The given initial value problem using the method of undetermined coefficients. The final solution to the initial value problem is y = cos(2x) + x - (1/9)*sin(3x).
To solve the given initial value problem, we begin by finding the general solution to the associated homogeneous equation. The homogeneous equation is given by y'' + 4y = 0. The characteristic equation is obtained by substituting y = e^(mx) into the equation, resulting in the quadratic equation m^2 + 4 = 0. Solving this equation yields two distinct roots: m_1 = 2i and m_2 = -2i. Thus, the general solution to the homogeneous equation is y_h = c_1cos(2x) + c_2sin(2x), where c_1 and c_2 are arbitrary constants.
Next, we assume a particular solution in the form of y_p = Ax + B + Csin(3x) + Dcos(3x), where A, B, C, and D are undetermined coefficients. We substitute this particular solution into the given differential equation and solve for the coefficients. Comparing the coefficients of like terms, we find A = 0, B = 1, C = -1/9, and D = 0.
The particular solution is y_p = x - (1/9)*sin(3x), and the complete solution is obtained by adding the particular solution to the homogeneous solution: y = y_h + y_p. Applying the initial condition y(0) = 1, we find that c_1 = 1 and c_2 = 0. Therefore, the final solution to the initial value problem is y = cos(2x) + x - (1/9)*sin(3x).
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A backpack is on sale for 30% off. If the sales price is $15.75, what is the original price? Show your work.
Answer:
$22.50
Step-by-step explanation:
As it is 30% off, $15.75 is 70% of the full price. You can then divide 15.75 by 70 [= 0.225] to get 1% of the full price. Multiply 0.225 by 100 to get the full price. 0.225 x 100 = 22.5
We can check that this answer is correct by multiplying 22.50 by 0.7. If you get 15.75 you know the answer is correct as 15.75 is 70% of the full price.
In a right triangle, one acute angle measure 35 degrees and its adjacent side is 40 yards.
Find the opposite side.
Paragraph. Describe how to find the opposite side of one right triangle with one acute angle of 35 degrees and adjacent side of 40 yards.
Word Bank: right triangle, opposite and adjacent side,
Answer:
Opposite side =28 yards
Step-by-step explanation:
Tan_°=Opposite÷ Adjacent
Tan 35° =Opposite÷40yards
Opposite=40*Tan35°
Opposite=28yards
when loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is there times that of the empty lorry . find the mass or iron.
Complete Question
When loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is three times that of the empty lorry, find the mass of iron.
Answer:
3000kg
Step-by-step explanation:
Let us represent
Mass of lorry = x
Mass of iron rods = y
x + y = 12000kg..... Equation 1
x = 12000kg - y
We are told that:
If the mass of iron rods is three times that of the empty lorry, find the mass of iron.
x = 3y
We substitute 3y for x in Equation 1
x = 12000kg - y
3y = 12000kg - y
Collect like terms
3y + y = 12000kg
4y = 12000kg
Divide both sides by 4
y = 12000kg/4
y = 3000kg
Note that:
Mass of iron rods = y
Hence, Mass of iron rods = 3000kg
Find the radius of the button.
3 and 1/2 in
radius:
Answer:1.75
Step-by-step explanation:
formula= R= D/2
convert 3 1/2 into a decimal
3.5
do 3.5 divided by 2 (R= 3.5/2) = 1.75
so the Radius is 1.75 inches !! hope this helped :)
The radius of the button 3 and 1/2 in would be; 1.75
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
The formula= Radius= D/2
Now convert 3 and 1/2 into a decimal;
3.5
Now, 3.5 divided by 2 (R= 3.5/2)
= 1.75
Hence, the Radius is 1.75 inches .
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If cot θ= tan (pi/6) what is cos θ? Round your answer to the nearest hundredth.
Answer:3.46
Step-by-step explanation:
Write an equation in point-slope form and slope-intercept form for each line
1. passes through (1, 9), slope = 2
2. passes through (4, -1), slope = -3
An equation of a line in point-slope form: y - y₁ = m(x - x₁)
1.
passes through (1, 9) ⇒ x₁ = 1, y₁ = 9
slope: m = 2
The equation:
y - 9 = 2(x - 1) ← point-slope form
y - 9 = 2x - 2 {add 9 to both sides}
y = 2x + 7 ← slope-intercept form
2.
passes through (4, -1) ⇒ x₁ = 4, y₁ = -1
slope: m = -3
The equation:
y + 1 = -3(x - 4) ← point-slope form
y + 1 = -3x + 12 {subtract 1 from both sides}
y = -3x + 11 ← slope-intercept form
someone please help
Answer:
B
Step-by-step explanation:
Hi,
Your slope is in front of the x and your y-intercept is what's being added or subtracted. In this case, 4x is your slope, and +1 is your y-intercept which means that B is correct.
I hope this helps :)
Need to know if this is write. if not, please correct.
Classify each pair of angles listed below as adjacent or vertical.
What is the volume 9inches 3inches 5inches
Answer:
135 can i have brain list
Step-by-step explanation:
9X3X5
Which equation is equivalent to 29p + 32?
