the required solution of the given differential equation is
y = - (In (x) + 7) / 25 + (3√11/25)sin√11/2(x) + (2√11/25)cos√11/2(x).
Given differential equation is x²y''(x) + 3xy'(x) + 5y(x) = In (x).Let us solve the given initial value problem. Differential equation is x²y''(x) + 3xy'(x) + 5y(x) = In (x).
The characteristic equation of this equation is given as
x²m² + 3xm + 5 = 0.
Using quadratic formula,
m₁= (−3x+i√11x²)/2x² and m₂= (−3x−i√11x²)/2x².
As m₁ and m2 are complex roots so the general solution is
y = [tex]c_1e^{(-3x)/2}cos \sqrt{(11x)} /2+ c_2e^{(-3x)/2}sin\sqrt{(11x)}/2[/tex]
Now, we find the first and second derivatives of y.
y = [tex]c_1e^{((-3x)/2)}cos \sqrt{(11x)}/2 + c_2e^{(-3x)/2}sin\sqrt{(11x)}/2[/tex]
y' = [tex](−3c_1/2)e^{(-3x)/2}cos\sqrt{(11x)}/2 + (−3c_2/2)e^{(-3x)/2}sin\sqrt{(11x)}/2 + \\c_1(e^{(-3x)/2)}(−\sqrt{(11x)}/2)sin \sqrt{(11x)}/2 + c_2(e^{(-3x)/2)}(\sqrt{(11x)}/2)cos\sqrt{(11x)}/2[/tex]
y'' = [tex](9c_1/4)e^{(-3x)/2)}cos\sqrt{(11x)}/2 + (9c_2/4)e^{(-3x)/2}sin\sqrt{(11x)}/2 - \\(3c_1/2)(e^{((-3x)/2))}(\sqrt{(11x)}/2)sin\sqrt{(11x)}/2 + (3c_2/2)(e^{(-3x)/2)}(\sqrt{(11x)}/2)cos\sqrt{(11x)}/2\\ - (c_1e^{((-3x)/2))}(11x/4)cos\sqrt{(11x)}/2 - (c_2e^{((-3x)/2))}(11x/4)sin\sqrt{(11x)}/2[/tex]
Putting the values of y, y' and y'' in the differential equation, we get the value of c₁ and c₂ as
y = - (In (x) + 7) / 25 + (3√11/25)sin√11/2(x) + (2√11/25)cos√11/2(x)
Now, we substitute the initial values in the above equation.
y(1) = - (In (1) + 7) / 25 + (3√11/25)sin√11/2(1) + (2√11/25)cos√11/2(1) = 1.
So, c₁ = (In (1) + 7) / 25 - (3√11/25)sin√11/2(1) - (2√11/25)cos√11/2(1).
y'(1) = (-3c₁/2)[tex]e^{((-3(1))/2)}[/tex]cos√11/2(1) + (-3c₂/2)[tex]e^{((-3(1))/2)}[/tex]sin√11/2(1) + c₁([tex]e^{((-3(1))/2)}[/tex](−√11/2)sin√11/2(1) + c₂([tex]e^{((-3(1))/2)}[/tex](√11/2)cos√11/2(1) = 1.
So, c₂ = (2√11/25) - (3c₁/2)[tex]e^{((-3)/2)}[/tex]cos√11/2(1) - (c₁[tex]e^{((-3)/2)}[/tex])(11/4)cos√11/2(1) - (1/2)[tex]e^{((-3)/2)}[/tex])sin√11/2(1).
Therefore, the required solution of the given differential equation is
y = - (In (x) + 7) / 25 + (3√11/25)sin√11/2(x) + (2√11/25)cos√11/2(x).
Learn more about differential equation here
brainly.com/question/25731911
#SPJ4
Compute the indicated quantity using the following data.
sin α = 15/17 where π/2< α < 3π/2
sin β= -4/5 where π < β < 3π/2
sin (α + β) =_________
Using trigonometric identity, sin(α + β) = -28/85.
