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]
Find the value of using identities 996^2
Answer:
992,016
Step-by-step explanation:
[tex] {996}^{2} \\ = {(1000 - 4)}^{2} \\ = {1000}^{2} - 2 \times 1000 \times 4 + {4}^{2} \\ = 1000000 - 8000 + 16 \\ = 1000016 - 8000 \\ = 992,016 \\ [/tex]
If a side of a square is 10 what the other sides will be
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
all sides are equal
i need to finish my homework
Help!!to show your work!!
1 1/4 times 2/5 divided by 3 1/3
What is non-collinear?
Answer:
Non-colinear means that three given points do not have a single line connecting all 3 of the points.
A scuba driver was swimming at an elevation of -8 meters. A shark was swimming at an elevation of -29 meters. Find the difference between these two elevations.
Answer:
-21
-29-(-8)=-21
Are all numbers rational?
36599 round to the nearest thousand
Answer:
If you round to the nearest thousand, you get; 37,000
74.052 using expanded form with fractions and expanded form with decimals
Answer:
[tex]74.052 = 7 * 10 + 4 * 1 + 0 * 0.1 + 5 * 0.01 + 2 * 0.001[/tex]
[tex]74.052 = 7 * 10 + 4 * 1 + \frac{0}{10} + \frac{5}{100} + \frac{2}{1000}[/tex]
Step-by-step explanation:
Given
74.052
Required
Write in Expanded Form
In Decimals
[tex]7 = 7 * 10[/tex]
[tex]4 = 4 * 1[/tex]
[tex]0 = 0 * 0.1[/tex]
[tex]5 = 5 * 0.01[/tex]
[tex]2 = 2 * 0.001[/tex]
Bring these together,
[tex]74.052 = 7 * 10 + 4 * 1 + 0 * 0.1 + 5 * 0.01 + 2 * 0.001[/tex]
In Fraction
[tex]74.052 = 7 * 10 + 4 * 1 + 0 * 0.1 + 5 * 0.01 + 2 * 0.001[/tex]
Convert decimals to fraction
[tex]74.052 = 7 * 10 + 4 * 1 + 0 * \frac{1}{10} + 5 * \frac{1}{100} + 2 * \frac{1}{1000}[/tex]
[tex]74.052 = 7 * 10 + 4 * 1 + \frac{0}{10} + \frac{5}{100} + \frac{2}{1000}[/tex]
What are the quadrants of the standard (x, y) coordinate plane below that contain points on the graph of the equation 4x - 2y = 8 ?
Answer:
Step-by-step explanation:
4x-2y=8
divide by 8
[tex]\frac{x}{2}+\frac{y}{-4}=1\\x~intercept=2\\y~intercept=-4\\also ~2y=4x-8\\y=2x-4\\slope=2\\[/tex]
so graph lies in third and fourth and first quadrants.
The graph lies in third and fourth and first quadrants.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.
Given:
4x - 2y = 8
Now, make the equation in standard form
4x/8 - 2y/8 = 8/8
x/2- y/4 = 1
Now,
y- intercept is -4
and x- intercept is 2.
Also, we can write 4x - 2y = 8 as
y= 2x-4 and slope= 2
Hence, graph lies in third and fourth and first quadrants.
Learn more about graph here:
https://brainly.com/question/10712002
#SPJ2
Find the area of a square with sides of length 6.5 inches
Answer:
A=42.25
Step-by-step explanation:
6.5^2
What is the solution?
Answer:
1)x=13-15 => x=-2
2)-6x=-30 => x=5
3)x/4=18 => x=72
4)x-2=-11 => x=9
Step-by-step explanation:
22/44 rational or irrational?
Answer:
RATIONAL NUMBER
Step-by-step explanation:
22/44=2/4
IT IS IN THE SIMPLEST FORM AND IN THE FORM OF P/Q where as q is not equal to 0.
Solve the equation for the specified variable
S=gr-5gk*3, for g
Answer:
[tex]g = \sqrt{\frac{S}{3kr^{-5}}}[/tex]
Step-by-step explanation:
Given
[tex]S=gr^{-5}gk*3[/tex]
Required
Solve for g
[tex]S=gr^{-5}gk*3[/tex]
Split into different entities
[tex]S=g * r^{-5}*g*k*3[/tex]
Reorder in terms of like terms
[tex]S=g*g * r^{-5}*k*3[/tex]
[tex]S=g^2 * r^{-5}*k*3[/tex]
[tex]S=g^2 * 3kr^{-5}[/tex]
Solve for [tex]g^2[/tex]
[tex]g^2 = \frac{S}{3kr^{-5}}[/tex]
Take square root of both sides
[tex]g = \sqrt{\frac{S}{3kr^{-5}}}[/tex]
When using 3 letters to make an angle the middle letter is
For her phone service, Rita pays a monthly fee of $17, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is $83.90.
What are the possible numbers of minutes she has used her phone in a month?
Use M for the number of minutes, and solve your inequality for M.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Monthly fee = $17
Additional fee per unit of use = $0.05
Least amount she's been charged in a month = $83.90
Equation to represent the number of minutes 'M':
monthly fee + (additional fee per minute × M) = $83.90
Possible number of minutes :
83.90 ≤ $17 + 0.05M
$17 + $0.05 × M = $83.90
$0.05*M = $83.90 - $17
$0.05*M = $66.90
M = $66.90 / 0.05
M = 1,338 minutes
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.
