Write the given second order equation as its equivalent system of first order equations. u′′−5u′−4u=1.5sin(3t),u(1)=1,u′(1)=2.5 Use v to represent the "velocity function", i.e. v=u′(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.)
Answers
Answer:
hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to
Answer: v = 5v + 4u + 1.5sin(3t),
0 1 4 5 0 1.5sin(3t) 1 2.5Step-by-step explanation:
u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1
v represents the "velocity function" i.e v = u'(t)
As v = u'(t)
u' = v
since u' = v
v' = u"
v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )
= 5v + 4u + 1.5sin(3t) ( noting that v = u' )
so v' = 5v + 4u + 1.5sin(3t)
d/dt [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex]= [tex]\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex] + [tex]\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right][/tex]
Given that u(1) = 1 and u'(1) = 2.5
since v = u'
v(1) = 2.5
note: the initial value for the vector valued function is given as
[tex]\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1\\2.5\\\end{array}\right][/tex]
Related Questions
find the distance from the origin to the graph of 6x+3y+2=0
Answers
Y-intercept—2/3
Answer:
C. 0.3
Step-by-step explanation:
Please help photo attached
Answers
Answer:
see below
Step-by-step explanation:
You can determine the correct function by looking at the function and graph values at x = 1.
For some constant k, the function is ...
(g·h)(x) = g(x)·h(x) = (-3^x)(kx) = -kx·3^x
For x=1, the graph shows (g·h)(1) = 6. Using this in our expression for (g·h)(x), we have ...
(g·h)(1) = 6
-k(1)(3^1) = 6 . . . . use the expression for (g·h), filling in x=1
k = -2 . . . . . . . . . divide by -3
The function h(x) is ...
h(x) = -2x
What evidence from Tutankhamen's tomb supports the theory that he had a genetic disease that made it difficult for
him to walk? Check all that apply.
please help
Answers
Answer:
the first and the second answer
Step-by-step explanation:
Answer:
A and B
Step-by-step explanation:
This is correct believe me it is.
Brady can feed, water, and clean up after 24 cows in 120 minutes. McKenna takes 360 minutes to care for 24 cows. How long will it take Brady and McKenna working together to care for 24 cows?
Answers
Answer:
Minutes= 90
Step-by-step explanation:
Brady will take care of 24 cows in 120 minutes.
Rate of Brady = 24/120
Mc Kenna takes care of same 24 cows in 360 minutes.
Rate of Mc Kenna = 24/360
Sum of rates = 24/120 + 24/360
Sum of rates =( 72+24)/360
Sum of rates = 96/360
Sum of rates = 96/360
Let's determine how many minutes it will take them total to take of Same 24 cows
Minutes = 24/rate
Minutes = 24/(96/360)
Minutes =( 24*360)/96
Minutes= 90
f(x)=6x-4 what is f(x)whence=8
Answers
Answer:
44
Step-by-step explanation:
Put 8 where x is and do the arithmetic.
f(8) = 6·8 -4 = 48 -4
f(8) = 44
What is the value of y
Answers
Answer:
B 63 degrees
Step-by-step explanation:
180 - 54 = 126
126 / 2 = 63
Suppose the number of defects in a sweater from a population of sweaters produced from a textile factory are normally distributed with an unknown population mean and a population standard deviation of 0.06 defects. A random sample of sweaters from the population produces a sample mean of x¯=1.3 defects. What value of z should be used to calculate a confidence interval with a 95% confidence level? z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576
Answers
Answer:
Z = 1.96.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
The value of z that should be used is Z = 1.96.
Please answer this correctly
Answers
Answer:
22 1/8 mm.
Step-by-step explanation:
First add the whole numbers, then the fractions:
3 + 5 + 5 + 7 = 20
7/8 + 7/8 + 3/16 + 3/16 Change the 7/8's to 14/16:
= 14/16 + 14/16 + 3/16 + 3/16
= 28/16 + 6 /16
= 34 /16
= 2 2/16
= 2 1/8
So the final answer is 20 + 2 1/8
= 22 1/8 mm.
