[/tex]
Divide both sides by 10
[tex]y = 31[/tex]
Recall that [tex]x = y + 2[/tex]
[tex]x = 31 +2[/tex]
[tex]x = 33[/tex]
Hence;
The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour
Suppose that 45% of people have dogs. If two people are randomly chosen, what is the probability that they both have a dog
Answer:
[tex]P(Dogs) = 0.2025[/tex]
Step-by-step explanation:
Given
[tex]Proportion, p = 45\%[/tex]
Required
Probability of two people having dog
First, we have to convert the given parameter to decimal
[tex]p = \frac{45}{100}[/tex]
[tex]p = 0.45[/tex]
Let P(Dogs) represent the required probability;
This is calculated as thus;
P(Dogs) = Probability of first person having a dog * Probability of second person having a dog
[tex]P(Dogs) = p * p[/tex]
[tex]P(Dogs) = 0.45 * 0.45[/tex]
[tex]P(Dogs) = 0.45^2[/tex]
[tex]P(Dogs) = 0.2025[/tex]
Hence, the probability of 2 people having a dog is [tex]P(Dogs) = 0.2025[/tex]
The lines shown below are parallel. If the green line has a slope of -2, what is the slope of the red line?
A.
2
B.
-2
C.
D.
-
Answer:
the slope of the read line is also -2
Step-by-step explanation:
which graph shows the line y-1 = 2(x+2)
Answer:
The graph which shows the line y-1=2(x+2) is shown in the attachment
which was the last palindromic date?
Answer:
The previous palindrome date in all formats came 909 years ago on 11/11/1111. The next will come in 101 years on 12/12/2121 and after that there will not be another until 03/03/3030.
It depends how you format the date. If you do mm/dd/yyyy format
mm = month
dd = day
yyyy = year
then the last palindromic date was September 10th, 2019 since this would be written as 9/10/2019 in the mm/dd/yyyy format
Taking out the slash symbols, we have the number 9102019 which is the same when we reverse the digits.
The answer will be different if you have the date format as dd/mm/yyyy
A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
n xbar s
Sham 20 0.41 1.26
Magnet 20 0.46 0.93
Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:
[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]
[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]
To test it, use F-test statistics and compare variances of each treatment.
Calculate F-value:
[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]
[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]
[tex]F=\frac{1.5876}{0.8649}[/tex]
F = 1.8356
The critical value of F is given by a F-distribution table with:
degree of freedom (row): 20 - 1 = 19
degree of freedom (column): 20 - 1 = 19
And a significance level: α = 0.05
[tex]F_{critical}[/tex] = 2.2341
Comparing both values of F:
1.856 < 2.2341
i.e. F-value calculated is less than F-value of the table.
Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.
the definition of parallel lines requires the undefined terms line and plane by the definition of perpendicular lines requires the undefined terms of line and point. what charcteristics of these geometric figures create the different requirements?
Answer:
Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.
Step-by-step explanation:
Please help me answer the question
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
Which best describes the relationship between the line that passes through the points (–6, 5) and (–2, 7) and the line that passes through the points (4, 2) and (6, 6)?
Answer: intersecting lines
Step-by-step explanation:
Answer:
The relationship of the lines would be Parallel.
Following are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event.
1st 2nd 3rd
Boy Boy Boy
Boy Boy Girl
Boy Girl Boy
Boy Girl Girl
Girl Boy Boy
Girl Boy Girl
Girl Girl Boy
Girl Girl Girl
a. Among three children, there are exactly 2 boys.
b. Among three children, there are exactly o girls.
c. Among three children, there is exactly 1 girl.
1. What is the probability of exactly 2 boys out of three children?
2. What is the probability of exactly 0 girls out of three children?
3. What is the probability of exactly 1 girl out of three children?
Answer:
a.0.375
b.0.125
c.0.375
1.0.375
2.0.125
3.0.375
Step-by-step explanation:
a.
The total events in a sample space are n(S)=8
The events that contains exactly two boys
Boy Boy Girl,Boy Girl Boy,Girl Boy Boy.
Let A be the event that there are exactly two boys. Thus, n(A)=3.
So, probability of exactly 2 boys is P(A)=n(A)/n(S)=3/8=0.375.
b.
The event that contains exactly 0 girls.
Boy Boy Boy
Let B be the event that contains exactly 0 girls. Thus, n(B)=1.
So, probability of exactly 0 girls is
P(B)=n(B)/n(S)=1/8=0.125.
c.
The events that contains exactly 1 girl.
Boy Boy Girl,Boy Girl Boy,Girl Boy Boy
Let C be the event that contains exactly 1 girl. Thus, n(C)=3.
So, probability of exactly 1 girl is
P(C)=n(C)/n(S)=3/8=0.375.
Q1 is same as part a.
Q2 is same as part b.
Q3. is same as part c
