Complete Question
Find a particular solution to [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]
[tex]y_1 = 1 + t , \ y_2 = e^t[/tex]
Answer:
The solution is [tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]
Step-by-step explanation:
Now the given equation is [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]
dividing through by t
We have
[tex]y'' - \frac{1 + t }{t}y' + \frac{1}{t} y = te^t \\\\ let's\ call\ it \ g(t)[/tex]
Now for the given initial value we can generate our Wronskian as follows
[tex]W(y_1 ,y_2) = | \left y_1} \atop {y_1'}} \right. \left y_2} \atop {y_2'}} \right | = | \left {(1 + t)} \atop {1}} \right. \left e^t} \atop {e^t}} \right | = (1 + t )e^t - e^t = te^t[/tex]
Now applying method of variation of parameters to obtain the particular solution
So here we assume that
[tex]y_p = v_1 y_1 + v_2 y_2[/tex]
So
[tex]v_1 = - \int\limits {\frac{y_2 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{e^t te^t}{te^t} } = - \int\limits { e^t} } = -e^t[/tex]
And
[tex]v_2 = - \int\limits {\frac{y_1 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{(1 + t) te^t}{te^t} } = - \int\limits (1 + t) = t + \frac{t^2}{2}[/tex]
So
[tex]y_p = -e^t * e^t + t + \frac{t^2}{2} * 1 + t[/tex]
[tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]
You are buying tickets to a Star Wars Convention. The tickets cost $10 per adult and $3 per child. Parking is a one-time fee of $5. If you
purchased two adult tickets, a, and the total cost was $109, how many child tickets, c, were purchased?
Answer:
28 children tickets
Step-by-step explanation:
$109 for the whole cost
bought 2 adult tickets that costed 10$ each and payed 5$ for parking fee
add them together 25$
109-25 =84
84/3 =28
A candy store sells mints in 14, 12 , and 34 lb packages. John purchases several packages of each weight.
What is the weight of 6 packages of the 14 lb package?
Answer:
84 lbs
Step-by-step explanation:
Multiply 14*6 to get the total weight
The perimeter of a rectangle is 40 m. The length is 4 m more than three times the width. Find the length and the width of the rectangle.
Answer:
Width = 4 m, Length = 16 m
Step-by-step explanation:
Perimeter = 40
Width = x
Length = 3x + 4
x + x + 3x + 3x + 4 + 4 = 8x + 8
40 - 8 = 32
32/8 = x
x = 4
Width = 4
Length = 16
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fill in the table using the function rule: y=1 + 4x
Answer:
13, 25, 37, 41
Step-by-step explanation:
By plugging each x value given for x, you are able to solve for y. Just multiply x by 4 and add 1.
27. Give the perimeter of the rectangle below in
simplest form.
Answer:
The permeter will be 26 units
Step-by-step explanation:
First to find this you need to know what the value of x is to do this I will use the equation 3x - 7 = x + 2
1. add seven to both sides leaving 3x = x + 9
2. Then subtract the 1x from both sides leaving 2x = 9
3. Then divide 9 by 2 which will be 4.5, x = 4.5
Then just plug 4.5 into each x value 4.5 + 2 and 3(4.5) - 7
1. 4.5 + 2 = 6.5
2. 3(4.5) - 7 13.5 - 7 = 6.5
The perimeter of the rectangle below in simplest form will be 4(x - 3).
Length of the rectangle = 3x - 7
Width of the rectangle = x+2
The perimeter of a rectangle is given as 2(length + width). The perimeter of the rectangle given will then be:
= 2(length + width)
= 2(3x - 7) + 2(x + 2)
= 6x - 14 + 2x + 4
= 4x - 12 = 4(x - 3)
Therefore, the perimeter of the rectangle in simplest form will be 4(x - 3).
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Evaluate =f(×) r 6x-2 for f (2a-3)
Answer:
[tex] \boxed{\sf f(2a - 3) = 12a - 20} [/tex]
Step-by-step explanation:
Function given:
⇒f(x) = 6x - 2
Substitute 2a - 3 into the function in place of x:
⇒f(2a - 3) = 6(2a - 3) - 2
Expand bracket:
⇒f(2a - 3) = 12a - 18 - 2
Add the like terms:
⇒f(2a - 3) = 12a - 20
What is the equation shown in standard form of the line shown on the graph?
O x = 4
O y = 4
O x - y = 4
Answer:
[tex]y = 4[/tex]
Step-by-step explanation:
Because no matter what value x is, y is always 4
Which statements are true regarding f(x)=10/x+5
? Check all that apply.
The domain of f(x) is (–∞, –5) U (–5, ∞).
The range of f(x) is (–∞, 2) U (2, ∞).
The x-intercept is at (–5, 0).
The y-intercept is (0, 2).
There is a vertical asymptote at x = –5.
The end behavior is x → –∞, f(x) → 0 and x → ∞, f(x) → 0.
