Find A, B so that y = A sin(2) + B cos(2) is a solution to the differential equation
4y'' +y' + 5y = 2 cos(x).
A=
BE
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Answers
If y = A sin(x) + B cos(x), then
y' = A cos(x) - B sin(x)
y'' = -A sin(x) - B cos(x)
Substitute these into the ODE:
4y'' + y' + 5y = 2 cos(x)
4 (-A sin(x) - B cos(x)) + (A cos(x) - B sin(x)) + 5(A sin(x) + B cos(x)) = 2 cos(x)
(-4A - B + 5A) sin(x) + (-4B + A + 5B) cos(x) = 2 cos(x)
(A - B) sin(x) + (A + B) cos(x) = 2 cos(x)
Then
A - B = 0
A + B = 2
Adding these equation gives
(A - B) + (A + B) = 0 + 2
2A = 2
A = 1 → B = 1
Related Questions
If you have two horse pastures, one is. 25 feet by 45 feet and the other is 40 feet by 60 feet, what is the perimeter of the two horse pastures together? Only the perimeter;)
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Second field is 40 + 60 + 40 + 60 = 200 feet.
Therefore, all together, the two fields are 340 feet in perimeter together
I need this quick pls.
Answers
Answer:
8/3
Step-by-step explanation:
Slope is rise/run. The rise here is 8. The run is 3. The line rises left to right so the slope is positive.
Hope it helps!
Find the distance between the two points in simplest radical form.
(0,8) and (4,0)
Answers
exact form 4 sqare root 5
The classroom rug is 9 feet long and has an area of 72 square feet. What is the perimeter of the rug?
Answers
Answer:
34 Ft.²Explanation:
Area = width · length
The length of the rug is 9 feet. We need to find the width.
72 ÷ 9 = 8
Check to see if this is correct: width (8) · length (9) = area (72)
Now add the length and width together two times since a rug has 4 sides
8 + 8 + 9 + 9 = 34
The perimeter of the rug is 34 ft.²
An infinite number of ratios are equivalent to 3:8. How
can that be possible, when the multiplication table only
goes to 9?
Answers
Answer:
See below, please!
Step-by-step explanation:
There are infinite number of ratios equivalent to 3:8 because both numbers can be multiplied by a common number or divided by a common number.
For example, 9:24 would still be equivalent to 3:8 because the common number in our case is 3. See what I mean?
Hope this helped!
12
A model maker wants to make a model of a
ship
He will use a scale of 1:50
The ship was 100ft long
1 foot = 0.3 m
How long will the ship be in cm?
Answers
9514 1404 393
Answer:
60 cm
Step-by-step explanation:
The model ship will be x feet long, where ...
x/100 = 1/50
x = 100/50 = 2
In meters, that is ...
2(0.3 m) = 0.6 m
A meter is 100 cm, so the length in centimeters is ...
(0.6)(100 cm) = 60 cm
K/4 < -4
What could k be???
Answers
Answer:
-17
Step-by-step explanation:
-17/4 = -4.25
and 4 is greater than that, so i think
K = -17
The quotient of x miles and 8 hours
is 55 miles per hour.
Answers
440/8=55
HELP ME PLEASE! I need this !
Answers
Answer:
Step-by-step explanation:
[tex](3x+7)8x^2\\ \\ 3x(8x^2)+7(8x^2)\\ \\ 24x^3+56x^2[/tex]
Find the difference
(4y+3)-(y-2)
need it quick
Answers
Answer: 3y+5
Step-by-step explanation: 4y+3−(y−2)
4y+3+−1(y−2)
4y+3+−1y+(−1)(−2)
4y+3+−y+2
(4y+−y)+(3+2)
3y+5
10. If log10x = 1 + a and log10y = 1 – a, show that xy = 100.
How?
Answers
Step-by-step explanation:
log x = 1 + a
a = log x - 1
log y = 1 - a
a = 1 - log y
So
log x - 1 = 1 - log y
log x + log y = 2
log (xy) = 2
xy = 100
Brianna had a garden Box that is 8' by 12' this summer she decided that it is too big and wants to reduce it by a scale factor of 1/2 find the area of her new garden
Answers
Given:
Brianna had a garden Box that is 8' by 12'.
She decided to reduce it by a scale factor of [tex]\dfrac{1}{2}[/tex].
To find:
The area of her new garden.
Solution:
Let the length and width of the original garden are 8 ft by 12 ft respectively.
Reduce the dimensions by a scale factor of [tex]\dfrac{1}{2}[/tex].
Length of the new garden is
[tex]\dfrac{8\ ft}{2}=4\ ft[/tex]
Width of the new garden is
[tex]\dfrac{12\ ft}{2}=6\ ft[/tex]
Now, the area of the new garden is
[tex]Area=Length\times Width[/tex]
[tex]Area=(4)\times (6)[/tex]
[tex]Area=24[/tex]
Therefore, the area of the new garden is 24 sq. ft.
In the real world describe 2 objects that are similar
Answers
Answer:
How much money people make and how much we waste/spend
Step-by-step explanation:
Answer
pad and phones?
Step-by-step explanation:
Jeffrey has an aquarium in the shape of a rectangular prism. He is going to place a layer of sand over the base for his iguana. The area of the base of the aquarium can be represented by the expression (42x3−14x2+21x) feet3. If the width of the aquarium is represented by the expression (7x) feet, what is the length of the aquarium?