Step-by-step explanation:
the perimeter of this
3 7/8 + 5 3/16 + 5 3/16 + 7 7/8
= 31/8 + 83/16 + 83/16 + 63/8
= 62 + 83 + 83 + 126/ 16
= 354/16 ans
30 POINTS FOR THE GENUIS WHO CAN ANSWER THIS!!
Answers
Answer:
Answers are below in bold
Step-by-step explanation:
1) A = 1/2bh Use this equation to find the area of each triangular base
A = 1/2(8)(6) Multiply
A = 1/2(48) Multiply
A = 12cm² Area of each triangular base
2) A = L x W Use this equation to find the area of the bottom rectangular face
A = 20 x 8 Multiply
A = 160 cm² Area of the bottom rectangular face
3) A = L x W Use this equation to find the area of the back rectangular face
A = 20 x 6 Multiply
A = 120 cm² Area of the back rectangular face
4) A = L x W Use this equation to find the area of the sloped rectangular face
A = 20 x 10 Multiply
A = 200 cm² Area of the sloped rectangular face
5) To find the total surface area of the triangular prism, add together all of the numbers.
A = 12 + 12 + 160 + 120 + 200 Add
A = 504 cm² Total area of the triangular prism
Do oddsmakers believe that teams who play at home will have home field advantage? Specifically, do oddsmakers give higher point spreads when the favored team plays home games as compared to when the favored team plays away games? Two samples were randomly selected from three complete National Football League seasons (1989, 1990, and 1991). The first sample consisted of 50 games, where the favored team played in a home game, while the second sample consisted of 50 games, where the favored team played in an away game. The oddsmakers’ point spreads (which are the number of points by which the favored team is predicted to beat the weaker team) were then collected. The following hypotheses were tested: H0: µ1 = µ2 Ha: μ1 > μ2 Analyses were run. The following is the (edited) output for the test: Which of the following is an appropriate conclusion based on the output?1. The data provide sufficient evidence to reject H0; thus, we can conclude that the mean point spread for home games is higher than that of away games.2. The data provide sufficient evidence reject the H0; thus, we cannot conclude that the mean point spread of home games is higher than that of away games.3. The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread of home games is higher than that of away games.4. The data do not provide sufficient evidence reject the H0; thus, we can conclude that the mean point spread for home games is higher than that of away games.
Answers
Answer:
Option 3 is correct.
The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread of home games is higher than that of away games.
Step-by-step explanation:
Before anything else, we first give the null and alternative hypothesis for this question.
Null hypothesis would be that there isn't significant evidence to conclude that the mean point spread of home games is higher than that of away games.
H0: µ1 = µ2
And the alternative hypothesis would be that there is significant evidence to conclude that the mean point spread of home games is higher than that of away games.
Ha: μ1 > μ2
The data from the output of the analysis of the hypothesis test is missing from the question. It was obtained online and is attached to this solution of the question.
The table consists of the difference, the sample mean, the standard error of the mean, degree of freedom, the test statistic and most importantly, the p-value. It is the p-value that absolutely gives us the concluding statement of the hypothesis testing.
When the significance level for a test isn't provided, the convention is usually to use 5% significance.
Interpretation of p-value
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.4351
0.4351 > 0.05
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & say that 'The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread of home games is higher than that of away games'.
Hope this Helps!!!
Unit sales for new product ABC have varied in the first seven months of this year as follows: Month Jan Feb Mar Apr May Jun Jul Unit Sales 148 329 491 167 228 285 441 What is the interquartile range (IQR) of the data? Please specify your answer as an integer. Note: Use the following formula to find quartile locations: Lq=(n+1)⋅(q4) where q is the quartile index (e.g., q=1 for the first quartile) and n is the number of data points.
Answers
Answer:
IQR = 274
Step-by-step explanation:
Given the unit sales for the months as:
148, 329, 491, 167, 228, 285, 441
Let's rearrange in ascending the values in ascending order (from lowest to highest), we have:
148, 167, 228, 285, 329, 441, 491
Here the total number of data, n is 7
Let's find the quartile locations using the formula:
[tex] Lq = (n + 1) * (\frac{q}{4}) [/tex]
where q is quartile index.