To compute sin(α + β), we can use the trigonometric identity:
sin(α + β) = sin α cos β + cos α sin β
Given the values:
sin α = 15/17 (π/2 < α < 3π/2)
sin β = -4/5 (π < β < 3π/2)
To find sin α, we can use the Pythagorean identity:
cos α = ±√(1 - sin² α)
Since α is in the range π/2 < α < 3π/2, sin α is positive, so cos α will be negative.
sin α = 15/17
cos α = -√(1 - (15/17)²)
= -√(1 - 225/289)
= -√(64/289)
= -8/17
Now, we can substitute the values into the formula for sin(α + β):
sin(α + β) = (sin α cos β) + (cos α sin β)
= (15/17) * (-4/5) + (-8/17) * (-4/5)
= -60/85 + 32/85
= -28/85
Therefore, sin(α + β) = -28/85.
Learn more about range here:
https://brainly.com/question/31062578
#SPJ11
A manufacturer has cube shaped cardboard boxes with an exact volume of 12000 cubic inches. What is the volum of the largest sphere that can be packed inside the cube shaped box? Give you answer rounded to the nearest whole cubic inch
Answer:
6283 in³
Step-by-step explanation:
The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.
Since the cardboard box is in the shape of a cube, its volume V = L³
So, L = ∛V
Since V = 12000 in³,
L = ∛(12000 in³)
L= 22.89 in
So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2
So, V = 4π(L/2)³/3
= 4πL³/8 × 3
= πL³/2 × 3
= πL³/6
= πV/6
= π12000/6
= 2000π
= 6283.19 in³
≅ 6283.2 in³
= 6283 in³ to the nearest whole cubic inch
Is the cost of candy proportional to pounds of candy?
Answer:
Step-by-step explanation:
Yes
Answer:
yes because for every pound it is $3
Step-by-step explanation:
i know this because 1 times 3 is 3 and 3 times 3 is 9 and 7 times 3 is 21 and 10 times 3 is 30
How many students choose strawberry kiwi
Need help with the answer please
NO LINKS!!!
Answer:
15 students. 30%
Step-by-step explanation:
envision a totem pole, Estimate the height of the totem pole in the front. How did you go about deciding how to estimate its own height.
Answer:
(5.1×10^15)×(8.1×10^5
Which is greats 1,200 mm or 12 m
Answer:
12m
Step-by-step explanation:
1m = 1000mm
12m to mm
12 × 1000
= 12000mm
1200mm to m
1200 ÷ 1000
= 1.2m
Ava makes bead necklaces. She has a total of 6048 beads. Each necklace has 24 beads. Her friend maria says that the greatest number of necklace she can make with the beads is 162. Marias. Work is shown here
The question is incomplete:
Ava makes bead necklaces. She has a total of 6048 beads. Each necklace has 24 beads. Her friend maria says that the greatest number of necklace she can make with the beads is 162. Marias. Work is shown here. Explain why Maria is incorrect and how she can find the correct answer.
Answer:
Maria is incorrect because when you divide the number of beads by the beads in each necklace, you find that she can make 252 necklaces.
Step-by-step explanation:
You can find the number of necklaces Avan can make by dividing the number of beads she has by the amount in each necklace:
6048/24=252
According to this, you can say that Maria is incorrect because when you divide the number of beads by the beads in each necklace, you find that she can make 252 necklaces.
What is the measure of the other acute angle.....?
I really need to get this right plsss help me ❤️ I really need to get to an 90
the answer is 30°
EXPLAINATION:
since the angle is a right angle triangle one of it's angles is 90°, and all the angles of a triangle always add up to 180°
so, 90° + 60° + x = 180
150° + x = 180°
so x = 180° - 150° = 30°
hence, the other acute angle is 30°.
Please answer correctly! I will mark you as Brainliest!
Answer:
C
Step-by-step explanation:
trust me if you really need this done
Answer:
Angelo needs to use the formula V = [tex]\frac{4}{3} \pi (8.5)^3[/tex].
