Solve the differential equation by variation of parameters. y + 2y' + y = e^-t ln t y(t)=
The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.
(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.
Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.
Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian
W(t) = e-2t, to derive the specific integral related to f(t) = e-t.
Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y
Obtain yp = (1/2)(t2)e-t for the given situation.
As a result, the general integral is provided by
y = C1e-t + C2te-t + (1/2)(t2)e-t.
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What is the numerical coefficient of the term − 6xy?
The numerical coefficient of xy in the given expression 6xy is 6.
In mathematical terms, a coefficient is a numerical value that is multiplied by a variable in an algebraic expression. The coefficient is the number that appears in front of the variable.
For example, in the expression 3x, the coefficient is 3. In the expression 2[tex]y^2[/tex], the coefficient is 2. In the expression -5[tex]z^3[/tex], the coefficient is -5.
In the case of a constant term in an expression, the coefficient is the constant term itself.
For example, in the expression 3x + 4, the coefficient of x is 3 and the coefficient of the constant term 4 is 4.
Here, in the expression 6xy, the numerical coefficient of xy is 6.
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If the selling price of a home is $506,000 with a 15% down payment, what is the amount of the down payment?
Help pleanbehehdhddhdhdhdhdhdhdhhd
Answer:
Step-by-step explanation:
h
------ - 1 = -3
6
To solve for h, first add 1 to both sides to isolate h/6:
h
---- = -2
6
Now isolate h by multiplying both sides by 6:
h = -12
Answer:
h is -12
..... .. . . . . .. . . .
What is the name of the angle in the picture below?
Answer:
Acute Angle
Step-by-step explanation:
Answer:
obtuse angle because it is more than 90 degrees
Audrey Patterson purchased a chicken sandwich for $4.59 and a $1.79 drink. She used a $0.50 store coupon when she paid .
Answer:
Audrey paid $5.88
Step-by-step explanation:
$4.59+$1.79=$6.38. That is her total order.
The coupon gives her 50 cents off, so $6.38-$0.50=$5.88
Audrey paid $5.88.
Answer:
answer $5.88 dollars hope this helps. :D
find the value of x on both problems please help this is urgent and please show work
Answer:
Step-by-step explanation:
1) the triangle is right, so we can use the Pythagorean theorem
x^2 + 24^2 = (16+x)^2
x^2 + 576 = x^2 + 256 + 32x
32x = 320
x = 10
2) the two segment are congruent, so
7x - 13 = 9x - 23
2x = 10
x = 5
Solve the following equations for ×. Check for extraneous solutions.
The solution for given question of algebra are 10, -42, -38 for question 1st, 2nd and 3rd.
Which four types of algebra are there?There are several sub-branches of algebra, including commutative algebra, abstract algebra, linear algebra, and elementary algebra.
For question 1x + 6/x + 3 = 4/7
7x + 42 = 4x + 12
7x - 4x = 42-12
3x = 30
x = 10
For question 22/x+8 = 3/x+9
2x - 18 = 3x + 24
x = -42
For question 3x+2/6 = x-4/7
7x+14 = 6x-24
x = -38
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PLEASE HELP QUICK!!!
The function, f(x), is plotted below.
On a coordinate plane, a function curves up to (StartFraction pi Over 4 EndFraction, 0), curves down through (0, negative 0.5) to (StartFraction 3 pi Over 4 EndFraction, negative 4) and then curves back up.
What is reasonable estimate for the limit?
Limit of f (x) as x approaches StartFraction pi Over 4 EndFraction f(x) =
Answer:
-2
Step-by-step explanation:
Answer:
the answer is -2
Write the expression using a single exponent.
7^5 • 7^6
A. 49^30
B. 7^30
C. 49^11
D. 7^11
Answer:
D
Step-by-step explanation:
keep the base and add the exponents
Can u please help...............
A graph of ΔABC with vertices A(0, 0), B (3, 3), and C (4, 0) and its image after a 90° rotation about the origin is shown in the image attached below.