Answers
Answer:
[tex]Length = 6x^2 - 2x + 3[/tex]
Step-by-step explanation:
Given
[tex]Area = 42x^3 - 14x^2 + 21x[/tex]
[tex]Width = 7x[/tex]
Required
Determine the length of the aquarium
The area of a rectangular base is calculated as:
[tex]Area = Length * Width[/tex]
Substitute values for Area and Width
[tex]42x^3 - 14x^2 + 21x = Length * 7x[/tex]
Make Length the subject
[tex]Length = \frac{42x^3 - 14x^2 + 21x}{7x}[/tex]
Factorize the numerator
[tex]Length = \frac{7x(6x^2 - 2x + 3)}{7x}[/tex]
[tex]Length = 6x^2 - 2x + 3[/tex]
-15 - 4x = -11
help please?
Answers
Answer:
if ur solving for x the answer is x=-1
Step-by-step explanation:
-15 - 4x = -11
=> -4x = -11 + 15
=> -4x = 4
[tex] = > x = \frac{4}{ - 4} [/tex]
=> x = -1 (Ans)
Choose the correct classification of 3x^2 + 2.
A) cubic binomial
B) quartic trinomial
C) quadratic binomial
D) quintic polynomial
Answers
Answer:
The answer is C. Quadratic Binomial
member owes $16.00 and pays $20.00 in Cash. The change due is $3.50.Provide the amount owed using the smallest number of bills and coins possible
Answers
Answer:
10 dollar bill, 5 dollar bill, and one dollar.
Mike took a taxi from his home to the airport. The taxi driver charged an initial fee of $6 plus $3 per mile. The total fare was $24, not including the tip. How many miles did Mike travel by taxi on his ride?
Answers
What operation does 6y represent?
Multiplication
Subtraction
Addition
Division
Answers
Answer:
multiplication
Step-by-step explanation:
whenever a number and a variable are together it means they are being multiplied together
Answer:
6y represents Multiplication.
A rectangular honeycomb measures 35.1 cm by 32.4 cm. Approximately how many cells does it contain?
Answers
Answer:
1,137.24
Step-by-step explanation:
Every worksheet is made up of thousands of rectangles, which are called cells. A cell is the intersection of a row and a column—in other words, where a row and column meet. Columns are identified by letters (A, B, C), while rows are identified by numbers (1, 2, 3).
So all you do is multiply like if you were finding the area:
35.1 x 32.4 = 1137.24.
Can somebody help me Graph y=-3/2X-3???
Answers
Step-by-step explanation:
try desmos its a life saver
9. Given: TE = GH, EF = HF,
Proof
Fis the midpoint of GI
Prove: AEFI > AHFG
G
10. G
Proof
PE
E
ZE
H
Answers
Souljem
Step-by-step explanation:
souljem yes yes yes
Graph x<29 on a number line
Answers
Answer:
plot it 2 higher ticks then the zero. hope this helps
Step-by-step explanation:
it should look like this
Estimate the sum of 412.02 and 513.87 to the nearest whole number?
Answers
2x plus 3 plus x2; for x = 4
Answers
Answer:
2x+3+x2 if x=4 is 27
Step-by-step explanation:
2*x or 2*4=8
8+3=11;
and x or 4 times itself is 16
so we add it all together and get 27.
Have a great day!
Answer:
27
Step-by-step explanation:
Not sure if you mean x to the power of 2, so I'll assume that.
Replacing the variable for 4 should look like:
2(4) + 3 + 4^2
8 + 3 + 16 (4 to the power of 2 is equivalent to 4 x 4 which is 16)
Now add them all, 27.
Ann borrowed $3000 from a lender that charged simple interest at an annual rate of 7% When Ann paid off the loan, she paid $420 in interest. How long was the loan for, in years?
Answers
Answer:
it was a 2 year loan with $210 contributed each year
Step-by-step explanation:
you take 7 percent of 300 which is 210 and see how many times it goes into the total interest amount and then your answer is how many years the loan was for
4 less than a number equals 12.
Answers
Answer:
16 brainliest?
Step-by-step explanation:
Can anyone solve ? This one is beyond me
Answers
Answer:
[tex]Rate = 0.13[/tex]
Step-by-step explanation:
Given
[tex]y = \sqrt[3] x[/tex]
Required
Determine the average rate of change over [2,7]
This is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
In this case:
[tex]b = 7[/tex] and [tex]a = 2[/tex]
So, we have:
[tex]Rate = \frac{f(7) - f(2)}{7-2}[/tex]
[tex]Rate = \frac{f(7) - f(2)}{5}[/tex]
From the table:
f(7) = 1.91
f(2) = 1.26
[tex]Rate = \frac{1.91 - 1.26}{5}[/tex]
[tex]Rate = \frac{0.65}{5}[/tex]
[tex]Rate = 0.13[/tex]
Express each ratio as a fraction in simplest form. 3 pints to 4 quarts.
Answers
Answer:
3/4
Step-by-step explanation:
that's as simple as it gets
The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit. What are the slope and y- intercept of the line that models this situation?
A. Slope=- 0.0018, y-intercept = 212
B. Slope= 0.0018, y-intercept =-212
C. Slope =212, y- intercept= 0.0018
D. Slope=-212, y-intercept = 0.0018
Answers
Answer:B
Step-by-step explanation
The slope of the linear relation is -0.0018 and the y-intercept will be 212. The correct option is B.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data in the table is,
Altitude(x) Boiling point (y)
0 212.0
500 211.1
The slope will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 211.1 - 212 ) / (500 - 0 )
Slope = -0.0018
The y-intercept will be calculated as,
y = mx + c
212 = 0 + c
c = 212
Therefore, the slope of the linear relation is -0.0018 and the y-intercept will be 212. The correct option is B.
To know more about an equation of the line follow
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