Solve for x: 3 < x + 3 < 6
Steps to solve:
3 < x + 3 < 6
~Subtract 3 to everything
0 < x < 3
Best of Luck!
yolandaa sunflower is 12 centimeters more than jean sunflower yolanda sunflower is 75 centimeters tall. how tall is jeans sunflower?
Answer:
63 centimeters
Step-by-step explanation:
Answer: 63 cm tall.
Step-by-step explanation: Yolanda's sunflower is 12 cm more than Jean's sunflower. Yolanda's sunflower is 75cm. To find Jean's sunflower's size in cm simply subtract 12 cm from 75 cm.
75 = 12 = 63
So, Jean's sunflower is 63 centimeters tall.
Emma was given a system of equations to solve by graphing. Which statement correctly identifies Emma’s error?
Answer:
line one should have a y-intercept at (0,2).
Step-by-step explanation:
Answer: A
Step-by-step explanation: line one should have a y-intercept at (0,2).
Classify the equation as a conditional equation, an identity, or a contradiction. 6x−10−8=9+4x−4x
Step-by-step explanation:
this is your answer.........
Answer:
conditional equation
Step-by-step explanation:
Collecting terms on both sides, we get
6x−10−86x−18=9+4x−4x=9
Adding 18 to both sides of the equation, we get
6x=27
This can be solved by dividing by 6 on both sides of the equation, which gives a unique solution of 92. So, this is a conditional equation.
Q
100%
Laurissa rolls two number cubes, each with the numbers 1 through 6. Laurissa adds the numbers that appear on the roll.
Which two sums have an equal chance of occurring?
A. 3 and 11
B. 4 and 7
C. 5 and 8
D. 6 and 9
Answer:
Step-by-step explanation:
it’s B
7 and 4 is the only number that has a unique chance. The correct option is B.
What are permutation and combination?Combination and permutation are two different ways of grouping elements of a set into subsets in mathematics. The elements of the subset can be listed in any order in a combination. The elements of the subset are listed in a specific order in a permutation.
Let's analyze the possible sums of both dice, using the notation:
Dice₁ + Dice₂ = sum.
Also remember that we have 2 dice, with 6 options each. The total number of combinations is 6 x 6 = 36. we have 36 possible outcomes.
I will start at the extremes, the minimum that we can sum is 2, and the maximum is 12, then:
We can have 2 if:
1 + 1 = 2
Only one permutation.
and 12 if:
6 + 6 = 12
Again, only one permutation.
so 2 and 12 have the same chance (1 out of 36)
now, to have 3 we can have the:
2 + 1 = 3
1 + 2 = 3.
and to have 11
5 + 6 = 11
6 + 5 = 11
Again, 3 and 11 have the same probability (2 out of 36 options)
And now we can see a pattern.
4 and 10 will have the same chance.
5 and 9 will have the same chance
6 and 8 will have the same chance
7 is the only number that has a unique chance (and it has the largest one)
To know more about permutation and combination follow
https://brainly.com/question/17694869
#SPJ5
4/9(3/8x-27/16)=13/4
Answer:
x=24
Step-by-step explanation:
What is estimation? When is it helpful to use estimation?
Answer:
Estimation is the process of arriving at an approximate answer to a question. It is helpful to use estimation when you need to calculate something fast or the data/information your given is uncertain or unstable
Step-by-step explanation:
A 12-inch candle burns at a rate of 2 inches per hour. What is the graph of the equation that models the height of the candle over time?
The candle burns at a rate of 1 inch per hour.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
here, we have,
Given,
A 12-inch candle burns down in 12 hours.
∴ The rate at which it burns per hour is the total length of the candle divided by the total time it brunt for which is,
= (12/12) inch/hr.
= 1 inch/hr,
Hence, The candle burns at a rate of 1 inch per hour.
learn more about the unitary method here :
brainly.com/question/28276953
#SPJ2
complete question:
A 12 inch candle burns down in 12 hours. at what rate does the candle burns, in inches per hour?
Need helpw ith this plz
If g(x) = 10 + 2x what is g(-3)
Answer:
4
Step-by-step explanation:
[tex]g(x)=10+2x\\\\g(-3)=10+2(-3)\\\\g(-3)=10+-6\\\\g(-3)=10-6\\\\\boxed{g(-3)=4}[/tex]
Hope this helps.
On a number line, which number is 7/9 of the way from -6 to 3
Answer:
1?
Step-by-step explanation:
if you go from -6 to 3 it is 9 spaces. so 7 spaces equals one.
There are many ways to produce crooked dice. To load a die so that 6 comes up too often and 1 , which is opposite 6 , comes up too seldom, add a bit of lead to the filling of the spot on the 1 face. If a die is loaded so that 6 comes up with probability 0.2 and the probabilities of the 2,3,4 , and 5 faces are not affected, which of the choices is the correct assignment of probabilities to the six faces
Answer:
1 2 3 4 5 6
2 ÷ 15 1 ÷ 6 1 ÷ 6 1 ÷ 6 1 ÷ 6 1 ÷ 5
Step-by-step explanation:
As it is mentioned in the question that the probability of faces like 2,3,4,5 are not affected so in this case
P(2) = P(3) = P(4) = P(5) = 1 ÷ 6
And, P(6) = 0.2
As we know that
P(1) + P(2) +P(3) +P(4) +P(5) +P(6) = 1
This results P(1) = 2 ÷ 15
So,
1 2 3 4 5 6
2 ÷ 15 1 ÷ 6 1 ÷ 6 1 ÷ 6 1 ÷ 6 1 ÷ 5
Hence, the correct option is 2nd