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of triangle ABC (∆ABC), the coordinates of the vertices of the image (∆A′B′C′) are as follows:
(x, y) → (-y, x)
Ordered pair A = (0, 0) → Ordered pair A' = (0, 0)
Ordered pair B = (3, 3) → Ordered pair B' = (-3, 3)
Ordered pair C = (4, 0) → Ordered pair C' = (0, 4)
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Identify the simplest polynomial function having integer coefficients with the given zeros. 0,-4,√3.
A. P(x) = x^4 + 4x³ - 3x² -12x
B. P(x) = x^4 + 4x³ -12x² - 3x
C. P(x) = x³ + 4x² - 12x - 3
D. P(x) = x³ + 4x² - 3x - 12
Answer:
x^4+x^3-3x^2-12x
Step-by-step explanation:
0,-4,√3 are the zeros of polynomial. P.
If x=√3 is a zero and P has integer coefficients, then x=-√3 is also a zero. Both of these results come from solving the equation x^2=3 or x^2-3=0 so x^2-3 is a factor of P.
x=0 is a zero, means x-0 or x is a factor.
x=-4 is a zero, means x-(-4) or x+4 is a factor.
So the polynomial, P, in factored form is
x(x^2-3)(x+4)
Let's write in standard form.
I will begin by multiplying the last two factors.
x(x^3+x^2-3x-12)
Distribute x
x^4+x^3-3x^2-12x
E) how to find the first 4 terms in the expantion of ( 1 + 2x ) to power 6 ?
the first 4 term is (1+2x)^6
the equation t= 12q + 12 gives the total cost t if a meal with a too of p percent the independent variable is ?
the dependent variable is ?
sin Ø = -8/17 and cos Ø = 15/17. Find tan Ø
Answer:
-8/15
Step-by-step explanation:
So remember what sin, cos, and tan are.
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent
Now, using what we know of sin and cos, lets find opposite and adjacent to solve for tan.
Sin=-8/17
So this must mean that opposite is -8, and the hypotenuse is 17.
Next, lets find adjacent. Cos = 15/17
So this must mean that adjacent is 15, and again, hypotenuse is 17.
Now lets take the -8 of the opposite, and 15 of the adjacent, and get tan.
Tan: -8/15.
17 is not included in this whatsoever, since hypotenuse is not included in tan. And remember that it cannot be -15/8, since its opposite/adjacent, not adjacent/opposite.
Hope this helps!
Please enter the missing number: 3, 5, 18, 72, ?
A. 144
B. 214
C. 272
D. 360
E. 432
Please explain precisely
Step-by-step explanation:
18 and 5 are both missing if that's what you mean
Answer:
D. 360
Step-by-step explanation: It's being multiplied by plus one more every time you move on to a new term.
So 2*3=6, 6*3=18, 18*4=72, 72*5=360
Seaside Bike Shop rents bikes for $10 plus 54 per hour. Jack paid $30 to rent a bike. Which equation, when solved for x, gives the
number of hours he rented the bike?
This is a special right triangles multi-step problem. Please explain how to do this and the steps to how you got that answer please!
Answer:
This is an example of a combined 45 45 90 triangle and a 60 30 90 triangle. I have put the pictures showing the side lengths.
Step-by-step explanation:
On the 30 60 90, the hypotenuse is 6.
6 = 2x
x = 3
therefore, the two legs of the triangle are measured as 3 and 3[tex]\sqrt3}[/tex]
Now that we have 3[tex]\sqrt3}[/tex] as one of the legs for the other triangle, using the picture of the 45 45 90 triangle, the hypotenuse must be x[tex]\sqrt{2}[/tex].
Since x = 3[tex]\sqrt3x}[/tex], x[tex]\sqrt{2}[/tex] is 3[tex]\sqrt3}[/tex] x
Therefore x=3[tex]\sqrt{6}[/tex]
If this helps you mark me brainliest pls
What is the value of 2 by 7 and 3 by 7?
the value of 2 by 7 and 3 by 7 is: 5/7. This can be solved using the concept of fraction of addition.