For first quartile, Q1:
[tex] Lq = (7 + 1) * (\frac{1}{4}) [/tex]
[tex] Lq = 8 * (\frac{1}{4}) = 2 [/tex]
Thus, the 2nd observation in the data is 167.
Q1 = 167
For third quartile, Q3:
[tex] Lq = (7 + 1) * (\frac{3}{4}) [/tex]
[tex] Lq = 8 * (\frac{3}{4}) = 6 [/tex]
Thus, the 6th observation in the data is 441.
Q3 = 441
The interquartile range, IQR will be:
Q3 - Q1
= 441 - 167
= 274
IQR = 274
35.76 and 35.8 and make the inequality 35.76<________<35.8 a true statement?
Answers
Corrected Question
Find a number in between 35.76 and 35.8 and make the inequality 35.76<________<35.8 a true statement?
Answer:
One example is 35.77
Step-by-step explanation:
Given the numbers 35.76 and 35.8
To make the inequality [tex]35.76< x <35.8[/tex] a true statement, we look for a value of x such that:
[tex]x>35.76; and\\x<35.8\\$Let x=35.77\\Cearly:$\\35.77 > 35.76;$ and$\\35.77<35.8[/tex]
Therefore:
[tex]35.76< 35.77 <35.8[/tex] is a true statement.
The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 400. a. 84% b. 16%
Answers
Answer:
b. 16%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 500
Standard deviation = 100
Percentage of students who scored less than 400:
400 = 500 - 1*100
So 400 is one standard deviation below the mean.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Of those who are below, 68% are within 1 standard deviation of the mean, that is, between 400 and 500. So 100-68 = 32% are below 400.
0.5*0.32 = 0.16 = 16%
So the correct answer is:
b. 16%
You launch a water balloon. The function h=-0.08t^2+1.6t+2 models the height h (in feet) of the water balloon after t seconds. What is the initial height of the balloon?
Answers
Answer:
The initial height of the balloon is 2 feet.
Step-by-step explanation:
The height of the balloon in feet after t seconds is given by the following equation:
[tex]h(t) = -0.08t^{2} + 1.6t + 2[/tex]
What is the initial height of the balloon?
This is h when t = 0, that is, h(0). So
[tex]h(0) = -0.08*0^{2} + 1.6*0 + 2 = 2[/tex]
The initial height of the balloon is 2 feet.
Last week Malia spent $13,000 on advertising. This week, she plans to spend three times as much. Next week, she wants to spend 60% of what she spent the previous two weeks. How much should she plan to spend on advertising next week?
Answers
Answer:
31200 dollars
Step-by-step explanation:
you multiply 13 by 4, because its last week and this week, then find 60 percent of that. Proportion: x/52000=60/100. When solved, it is $31200
The solution is, $31200 should she plan to spend on advertising next week.
What is percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
given that,
Last week Malia spent $13,000 on advertising.
This week, she plans to spend three times as much.
Next week, she wants to spend 60% of what she spent the previous two weeks.
now, we have,
you multiply 13000 by 4,
i.e. 13000 *4 = 52000
because its last week and this week,
then find 60 percent of that.
let, she plan to spend on advertising next week is x .
Proportion:
x/52000=60/100.
When solved, it is $31200.
Hence, The solution is, $31200 should she plan to spend on advertising next week.
To learn more on percentage click:
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smplify the following algebraic expression: 6(2y + 8) - 2(3y - 2)
Answers
Answer:
6y +52
Step-by-step explanation:
6(2y + 8) - 2(3y - 2)
Distribute
12y + 48 - 6y +4
Combine like terms
6y +52
A=b.h,for h V=3k+2,for k
Answers
Answer:
see explanation
Step-by-step explanation:
Given
A = bh ( isolate h by dividing both sides by b )
[tex]\frac{A}{b}[/tex] = h
-----------------------------
Given
V = 3k + 2 ( subtract 2 from both sides )
V - 2 = 3k ( divide both sides by 3 )
[tex]\frac{V-2}{3}[/tex] = k
What is the sum of the fractions? Use the number line to help find the answer. 3/5 + ( - 7/5) Answers: Wh Three-fifths + (Negative StartFraction 7 over 5 EndFraction A number line going from negative 2 to positive 2 in increments of one-fifth. Negative 2 Negative four-fifths Four-fifths 2
Answers
Answer:
[tex]\frac{-4}{5}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5} - \frac{7}{5} = \frac{3-7}{5} = \frac{-4}{5}[/tex]
The sum of the fractions is -4/5.