Step-by-step explanation:
The formula for finding the volume of a sphere is [tex]V=\frac{4}{3} \pi r^3[/tex], wherein the variable, r, is the radius. Diameter is one half of the radius; thus, it would be 17/2 = 8.5. Substitute the values into the equation (i.e. V = [tex]\frac{4}{3} \pi (8.5)^3[/tex]).
explain why a divergent infinite series such as [infinity]x n=1 1 n can have a finite sum in floating-point arith- metic. at what point will the partial sums cease to change?
The partial sums will cease to change when the terms of the series become smaller than the smallest representable number in the floating-point system.
In floating-point arithmetic, there is a finite range of representable numbers and a limited precision for calculations. When dealing with infinite series, the terms are added or subtracted sequentially, but due to the limitations of numerical precision, there is a point at which the terms become too small to affect the sum significantly.
For the series 1/n, as n increases, the terms approach zero but never actually reach zero. Eventually, the terms become smaller than the smallest representable number in the floating-point system, and at this point, they essentially contribute zero to the sum. As a result, the partial sums of the series will cease to change beyond this point.
It's important to note that although the sum of the series may appear to be finite in floating-point arithmetic, mathematically, the series diverges and does not have a finite sum. The convergence to a finite value in floating-point arithmetic is a result of the limitations of numerical representation and precision. A divergent infinite series, such as the sum of 1/n from n=1 to infinity, can have a finite sum in floating-point arithmetic due to the limitations of numerical precision.
Learn more about divergent infinite series here:
https://brainly.com/question/29081414
#SPJ11
What is the slope and y intercept of 4x + 2y = 6?
NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!! NO FILES!!!!
Answer:
4x−2y=6 is 21
Step-by-step explanation:
Answer:
Y intercept=3
4(0)+2y=6
y=3
slop=m=-2
y=-2x+3
y=mx+b
M=-2
Step-by-step explanation:
assume that the weight loss for the first month of a diet program varies between 6 and 12 pounds
The probability of the weight loss falling between 8 pounds and 11 pounds is 1/2
Variation of weight = Between 6 to 12.
It is required to ascertain the percentage of the overall range that corresponds to that interval in order to calculate the chance that the weight reduction will fall between 8 pounds and 11 pounds.
Calculating the total range of weight -
Range = Higher weight - Lower weight
= 12 - 6
= 6
Similarly, calculating the total range of weight for 8 pounds and 11 pounds
Range = Higher weight - Lower weight
= 11 - 8
Calculating the probability -
Probability = Range of interest / Total range
= 3 / 6
= 1/2.
Read more about probability on:
https://brainly.com/question/25839839
#SPJ4
Complete Question:
Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost between 8 pounds and 11 pounds
a. 1/2
b. 1/4
c. 2/3
d. 1/3
An ounce is equal to about 28 g. If 1 g of soil contains 2.5 billion bacteria, how many bacteria are in 1 oz of soil?
Answer:
About 700 billion bacteria
Step-by-step explanation:
Given
[tex]1oz \approx 28g[/tex]
[tex]1g = 25\ billion\ bacteria[/tex]
Required
Number of bacteria in 1 oz
[tex]1g = 25\ billion\ bacteria[/tex]
Multiply both sides by 28
[tex]28 * 1g = 25\ billion\ bacteria * 28[/tex]
[tex]28g = 700\ billion\ bacteria[/tex]
Recall that
[tex]1oz \approx 28g[/tex]
This means:
[tex]1oz \approx 700\ billion\ bacteria[/tex]
AD is tangent to circle B at point C. What is the measure of BCA? O 40° O 50° O 90° O 180°
Answer:
C
90
Step-by-step explanation:
B is likely the center, I think. You can't do it otherwise.
The tangent and a radius of a circle meet at 90o
therefore the answer is 90.