For the function [tex]\frac{10}{x + 5}[/tex] , we can say
The domain of f(x) is (–∞, –5) U (–5, ∞).
The y-intercept is (0, 2).
There is a vertical asymptote at x = –5.
The end behavior is x → –∞, f(x) → 0 and x → ∞, f(x) → 0.
What is a function?A mathematical relationship from a set of inputs to a set of outputs is called a function.
What is domain of a function?The domain of a function is the set of all possible inputs for the function.
What is range of a function?The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs
What is asymptote?An asymptote is a straight line that can be horizontal, vertical or oblique that goes closer and closer to a curve which is the graphic of a given function.
What is intercept?An intercept of any function is a point where the graph of the function crosses, or intercepts, the x-axis or y-axis.To find the x-intercept we need to do y = 0To find the y-intercept, we need to do x = 0How to know the domain of function?The given function is [tex]\frac{10}{x + 5}[/tex]
Now, if x = -5 then the function becomes undefined.
∴ The domain of the function is all real numbers except -5
So, The domain of f(x) is (–∞, –5) U (–5, ∞).
So, option a is correct.
How to know the range of the function?Clearly, the range of the function includes all real numbers
So, option B is wrong
How to find the x-intercept?To find the x-intercept , we will have to solve f(x) = 0, which is not at all possible for this function.
So, option C is wrong
How to find the y-intercept?To find the y-intercept, we need to do x = 0So, putting x = 0 in the function we get f(x) = 2
So, the y- intercept is (0, 2).
So, option D is correct.
How to find vertical asymptote ?To find the vertical asymptote, we need to make the denominator = 0∴ x+ 5 = 0
∴ x = -5
So, there is a vertical asymptote at x = –5.
Hence option E is correct.
How to find the end behavior?We can see,
As x tends to -∞, x + 5 will also tend to -∞We know that a number divided by ∞ or -∞ becomes 0So, as x tends to -∞, f(x) will tend to 0
So, Option F is correct.
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Answer:
ADEF
Step-by-step explanation:
ADEF
Order from greatest to least 1.202;1.29;1.02
Answer:
1.29, 1.202, 1.02
Step-by-step explanation:
Which of the following trinomials could represent the product (x + m)(x + n) if m = 5 and n = -7? A x2 + 2x - 35 B x2 - 12x - 35 Cx2 + 35x + 2 D x2 - 2x - 35
Hey there! I'm happy to help!
Let's plug in these values.
(x+5)(x-7)
We use the FOIL method to multiply the two.
We multiply the Firsts.
x·x=x²
We multiply the Outsides.
-7·x=-7x
We multiply the Insides.
5·x=5x
And we multiply the Lasts.
-7·5=-35
We combine these all.
x²-7x+5x-35
x²-2x-35
Have a wonderful day! :D
The value of -31.45/-3.21 is around?
Which of the following inequalities is incorrect?
00>-2
6 >-12
-5<-8
0-7<-5
Step-by-step explanation:
First, is 0 greater than -2? Correct
Next, is 6 greater than -12? Correct
Is -7 less than -5? Correct
Finally, is -5 less than -8? NERP!!
So C. is incorrect. Or in this case, it is...
The manufacturer of pencils spends $0.05 to make each pencil and sells them for 0.25. The manufacturer also has fixed
costs each month of $2000. Find the number of pencils x that the manufacturer needs to sell in order to break even
Answer:
x=10000
Step-by-step explanation:
The break even point occurs when costs equal revenue. Write the break-even formula and solve to find
C(x)0.05x−20000.2xx=R(x)=0.25x=2000=10000.
Assuming that a local cost cutter provides cuts perms and hair styling service and you fix cost are $120,000 in the variable cost or 40% of the sales revenue last year’s revenue total of $250,000. What is the break even points in sales dollars?
Answer:
Unit selling price
$7 $9 $7
Unit variable costs
(4) (5) (1)
Unit contribution margin
$3, $4, $6
With monthly fixed costs of $306,000, the company sells two units of A for each unit of B and three units of B for each unit of C.
what is the answer to
5 1/6 times ( -2/5)
Answer:-31/15
Step-by-step explanation: step 1: make both fractions improper
step 2: multiply numerator and denominator 31/6 x -2/5= -62/30
step 3: simplify -31/15
There are 6 black marbles, 14 blue marbles, 8 white marbles,
and 12 clear marbles in a bag. If Andy chooses a second marble
without replacing the first marble, what is P(black, then clear)?
Answer:
3/65 = 0.046 = 4.6%
Step-by-step explanation:
Notice that the total number of marbles is:
6 + 14 + 8 + 12 = 40
Then , the probability of getting a black marble first is 6/40 = 3/20
Now, since the experiment is without replacing, he is left with a total of 39 marbles in the bag, and the probability of getting a clear one is now 12/39
The total probability is the product of these two:
(3/20) x (12/39) = 3/65 = 0.046 = 4.6%
What is the property of (4y + 1) x 0 =0
Answer: Zero Property
Step-by-step explanation:
The rate of auto thefts doubles every 5 months.