What is a number line?The real numbers arranged in order on a geometric line form a number line. The points on the geometric line represent real numbers.
On the number line, the addition of a positive number a to a number b moves the point at b to the right by a units.
The addition of a negative number -a to a number b moves the point at b by a units to the left.
The point H in the diagram is at the number 3/5, third stick to the right of 0.
Adding -7/5 to 3/5 means moving the point H to the left by 7 sticks. Doing so we find the point at -4/5 as shown in the figure.
The final position of the point after addition is -4/5.
The value of 3/5 - 7/5 is, thus, -4/5.
Learn more about number line here
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Y= 3x^2 + 12x + 7 in vertex form
Answers
Answer:
y=3(x+2)^2-5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
eifufjdbeiixjfbdbsisifbfbfbidid
From a sample of 25 graduate students, the mean number of months of work experience prior to entering an MBA program was 33.59. The national standard deviation is known to be 19 months. What is a 90% confidence interval for the population mean?
Answers
Answer:
The 90% confidence interval for the population mean is between 27.34 months and 39.84 months.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645*\frac{19}{\sqrt{25}} = 6.25[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 33.59 - 6.25 = 27.34 months
The upper end of the interval is the sample mean added to M. So it is 33.59 + 6.25 = 39.84 months
The 90% confidence interval for the population mean is between 27.34 months and 39.84 months.
10.
1
(1 point)
Which graph represents the linear function y=-x-4?
3
Answers
Answer:
Step-by-step explanation:
here are some of the graph points:
(-2,-2)
(-1,-3)
(0,-4)
(1,-5)
(2,-6)
(3,-7)
(4,-8)
The graph should have a negative slope and the slope should be -1, and the y-intercept should be -4. The pic you put is not the correct graph.
F(x)=4x>2+12x+9 Rewrite to function by completing the square F(x)=...(x+....)>2+...
Answers
Answer:
f(x) = 4( x + 3/2)^2
Step-by-step explanation:
F(x) =4 x^2 + 12x + 9
= 4 [ x^2 + 3x] + 9
Add (3/2)^2 - (3/2)^2 to the square bracket, we have:
4 [ x^2 + 3x+ (3/2)^2 - (3/2)^2] + 9
4[ (x + 3/2 )^2 - 9/4] + 9
4( x + 3/2)^2 - 9/4 ×4 + 9
4( x + 3/2)^2 - 9 + 9
4( x + 3/2)^2 +0
4( x + 3/2)^2
Note the (3/2)^2 - (3/2)^2 is decoded by dividing b by 2 and squaring it and then subtracting same. Look at the general equation of a circle given below
ax^2 + bx + c
To form a square expression we adopt (b/2)^2 - (b/2)^2 to the general equation provided a = 1;
To make a = 1; we had to factor out 4 from the coefficient of x; making perfect square is of concern when we have ax^2 + bx ; irrespective of 'c' or not.
This is usually referred to as method of completing the square in solving quadratic equation
i need help on this question
Answers
Answer:
1/2 or 0.5
Step-by-step explanation:
4x+8=10tothefirstpower x=1/2 or 0.5
The area of a parallelogram is 65 ft square. What is it height?
(The base is 13 ft)
Answers
Answer:
5
Step-by-step explanation:
Area equals bh
So 65 divided by 13
Answer:
h = 5 ft
Step-by-step explanation:
The area of a parallelogram is
A = bh
65 = 13h
Divide each side by 13
65/13 = 13h/13
5 = h
Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of 7 per hour. If it takes approximately 10 minutes to serve each customer, find the mean and variance of the total service time for customers arriving during a 1-hour period. Assume that a sufficient number of servers are available so that no customer must wait for service. What is the probability that the total service time will exceed 2.5 hours? (Use at least four digits after the decimal if rounding.)