All of this could be confirmed with a diagram.
could someone help me with this
These numbers tell how many books five different students read in the past six months. 8, 11, 15, 22, and 6 a) Create a different set of five pieces of data with a greater mean, but with at least two values less than the values in the set of data above. b) Create a different set of five pieces of data with a lower mean, but with at least two values greater than the values in the set of data above. How did you make it work? c) Create a different set of five pieces of data with a lower mean, but with a higher median than the original set.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Origibal data set
8, 11, 15, 22, 6
Rearranging The value :
x : 6, 8, 11, 15,22
Mean = Σx / n
n = sample size =5
Mean = (6+8+11+15+22) = 62
Mean = 62 / 5 = 12.4
Median = 1/2(n+1)th term
Median = 1/2(6)th term = 6/2 = 3rd term = 11
A.)
X = 4, 5, 15, 23, 19
MEAN = (4 +5 + 15 + 23 + 19) / 5 = 13.2
B.)
X = 2, 6, 5, 23, 34
Mean = (2+6+5+23+24) / 5
Mean = 60 / 2 = 12
C.)
X = 3, 7, 12, 21, 13
X = 3, 7, 12, 13, 21
Mean = (3+7+12+13+21) /5 = 11.2
Median = 1/2(6)th term = 6/2 = 3rd term = 12
44444444444444 help me ples
Answer:
a
Step-by-step explanation:
What is the answer. Please dont send me ‘links’. I seriously need help.
Answer:
Total Volume of composite figure = 635.2 cm³
Steps:
1.CV = h×3.14×(d/2)²
CV = 5×3.14(8/2)²
CV = 5×3.14(4)²
CV = 5×3.14×16
CV = 5×50.24
CV = 251.2 cm³
2.RV = h×w×l
RV = 4×8×12
RV = 4×96
RV = 384 cm³
3.TV = CV + RV
TV = 251.2 + 384
TV = 635.2 cm³
Use the points (0,60) and (4,90) from the line on the scatter plot What is the equation of the linear modal?
100
90
80
Test Score
70
60
0
0 1 2 3 4 5
Time Studying (hours)
Please help I'm begging a ACE OR GENES To help me please please help please please ASAP please please help please please ASAP please please help
Answer:
2/3
Step-by-step explanation:
the ratio of base1 ABCD to base 1 of WXYZ is
8 to 12
8/12 = 2/3
m - 12 = 11
A. -23
B. -1
C. 1
D. 23
Answer:
D. 23
Step-by-step explanation:
m-12-(11)=0
m-23 = 0
m = 23
Gavin divided his notebook into 8 equal parts. He plans to use 3 parts to take notes for math and 2 parts for reading. He has school from 8:30 A.M to 3:30 P.M. what fraction of his notebook does he have left?
Pls help I well mark you a brainliest...
Answer:
Gavin has 3 parts left.
Step-by-step explanation:
8-3-2=3. The time was not important.
Evaluate the expression 6 + 5 × 32 - 8.
43
11
6
91
(and its not 32 its just the 2 is suppose to be up)
(dont steal my points)
Answer:
43
Step-by-step explanation:
A is the answer
Answer:
Ima steal your points
Step-by-step explanation:
Each unit on the grid represents 2 kilometers. Find thedistance between Gabe's house and the library?
Answer:
8km
Step-by-step explanation:
there are 4 unit between Gabe's house and the library so distance is 4×2=8km
14. The diagonals of square ABCD intersect at E. If AE = 2, find the perimeter of ABCD.
Answer:
B, [tex]8\sqrt{2}[/tex]
Step-by-step explanation:
Diagonals of a square are congruent so AC= 4
using pythagorean theorem we can then do [tex]x^{2} +x^{2}[/tex]=[tex]4^{2}[/tex]
[tex]2x^{2} = 16\\x^{2} =8\\x=\sqrt{8} \\x=2\sqrt{2}[/tex]
Then for perimeter we times the [tex]2\sqrt{2}[/tex] by 4 and get
[tex]8\sqrt{2}[/tex]
Hope this helps and please mark brainliest!!