(a) Determine, to two decimal places, the base b for an exponential model y = Abt of the rate of auto thefts as a function of time in
months.
(b) Find the tripling time to the nearest tenth of a month.
months
I think first one is the answer
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Given the points A(-5, -6) and B(8, 2), if C is the midpoint of segment AB, find the coordinates of the midpoint of segment CB
James has 1,836 marbles. He decides to divide them equally among 23 boxes. How many marbles will James have left over?
Answer:
79.8260869565
Step-by-step explanation:
When dividing 1,836 by 23= 79.8260869565
Graph the linear equation by finding its intercepts.
3x + 6y = 18
OMG! I just answered the wrong question... so sorry
A box of books weighs 4.10 kg for every meter of it's height. Convert this ratio into pounds per foot.
Answer:
The ratio is k = 2.76 pounds / foot
Step-by-step explanation:
From the question we are told that
For 1 m height => 4.10 kg mass
generally 1 meter = 3.28084 feet
Also
1 kg = 2.20462 pound
4.10 kg = x pounds
So
[tex]x = \frac{4.10 * 2.20462}{1 }[/tex]
=> [tex]x = 9.04 \ pounds[/tex]
So
9.04 pounds = 3.28084 feet
z pounds = 1 foot
So
[tex]z = \frac{ 9.04 * 1 }{ 3.28084}[/tex]
=> z = 2.76 pounds
So the ratio is in pounds per foot is
k = 2.76 pounds / foot
Is the following number an integer?
30/6
Answer:
NO ! For 30, the answer is: No, 30 is not a prime number. The list of all positive divisors (i.e., the list of all integers that divide 30) is as follows: 1, 2, 3, 5, 6, 10, 15, 30.
Step-by-step explanation:
Find the sum of the squared residuals for each potential line of fit, and then determine which potential line is the true line of best fit. Equation 1 Square of residual .28 .167 .19 Equation 2 Square of residual .005 .110 .09 Equation 3 Square of residual .125 .125 .26 Equation 4 Square of residual .212 .009 .08 Question 8 options: Equation 4 Equation 1 Equation 3 Equation 2
Answer: Equation 2
Step-by-step explanation:
Equation 1 Square of residual .28 .167 .19
Sum of Square Residual :
( .28 + .167 + .19) = 0.637
Equation 2 Square of residual .005 .110 .09
Sum of Square Residual :
(.005 + .110 + .09) = 0.205
Equation 3 Square of residual .125 .125 .26
Sum of Square Residual :
( .125 + .125 + .26) = 0.51
Equation 4 Square of residual .212 .009 .08
Sum of Square Residual :
( .212 + .009 + .08) = 0.301
Equation 2 is the best potential line of best fit as it has lowest value of sum of square residual. And the best line of fit is one which the sum of Squared error is lowest.
Craig has acollection of 220 marbles. He lets his friend have 1/4 of his collection and sells 1/5 of his collection to the novelty store. He takes 15 marbles home to give to his brother. how many marbles remain in Craig's collection?
Answer:
he would have 106
Step-by-step explanation:
hope it helps
A rectangle is 3 times as long as it is wide. The perimeter is 24 feet. Find the dimensions.
Answer:
Width is 3 units, The Length is 9 units.
Step-by-step explanation:
Three times as much as 3, or 9, is how you find the lengths. This being- 3+3=6 and 9+9=18, 6+18=24, which is the perimeter, therefore 3 and 9 are the dimensions.
Help solve step by step please? 3/7➗4/5=
Answer:
15/28
Step-by-step explanation:
Step-by-step explanation:
3/7 divided by 4/5
Find the reciprocal of 4/5 which is 5/4
Multiply 3/7 by 5/4
3*5= 15 which is the numerator
7*4=28 which is the denominator
so the final answer is 15/28
which decimal is less than 0.8 and greater than 0.02
Answer:
0.02<x<0.80
0.4
Step-by-step explanation:
0.02 is equal to 2/100 and 0.8 is equal to 80/100
so you could really choose any number between 0.03 and 0.79
Answer:
Less than 0.8 and greater than 0.02
0.8 > a > 0,02
There are many decimals:
0.7
0.67
0.6
0.5
0.4
0.3
0.2
0.1
0.023
0.021
and many others
what value of x makes this equation true X over 3 = 24
Answer:
x=72
Step-by-step explanation:
Start with [tex]\frac{x}{3}[/tex]=24
Using the multiplication property of equality, multiply each side by 3
x=72
Please Help A) Find the perimeter B) The area of the rectangle
Answer:
A) 36.2m B) 70m
Step-by-step explanation:
5.6m + 5.6m = 11.2 m
12.5 + 12.5= 25 11.2 + 25 = 36.2m
Length x width equals area
12.5m = length and 5.6m= width
multiply 12.5 x 5.6= 70m