Answers
Answer:
the mean service time = 70 minutes
the variance of the total service time for customers arriving during a 1-hour period is 700
the probability that the total service time will exceed 2.5 hours is 0.0012
Step-by-step explanation:
Given that:
Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of 7 per hour.
If it takes approximately 10 minutes to serve each customer
From the given information:
The mean total service time= [tex]10 \ minutes * \lambda[/tex] (i.e the average number to turn up during the hour) .
where;
[tex]\lambda =[/tex] the average rate per hour i.e 7
Thus; the mean service time = 10 × 7 = 70 minutes
For a Poisson Distribution;
The variance of the the total service time for customers arriving during a 1-hour period can be expressed by the relation:
[tex]\sigma(aX) = a* \sigma(X). \\ \\ where ; \sigma = {\sqrt{S^2}} \\ \\ \sigma(service \ time) = 10 * \sigma(arrival \ time) \\ \\S^2 (service \ time) = (10* \sigma(arrival \ time))^2 \\ \\ S^2(service \ time) = 100 * S^2(arrival \ time) \\ \\ = 100*\lambda \\ \\ = 100*7 = 700[/tex]
where S² = variance
What is the probability that the total service time will exceed 2.5 hours?
If we convert 2.5 hours to minutes ; we have
2.5 × 60 minutes =150 minutes
The probability that the total service time will exceed 2.5 hours is as follows:
[tex]Z = \dfrac{S-70}{\sqrt {700}} \ \ \ \ follow \ N(0,1) \\ \\ P(S > 150) = \dfrac{S-70}{\frac{\sqrt{700}>(150-70)}{\sqrt{700}}} \\ \\ =P(Z > -2.5512) \\ \\ =0.0012[/tex]
Please slove for me would make my day
Answers
Answer:
x = 30°
Step-by-step explanation:
The sum of angles in a triangle is 180°, so you have ...
60° +2x +60° = 180°
2x = 60° . . . . . . . . .subtract 120° from both sides
x = 30° . . . . . . . . . . divide by 2
_____
Since the triangle is isosceles (base angles are congruent), the angle bisector is also an altitude that divides the triangle into congruent 30°-60°-90° triangles. The measure of the angle marked x is 30°.
What’s the correct answer for this?
Answers
Answer:
0.7 + 0.4 - 0.2 = 0.9
Step-by-step explanation:
Let's denote the probabilities as following:
The probability that the show had animals is
P(A) = 0.7
The probability that the show aired more than 10 times is
P(B) = 0.4
The probability that the show had animals and aired more than 10 times is
P(A⋂B) = 0.2
The probability that a randomly selected show had animals or aired more than 10 times is P(A⋃B)
The correct form of addition rule to determine the probability that a randomly selected show had animals or aired more than 10 times is:
P(A⋃B) = P(A) + P(B) - P(A⋂B) = 0.7 + 0.4 - 0.2 = 0.9
=> Option B is correct
Hope this helps!
Find the distance between the points (-5, 0) and (-4, 1).
Answers
Answer:
√2
Step-by-step explanation:
(-5, 0) and (-4, 1)
[tex]d=\sqrt{(x_{2}-x_{1} )^{2}+ {(y_{2}-y_{1} )^{2}}}[/tex]
[tex]d= \sqrt{(-4-(-5))^{2} + (1-0)^{2}} =\sqrt{1+1} =\sqrt{2}[/tex]
The lengths of the sides of a triangle are 3, 3, 32. Can the triangle be a right triangle?
Answers
Answer:
No
Step-by-step explanation:
Although two sides are equal, the 32 is simply too big for it to be a triangle.
Answer:
No it is not the sides of right angled triangle.
Step-by-step explanation:
IF a²+b²=c² then the triangle is right
3²+3²=32²
9+9=1024
18=1024
help me please
i will give you 5 stars and brainliest
Answers
Answer:
228incubed
Step-by-step explanation:
Area of prism is area of cross section x length.
So, área of trapezium is a plus b times h divided by 2.
Times that by height. Gives you 228