What is the fraction?A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.
Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.
the value of 2 by 7 and 3 by 7 is:
= (2/7) + (3/7)
= 5/7
When adding the fractions 2/7 and 3/7 we get 5/7, as the denominator is same.
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As the ball rolls downhill, its kinetic energy ___________
Maximum
Minimum
Answer:
Maximum
Step-by-step explanation:
Answer:
Maximum
Step-by-step explanation:
The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
The area of a right-angled triangle is represented by the expression
x(x + 2) = 24 having area 24 square feet.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a right-angled triangle is (1/2)×base×height.
Given, The area of a triangle is 24 square feet whose height is 2 more than it's base.
Let, The base of the triangle be 'x', Therefore the measure of the height is (x + 2).
Therefore, The area of the triangle is,
(1/2)×x(x + 2) = 24.
x(x + 2) = 24.
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Evaluate each numerical expression
7x(12+8)-6
Answer:
134
Step-by-step explanation:
If this is right can I get brainliest?
Answer:
140x − 6
Step-by-step explanation:
add the numbers
7x(12+8)-6
7x(20)-6
multiply the numbers
7x times 20-6
=140x-6
Which inequality is true?
1.-1.5>-0.5
2.-1/2>0
3.-2.5<-2
4.-1 1/2>1.5
Answer:
option
3 is the correct answer
A university has 33,810 students. In a random sample of 270 students, 18 speak three or more languages. Predict the number of students at the university who speak three or more languages.
The expected number of students at the university who speak three or more languages is_____?
Answer:
Approximately 2254 people.
Step-by-step explanation:
What is the side length of the square with an Area of 25/81 in^2?
Answer:
[tex]\frac{5}{9}[/tex] in
Step-by-step explanation:
The area (A) of a square is calculated as
A = s² ( s is the side length )
Given A = [tex]\frac{25}{81}[/tex] , then
s² = [tex]\frac{25}{81}[/tex] ( take the square root of both sides )
s = [tex]\sqrt{\frac{25}{81} }[/tex] = [tex]\frac{\sqrt{25} }{\sqrt{81} }[/tex] = [tex]\frac{5}{9}[/tex]
The sum of three numbers is 108. The first number is 7 more than the second. The third number is 3 times the first. What are the numbers?
First number:
Second number:
Third number
Answer:
23,16, and 69
Step-by-step explanation:
(x+7) +x +[3(x+7)]=108
(x+7) + x + (3x+21)=108
5x +28=108
5x=80
x=16
1st number 16+7=23
2nd number 16
3rd number 69
150 adults complete a survey.
80 are women.
Write the ratio
men women
in its simplest form.
Answer:
The number of men to number of women be 7 : 8 .
Explain if this student has made a mistake. Explain what the mistake was and how you would fix it. include the right answer
Answer:
Mistake => [tex] \frac{8x}{4} = \frac{4}{4} [/tex]
How it can be fixed => [tex] \frac{8x}{8} = \frac{4}{8} [/tex]
[tex] x = \frac{1}{2} [/tex] (correct answer)
Step-by-step explanation:
The student solved the problem correctly up to the second step where 6 was added to both sides of the equation.
The mistake he made was in his division.
Thus, instead of dividing both sides by 8, he divided both sides by 4, which is incorrect.
Mistake => [tex] \frac{8x}{4} = \frac{4}{4} [/tex]
How it can be fixed => [tex] \frac{8x}{8} = \frac{4}{8} [/tex]
[tex] x = \frac{1}{2} [/tex] (correct answer)
Answer:
SEE IMAGE FOR SOLUTION
Hope it helps
Have a great day
How many dimes are in 4.72
Answer:
There are 47 dimes and 2 pennies.
Step-by-step explanation:
10¢ = 1 dime
$4.70 = 470 ¢
470 dimes = 47 dimes
and 2 pennies