A 32 - 29p
B 32 + 29p
C 32p + 29
D 32(29-p)
The temperature increases from 18°F to 27° F.
What is the percent increase of the temperature
A) 3%
B) 9%
C) 33%
D) 50%
D) 50%
Explanation: 18 + (18x.50) = 27
Justin lives 5 4/5 miles from his grandfathers house. Write the mixed number as a fraction greater than 1
Answer:
29/5
Step-by-step explanation:
Answer:
29/5
Step-by-step explanation:
As an improper fraction, your answer is 29/5.
I'm not sure what it means by writing it as a fraction "greater than 1".
Six times the quantity x -2 is 24. Find the number x
Can someone plz help me
Answer:
IT's d!!!!!
Step-by-step explanation:
A recent study sought to determine if exercising after studying for an exam may help retain information. The 150 student volunteers that participated in the study were randomly assigned to three groups. All students were given a picture memory task that they studied for 15 minutes. After studying, one of the groups was instructed to exercise for 30 minutes immediately after studying. A second group was instructed to wait 1 hour after studying and then exercise for 30 minutes. The third group was instructed to not exercise after studying. The next day all 150 student volunteers were given a test to determine how well they could remember what they studied. Here are the results:
Answer:
The correct answer is (A).
Step-by-step explanation:
Because the data came from 3 groups in a randomized experiment, the appropriate test is a chi-square test for homogeneity.
Which is the most reasonable estimate of 132% of 48?
a.5.2
b.6.5
c.52
d.65
The most reasonable estimate of 132% of 48 is 60. The correct answer is (C) 52.
To find the most reasonable estimate of 132% of 48,
A reasonable estimate does not exceed the original numbers in a problem. Let us look at a reasonable estimate.
we need to use the following formula:
Most reasonable estimate = Closest multiple of 10To use this formula, we first need to find 132% of 48.132% of 48 can be calculated as follows:132/100 x 48 = 63.36
Now, we need to find the closest multiple of 10 to 63.36.The closest multiple of 10 to 63.36 is 60.
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To find out the most reasonable estimate of 132% of 48, we can multiply the given percentage with 48.
Therefore, the most reasonable estimate of 132% of 48 is 64.
132% of 48 = (132/100) × 48
= 63.36
Since we are looking for an estimate, we can round off the above answer to the nearest whole number. Here, we have two possible options:
63 and 64.132% of 48 is slightly greater than half of 48 (which is 24) + 24. So, the answer should be slightly greater than 48 + 24 = 72. Therefore, the most reasonable estimate of 132% of 48 is 64. Thus, the correct answer is b.6.5.
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whats is the answer to this equation?
who ever gets the right answer gets 25 points.
Answer:
51.2 m
Step-by-step explanation:
To find perimeter add all sides up
Which expression is equivalent to x+2+[4x-x^2+6x+8 over x+4?
Answer:
-x^3-7x^2-46x-16/x+4
Step-by-step explanation:
The slash is a fraction! Also the fraction is negative :)
Which type of display is for One-Variable data set
Answer:
If you look at the bar graphs, histograms, and circle graphs, they all look at one variable at a time and display the number of times or percentage of times an individual point or interval is counted.
Step-by-step explanation:
A bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag.
How many desired outcomes should Denato use in his probability calculation?
Answer: its 22
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
The number of desired outcomes is the total number of blue pens in the bag. There are seven outcomes that can be blue.
PLEASE HELP, ONLY HAVE A FEW MIN LFT!!!!
A bookstore tracked the data of the weight of their deliveries and the number of books in each box. They created a scatterplot and trend line based on the data.
Which statement would be a reasonable prediction based on the scatterplot and trend line?
A box with 10 books should weigh about 2 pounds.
A box with 10 books should weigh about 4 pounds.
A box with 10 books should weigh about 6 pounds.
A box with 10 books should weigh about 12 pounds.
Answer: According to the trendline it would be about 6 lbs
Step-by-step explanation:
Answer:
C.
Step-by-step explanation: I did the test </3
Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 4.8329
5.8304 is the standard deviation of the second sample.
The F-test statistic is approximately 1.455.
To find the F-test statistic to test the claim of equal variances for two populations, you need the standard deviations of both samples. Given that the standard deviation of the first sample is 4.8329 and the standard deviation of the second sample is 5.8304, we can proceed with the calculation.
The F-test statistic is calculated as the ratio of the variances of the two samples. In this case, since we only have the standard deviations, we need to square them to obtain the variances.
First, square the standard deviations:
Variance of the first sample (s1^2) = (4.8329)^2 = 23.3747
Variance of the second sample (s2^2) = (5.8304)^2 = 34.0051
Next, calculate the F-test statistic by dividing the larger variance by the smaller variance:
F-test statistic = (larger variance) / (smaller variance)
F-test statistic = s2^2 / s1^2
F-test statistic = 34.0051 / 23.3747
Using the given values, the F-test statistic is approximately 1.455.