What is the slope of the line through (-7,-2) and (−6,7)?
Answer:
slope = 9
Step-by-step explanation:
To find the slope of a line that passes through a pair of points, use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of (-7,-2) and (-6,7) into the formula and simplify:
[tex]m = \frac{(7)-(-2)}{(-6)-(-7)} \\m = \frac{7+2}{-6+7} \\m = \frac{9}{1} \\m = 9[/tex]
So, the slope is 9.
4/5 divided by 2/7 in simplest form
Answer:
2 4/5
Step-by-step explanation:
4/5 divided by 2/7 is 2.8. 2.8 in the form of a fraction is 2 4/5.
The fraction 4/5 divided by 2/7 in the simplest form, is 14/5.
Given that, (4/5) divided by (2/7).
To divide fractions, multiply the first fraction by the reciprocal of the second fraction
Let a, b, c and d be real numbers. Divide a fraction (a/b) by another fraction (c/d), we can multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of a fraction is obtained by swapping the numerator and denominator. So, the reciprocal of (c/d) is (d/c).
To divide (a/b) by (c/d), multiply the first fraction by the reciprocal of the second fraction:
(a/b) ÷ (c/d) = (a/b) x (d/c)
Multiplying the numerators and denominators:
(ad) / (bc)
Therefore, the result of (a/b) divided by (c/d) is (ad) / (bc).
To simplify this expression, and multiply the first fraction by the reciprocal of the second fraction:
(4/5) x (7/2)
Multiplying the numerators and denominators:
(4 x 7) / (5 x 2)
Simplifying the numerator and denominator:
28 / 10
To further simplify the fraction, and divide both the numerator and denominator by their greatest common divisor, which is 2:
28 ÷ 2 / 10 ÷ 2
This gives us:
14 / 5
Therefore, the fraction 4/5 divided by 2/7, in the simplest form, is 14/5.
Learn more about dividing fractions and simplifying fractions, click here:
https://brainly.com/question/10354322
#SPJ6
I need help im struggling
Answer:
62.80
Step-by-step explanation:
I hope this helped you out!!
Answer:
62.8
Step-by-step explanation:
Circumference is 2pi*radius. 2*pi*10 = 20 * 3.14 = 62.8
A woman bought bars
of truck soap for #200. If
a bar is #2.50 more expensive.
She could have bought 2 less.
how many bars did she buy?
Answer:
80
Step-by-step explanation:
200/2.50=80
Obtain the five-number summary for the given data The test scores of 15 students are listed below. 40 46 50 55 58 61 64 69 74 79 85 86 90 94 95 40,51.50, 71.5, 85.5,95 40, 55, 69, 86,95 40, 51.50, 69,
The five-number summary for the given data is as follows: Minimum = 40, First Quartile = 51.5, Median = 69, Third Quartile = 86, Maximum = 95.
To obtain the five-number summary, we consider the minimum, first quartile, median, third quartile, and maximum values of the dataset.
Minimum: The smallest value in the dataset is 40.
First Quartile: The first quartile (Q1) is the median of the lower half of the dataset. To find Q1, we arrange the data in ascending order: 40, 46, 50, 55, 58, 61, 64, 69, 74, 79, 85, 86, 90, 94, 95. Since there are 15 data points, the median is the 8th value (69), which becomes the first quartile.
Median: The median is the middle value of the dataset. In this case, since we have an odd number of data points, the median is the 8th value (69).
Third Quartile: The third quartile (Q3) is the median of the upper half of the dataset. Again, using the ordered data, we find Q3 as the median of the values above the median (69). This gives us the third quartile of 86.
Maximum: The largest value in the dataset is 95.
Thus, the five-number summary for the given data is Minimum = 40, Q1 = 51.5, Median = 69, Q3 = 86, and Maximum = 95.
Learn more about First Quartile here:
https://brainly.com/question/15075336
#SPJ11