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Solving systems of equations using Substitution
Y= -4x +3
Y= 4x +3
The total number of passengers riding a certain city bus during the morning shift is 1,100. If the child's fare is $0.5o, the adult fare is $1.25, and the total revenue from the fares in the morning shift is $1,200, how many children and how many adults rode the bus during the morming shift? (Letx and y denote the number of children and adults, respectively.)
=1,000
=1,200
A total of 233 children and 867 adults rode the bus during the morning shift.
Let x represent the number of children and y represent the number of adults riding the bus during the morning shift.
We know that the total number of passengers is 1,100, so we can write the equation:
x + y = 1,100
The child's fare is $0.50, and the adult fare is $1.25. The total revenue from the fares is $1,200, so we can write another equation:
0.50x + 1.25y = 1,200
To solve this system of equations, we can use substitution or elimination.
Let's use substitution to solve for x:
From the first equation, we have: x = 1,100 - y
Substituting this into the second equation:
0.50(1,100 - y) + 1.25y = 1,200
Simplifying the equation:
550 - 0.50y + 1.25y = 1,200
0.75y = 650
y = 650 / 0.75
y ≈ 866.67
Since we can't have a fraction of a person, we can approximate y to the nearest whole number:
y = 867
Substituting this value of y back into the first equation:
x + 867 = 1,100
x ≈ 233
Therefore, approximately 233 children and 867 adults rode the bus during the morning shift.
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question a circle has a radius of 21 inches. what is the length of the arc intercepted by a central angle that measures 4π7 radians? express the answer in terms of π . enter your answer in the box.
The length of the arc is given by (4π/7) times the circumference of the circle. Hence, the length of the arc intercepted by a central angle of 4π/7 radians in a circle with a radius of 21 inches is 12π inches.
The circumference of circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is 21 inches. Therefore, the circumference of the circle is C = 2π(21) = 42π inches.
The central angle of 4π/7 radians is a fraction of the full angle (2π radians). The ratio between the central angle and the full angle is (4π/7)/(2π) = 2/7.
To find the length of the intercepted arc, we multiply the ratio 2/7 by the circumference of the circle:
Length of arc = (2/7) * (42π) = 12π inches.
Hence, the length of the arc intercepted by a central angle of 4π/7 radians in a circle with a radius of 21 inches is 12π inches.
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explain why zero is excluded from the domain and range
Answer:
The range is also all real numbers except zero. You can see that there is some point on the curve for every y -value except y=0 . Domains can also be explicitly specified, if there are values for which the function could be defined, but which we don't want to consider for some reason.
Step-by-step explanation:
hope this helps
The graph of g(x) is a parabola that opens upward with a vertex at (-3, 4). Which statement is true?
PLEASE HELPPPPP
WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
From the given table,
A. The unit rate for each car is,
Car A = [tex]\frac{416}{13}[/tex]
= 32 miles per gallon
Car B = [tex]\frac{544}{16}[/tex]
= 34 miles per gallon
Car C = [tex]\frac{665}{19}[/tex]
= 35 miles per gallon
Car D = [tex]\frac{775}{25}[/tex]
= 31 miles per gallon
B. From the derived values in A, the car that uses the least amount of gas is Car C.
C. Total distance covered = 496 miles x 4
= 1984 miles
The gallons of gas the Car A would need for the journey can be determined by;
Car A requires 1 gallon for 32 miles
So that for 1984 miles = [tex]\frac{1984}{32}[/tex]
= 62 gallons
Car A would need 62 gallons of gas to make the trip.
D. Amount spent on gas for Car A = $2.12 x 62
= $131.44
E. speed = [tex]\frac{distance}{time}[/tex]
⇒ time = [tex]\frac{distance}{speed}[/tex]
Given the for Car A, speed = 68 miles per hour.
time = [tex]\frac{1984}{68}[/tex]
= 29.1765
time = 29 hours
It would take approximately 29 hours for Car A to cover the total distance of 1984 miles.
Luigi will roll two cubes with faces numbered 1 through 6. Eace face of each cube has one number on it. No number repeats on a cube Luigi records the product of the numbers that land face up. What is the probability that the product of the two numbers will be an odd number less than 20? ОА. ОВ. 8 ΟΟΟ m Ga A-N-ONS
Step-by-step explanation:
There are 36 possible rolls
to be an odd number product.....both dies must be odd numbers
1st 2nd
1 1 3 5
3 1 3 5
5 1 3 that is it for less than 20 product
8 rolls that would be less than 20 product
8 out of 36 probability
Mr. Cresta spends $6.00 for every $3.00 he saves. Write a ratio equivalent to Mr. Cresta's spending
Answer:
12:6 or $12 for every $6 he saves
Step-by-step explanation:
If he spends $6.00 for every $3.00, he would save $6 if he spends $12. In this case you could multiple or divide 6 by any number, and do the same to 3 to get an equivalent ratio. Ex. Multiple 6 times 2 to get $12 and 3 times 2 to get $6.
Answer:
300
Step-by-step explanation: