consider the following differential equation. x2y″ xy ′ 16y = 0 find all the roots of the auxiliary equation. (enter your answers as a comma-separated list.)
Solve the given differential equation. y(x) = ,X>0
Answers
The roots of the auxiliary equation are r = (-1 ± √(1 + 16/x^2)) / x.
The general solution of the differential equation is y(x) = c_1 x^4/16 + c_2 x^(-1/2) cos(ln x) + c_3 x^4/16 + c_4 x^(-1/2) sin(ln x), where c_1, c_2, c_3, and c_4 are arbitrary constants
The auxiliary equation for the given differential equation is obtained by assuming a solution of the form y(x) = e^(rx), where r is a constant. Substituting this solution into the differential equation, we get:
x^2(e^(rx))'' + x(e^(rx))' - 16(e^(rx)) = 0
Differentiating twice, we get:
r^2x^2 e^(rx) + 2rx e^(rx) + x e^(rx) + x e^(rx) - 16 e^(rx) = 0
Simplifying and factoring out e^(rx), we get:
e^(rx) (r^2x^2 + 2rx - 16) = 0
For nontrivial solutions, we must have e^(rx) ≠ 0, which implies that the quadratic expression in the parentheses must be zero. Thus, we need to solve the equation:
r^2x^2 + 2rx - 16 = 0
Using the quadratic formula, we get:
r = [-2x ± √(4x^2 + 64x^2)] / (2x^2) = [-x ± √(x^2 + 16)] / x
The roots of the auxiliary equation are therefore:
r = (-1 ± √(1 + 16/x^2)) / x
To solve the differential equation, we need to find two linearly independent solutions. Since the roots of the auxiliary equation are complex when x > 0, we can write the solutions in terms of exponentials of complex numbers as follows:
y_1(x) = x^4/16 + x^(-1/2) cos(ln x)
y_2(x) = x^4/16 + x^(-1/2) sin(ln x)
Thus, the general solution of the differential equation is:
y(x) = c_1 x^4/16 + c_2 x^(-1/2) cos(ln x) + c_3 x^4/16 + c_4 x^(-1/2) sin(ln x)
where c_1, c_2, c_3, and c_4 are arbitrary constants determined by the initial conditions of the problem.
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Related Questions
Find the value of each expression.
A) 3√9-16
B) -7√0.36+5.4
Answers
\(3 \sqrt{9} - 16 = ... \\ = 3(3) - 16 = 9 - 16 \\ = \bold{ - 5}\)
\( \: \)
B.)\( - 7 \sqrt{0.36} + 5.4 = ... \\ = - 7(0.6) + 5.4 = - 4.2 + 5.4 \\ = 5.4 - 4.2 = \bold{1.2}\)
in 2010, husson had 2000 undergraduate students. in 2018, husson had 2800 undergraduate students. find the percent increase in enrollment, and round to the nearest percent.
Answers
the percent increase in enrollment, and round to the nearest percent is 40%
Given that number of students enrolled in 2010= 2000
Given that number of students enrolled in 2018 = 2800
2800is more than 2000 so that means number of students enrollment is increasing.
increase = 2800-2000= 800
Percent increase is given by formula:
% increase = 800/2000*100= 40
which is approx 40%.
Hence final answer is that enrollment increases by 40%
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A line through which two points would be parallel to a line with a slope of 3/4?
a
(0,-2) and (-4,-2)
b
(0,5) and (-4,2)
c
(0,2) and (-4,1)
d
(0,0) and (0,-2)
Answers
Answer:
F. (0, 5) and (-4, 2)
Step-by-step explanation:
We need to calculate the slope of each of the given sets of points until we find the set associated with a slope of 3/4:
F. (0,5) and (-4,2) As we go from (-4, 2) to (0,5), x increases by 4 and y increases by 3, so the slope is m = rise / run = 3/4. This is the line with slope 3/4.
How much money do you beed to invest at 8% annual interest to have $1000 dollars of interest at the end of the year?
Answers
Answer: $925.93
Step-by-step explanation:
See image:
A:Write (⅔)² in expanded form,
B. And then evaluate.
Answers
Answer:
4/9
Step-by-step explanation:
(2/3)^2
(2/3) x (2/3)
2 x 2 is 4
3 x 3 is 9
4/9
Blake must choose between two job offer. Evergreen Landscape will pay him $9.75 hours to mow lawns, but its is a long way from his house. He would probably spend $25 per week on gas. Just Jean will pay Blake $6.50 per hour to work as a retail clerk. Since the store is very close to his house, he would probably only spend $5 per week on gas. let x be the number of hours that Blake will work in a week and y be the amount of money he will have end of the week if he does not spend any money expect on gas.
a. Explain how the following two rules reflect the two jobs offer that Blake has.
B. Solve the system of equations in part A. (9.75x - 25 = 6.50x -5) indicates what its tell you about blake job offers and the amount of money he will have at the end of the week.
C. blake plan to work at least 15 hours per week. Which job should he take.
Answers
Answer:
A. The explanation of the rules are;
For the job offer for the Evergreen Landscape, Blake will have 9.75 times by the number of hours worked less the $25 for gas at the end of the week
For the job offer for the Just Jean, Blake will have 6.50 multiplied by the number of hours worked less the $5 for gas at the end of the week
B. The solution to the equations is that the number of hours Blake will work to have the same amount in both Jobs is 6.1538 hours
C. Blake should take the Job at Evergreen Landscape
Step-by-step explanation:
The amount Evergreen Landscape will pay Blake to mow lawn = $9.75
The amount Blake would spend to work per week on gas for work at Evergreen Landscape = $25
The amount Just Jean will pay Blake to work per week as a retail clerk = $6.50
The amount Blake would spend to work per week on gas for work at Just Jean = $5
Whereby, x = The number of hours that Blake will work in a week
y = The amount of money he will have end of the week, if he does not spend any money except gas
A. The given rules are;
y = 9.75·x - 25
y = 6.50·x - 5
For the job offer for the Evergreen Landscape, we have;
y = 9.75·x - 25
Blake has to put aside $25 out of his weekly earnings for gas
Blake will have 9.75 multiplied by the number of hours worked less the $25 for gas
For the job offer for the Just Jean, we have;
y = 6.50·x - 5
Blake will have 6.50 multiplied by the number of hours worked less the $5 for gas
B. The common solution of the both equations is given by equating both values of y as follows;
9.75·x - 25 = 6.50·x - 5
9.75·x - 6.50·x = 25 - 5
3.25·x = 20
x = 20/3.25 = 6.15385
x = 6.15385
The number of hours Blake will work to have the same amount in both Jobs = 6.1538 hours
C. Given that the number of hours Blake can work each week = 15 hours, we have;
For the job offer for the Evergreen Landscape, we have;
y = 9.75 × 15 - 25 = 121.25
The amount of money he will have end of the week = y = $121.5
y = 6.50 × 15 - 5 = 92.5
The amount of money he will have end of the week = y = $92.5
Therefore, given that by working 15 hours a week, Blake earns $121.5 on the Evergreen Landscape job and $92.5 on the Just Jean job, Blake should take the Job at Evergreen Landscape.
What's the equation of the line that passes through the points (–3,–3) and (3,1)? ;)
Answers
Answer:
y= 2/3x - 1
Step-by-step explanation:
to find y intercept substitute x=0
y= 2/3x0-1
y= -1
y =mx + b
y=2/3x + -1
The customer must first pay an annual 300 a ductile in the policy covers 70% of cost of x-rays the first Insurance claim for Pacific year submitted by a person or two X-Rays the first x-ray cost 6:40 and the secondary x-ray cost 950 how much in total will he need to pay for these x-rays
Answers
Answer:
$177
Step-by-step explanation:
Given that:
Percentage covered by policy = 70%
Hence, person needs to pay (100 - 70)% = 30%
X - Ray cost :
1st = 640
2nd = 950
Total cost = (640 + 950) = 1590
Amount the person has to pay:
Total cost * 30%
1590 * 0.3 = $477
Since the person has $300 deductible :
$477 - $300 = $177
e table shows the height of a candle as it is continuously burned. a 2-column table with 5 rows. the first column is labeled time (hours) with entries 0, 0.25, 0.5, 0.75, 1. the second column is labeled height (centimeters) with entries 25, 24.375, 23.75, 23.125, 22.5. which statement describes the candle? the candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour. the candle starts at a height of 25 centimeters and burns at a rate of 2.5 centimeters per hour. the candle starts at a height of 22.5 centimeters and burns at a rate of 0.625 centimeters per hour. the candle starts at a height of 22.5 centimeters and burns at a rate of 2.5 centimeters per hour.
Answers
The candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.
What is the initial height and burning rate of the candle?The given table shows the height of a candle as it burns continuously over time. The first column represents time in hours, ranging from 0 to 1, while the second column represents the corresponding height in centimeters.
From the data, we can observe that the candle starts at a height of 25 centimeters when the time is 0 hours. As time progresses, the height of the candle decreases gradually. Specifically, for every hour that passes, the candle burns 0.625 centimeters.
Therefore, the main answer is that the candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.
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Demand history for the past three years is shown below, along with the seasonal indices for each quarter.
Year Quarter Demand Seasonal Index
Year 1 Q1 319 0.762
Q2 344 0.836
Q3 523 1.309
Q4 435 1.103
Year 2 Q1 327 0.762
Q2 341 0.836
Q3 537 1.309
Q4 506 1.103
Year 3 Q1 307 0.762
Q2 349 0.836
Q3 577 1.309
Q4 438 1.103
Use exponential smoothing with alpha (α) = 0.35 and an initial forecast of 417 along with seasonality to calculate the Year 4, Q1 forecast.
Answers
The Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.
Exponential smoothing is a forecasting technique that takes into account both the historical demand and the trend of the data. It is calculated using the formula:
Forecast = α * (Demand / Seasonal Index) + (1 - α) * Previous Forecast
Initial forecast (Previous Forecast) = 417
α (Smoothing parameter) = 0.35
Demand for Year 4, Q1 = 307
Seasonal Index for Q1 = 0.762
Using the formula, we can calculate the Year 4, Q1 forecast:
Forecast = 0.35 * (307 / 0.762) + (1 - 0.35) * 417
= 335.88
Therefore, the Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.
The forecasted demand for Year 4, Q1 using exponential smoothing is 335.88.
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In the function f(x) = (x^2 -6x + ___) + 20, what number belongs in the blank to complete the square?
Answers
Answer:
blank = -11
Step-by-step explanation:
The given function is :
\(f(x) = (x^2 -6x+x)+20\)
We need to find the number x such that it forms the complete square.
If x = -11, then it will becomes,
\(f(x) = (x^2 -6x+(-11))+20\\\\f(x)=x^2-6x+9\)
We can write it as follows :
\(f(x)=x^2-2(1)(3x)+(3)^2\) ..(1)
We know that,
\((a-b)^2=a^2-2ab+b^2\) ...(2)
Comparing (1) and (2).
\(f(x)=(x-3)^2\)
So, if we put the blank equals -11, then it will become the perfect square.
(0,4) and (-2,-2) what is the linear equation
Answers
Answer:
\(gradient = \frac{change \: in \: y}{change \: in \: x} \\ = \frac{y2 - y1}{x2 - x1} \\ = \frac{4 - - 2}{0 - - 2} \\ = \frac{6}{2} \\ = \frac{3}{1} \\ let \: (xy) \: also \: lie \: on \: the \: line \\ gradient \: = \frac{y2 - y1}{x2 -x1} \\ \frac{3}{1} = \frac{x - - 2}{y - - 2} \\ \frac{3}{1} = \frac{x + 2}{y + 2} \\ 3(y + 2) = 1(x + 2) \\ 3y + 6 = x + 2 \\ 3y + 6 - 2 = x \\ 3y + 4 = x\)
Hope that this is helpful.
Have a great day.
20 applicants from a pool of 90 applications will be hired. How many ways are there to select the applicants who will be hired?
Answers
The ways are the \(C_{20} ^{90}\) which are we there to select the applicants who will be hired with the help of combination.
According to the statement
we have to find that the number of ways are there to select the applicants who will be hired.
So, For this purpose, we know that the
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Here we use the combination.
And from the given information:
20 applicants from a pool of 90 applications will be hired.
And according to this the combination becomes:
\(C_{20} ^{90}\)
then solve it
\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)
\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)
Then after solve it
\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)
Now open another factorial
\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)
Now solve this then
\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).
So, The ways are the \(C_{20} ^{90}\) which are we there to select the applicants who will be hired with the help of combination.
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One square corral at a stable has an area of 625 ft2. If one side of the corral is along a barn, how much of the barn’s wall is used for the edge of the corral? A 25 ft B 50 ft C 100 ft D 200 ft
Answers
Answer:
Option A 25 ft is the correct answer.
Step-by-step explanation:
Given that:
One square corral at a stable has an area 625 \(ft^2\).
And one side corral is along a barn.
To find:
How much of a barn's wall is used for the edge of corral?
Solution:
First of all, kindly refer to the attached figure to have a better understanding of the given dimensions and situation.
Given that Corral is square shape with Area, A = 625 \(ft^2\)
Formula for area of a square is given as:
\(A = Edge^2\)
Putting the value of A as given to find the Edge:
\(625 = Edge^2\\\Rightarrow Edge^2 =25 \times 25\\\Rightarrow Edge = 25\ ft\)
It is given that one side of Corral is along a barn.
So, barn's wall used for the edge of corral = 25 ft
Option A 25 ft is the correct answer.
Answer: A 25ft I did it on edge and got it correct and please do as brainlest and have a good day.
Find the area, Show steps please
Answers
length of triangle 10.5-7= 3.5
area of triangle (3.5*4)/2= 7
area = 28+7 = 35cm
Answer is 35cm
Select the correct answer from the choices given (13 4i) n = 0 what is n? 0 1 –13 4i –13 - 4i
Answers
The correct answer from the choices given will be -13 - 4i. The numerical part is the real number while the term containing i is the imaginary part.
What is the complex number?
A complex number is one that both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.
The given complex number as;
\(\rm 13 + 4 i + n =0\)
By transfeering the left-hand side term to the right-hand side the sign will change. We will get the value of n as;
\(\rm n=-13 - 4i\)
Hence the correct answer from the choices given will be -13 - 4i.
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Answer: Its D and for the second part its B
Step-by-step explanation:
Suppose the vector p contains the price of 5 items and q contains the quantity bought of the items. Write the following functions in vector format (you can use only vector operations):
a. The average price of the items. [for example: if p=[10,20,30, 40, 50] then the average_price = 30]
b. Sum of the total cost of the items bought. [for example: for the above price vector p, if q=[1,0,0,0,5] then the total_cost = 260]
c. Difference between the quantity bought of the 1st and the 3rd item. [for example: if q=[1,0,0,0,5] then the difference = 1]
d. Suppose r is another 4-vector containing the price of 4 more items and s contains the quantity bought of those items. Use vector stacking/concatenation to construct a new price and quantity vectors for the 9 items and compute the total cost.
e. In vector computations, we also sometimes use element-wise multiplication (np.multiply(u,v) or uv, for shorthand where u and v are same sized vectors). Use this operation to compute the total cost of the 9 items except items 2 and 4.
Answers
Total cost without items 2 and 4 = Sum(new price vector * adjusted quantity vector)
To get the average price of the items, sum the elements in vector p and divide by the number of elements (5 in this case).
Average price = (p1 + p2 + p3 + p4 + p5) / 5
To get the sum of the total cost of the items bought, perform element-wise multiplication of vector p and vector q, then sum the resulting elements.
Total cost = (p1 * q1) + (p2 * q2) + (p3 * q3) + (p4 * q4) + (p5 * q5)
To get the difference between the quantity bought of the 1st and 3rd items, subtract the 3rd element of vector q from the 1st element.
Difference = q1 - q3
To construct new price and quantity vectors for the 9 items, concatenate vectors p and r for prices, and vectors q and s for quantities. Then, compute the total cost by performing element-wise multiplication of the new price and quantity vectors, and sum the resulting elements.
New price vector = p ⊕ r
New quantity vector = q ⊕ s
Total cost = Sum(new price vector * new quantity vector)
To compute the total cost of the 9 items except items 2 and 4, use element-wise multiplication for the new price and quantity vectors. Set the elements corresponding to items 2 and 4 in the new quantity vector to 0, then sum the resulting elements.
Adjusted quantity vector = new quantity vector with 2nd and 4th elements set to 0
Total cost without items 2 and 4 = Sum(new price vector * adjusted quantity vector)
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Help someone please I need this one correct to get a good grade
Answers
1) The square root of 8 is the least, since 3^2 equals 9, and 8 is less than 9, so its the least.
2) Then the cube root of 27, because 3 cubed is equal to 27
3) Finally, pi is the largest since it equals 3.142.
Good luck with your grades.
root 8 < pi < cube root 27
If two pieces of fruit are randomly picked out of a covered basket with 5 apples and 3 oranges, what is the probability that the two pieces of fruit are oranges?
Answers
Answer:
i would say 3/8 if thats an option
Step-by-step explanation:
Probability helps us to know the chances of an event occurring. The probability that the two pieces of fruit are oranges is 3/28.
What is Probability?Probability helps us to know the chances of an event occurring.
\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)
Given that the two pieces of fruit are randomly picked out of a covered basket with 5 apples and 3 oranges. Therefore, the probability that the two pieces of fruit are oranges is,
Probability = (3/8) × (2/7) = 6/56 = 3/28
Hence, the probability that the two pieces of fruit are oranges is 3/28.
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A software company wants to get an idea of their customers' level of satisfaction with their software. To do so, they included a phone number on the packaging of their most recent software release, with the message, "If you have any concerns with the product, please call this number." Based on the overwhelmingly negative response they received from these calls, the company decided to stop selling the product.
What could be wrong with their decision?
A.
The phone system screened out certain positive comments because of a malfunction.
B.
The release of the software coincided with the spread of a virus which affected the performance of the program.
C.
The note on the package only told customers to call in the event that they had a concern, which could bias the results negatively.
D.
The customers were misinformed about the purpose of the program.
Answers
Answer:
C. The note on the package only told customers to call in the event that they had a concern, which could bias the results negatively.
Explanation:
Since customers were only told to call if they had concerns, all of the calls were about concerns or problems that they were having - meaning all of the calls were negative. However, they were never informed to call if they were happy or content with the product, meaning they were never informed of the people who had positive comments, only negative.
14/6 + 1/5 marking brainliest (show me how you got it)
Answers
Answer:
\( \frac{14}{6} + \frac{1}{5} = \frac{70 + 6}{30} = \frac{38}{15} \)
Answer:38/15
Step-by-step explanation:
First we have to make the denominator of both the decimals,lets see:6 and 5 are the denominator.They can both be turned into 30! The 14/6 ’s 6 is time 5 to get to 30 so 14/6 x =70/30 and the other is 1/5 =6/30.
So: 70/30 + 6/30=76/30!
Simplified: 38/15
Hope this helped!
Hope you have a great day!
Good luck !
lfu29
Clues:
1. It is a three-digit whole number.
2. It is divisible by 2.
3. It is divisible by 4.
4. It is divisible by 5.
5. It is divisible by 3.
6. It is divisible by 6.
7. It is divisible by 9.
8. It is less than 300.
9. It is greater than 150.
10. It is a multiple of 90
Answers
Answer:
180
Step-by-step explanation:
hehe
2 90
3 60
4 45
5 36
6 30
9 20
90 = 2
<3
What is the nth term for 2 3 5 13
Answers
this is a number is can not devide
How many years had temperatures that were exactly one standard deviation from the mean?
Answers
To reply to this address, we require more data approximately the temperatures, such as the cruel and standard deviation, as well as the long time for which the temperatures are accessible.
Accepting we have this data, we will utilize the observational run of the show to gauge the rate of information that falls inside one standard deviation of the cruel. Agreeing with the show, around 68% of the information falls inside one standard deviation of the cruel.
If we know the number of long times for which the temperatures are accessible, able to appraise the number of years for which the temperatures were inside one standard deviation of the cruel. For illustration, on the off chance that we have information for 50 a long time.
We will appraise that around 68% of the information, or 34 a long time, falls inside one standard deviation of the mean.
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Help what is 35/17 as a decimal rounded to the nearest hundredth *you have to divide
Answers
Answer:
2.0588235294118
Step-by-step explanation:
I would just put 2.05
If Leah needs to make a batch of orange sherbet cupcakes with 32 cups of flour, how much sugar should she use?
Answers
Answer:
12 cups of sugar
Step-by-step explanation:
The recipe uses 3 cups of sugar for every 8 cups of flour.
The diagram that models the ratio is the upper one with 3 pink squares of sugar and 8 green squares of flour.
If she uses 32 cups of flour, she is making 4 times the recipe since 32 = 4 × 8.
Then she also needs 4 times the amount of sugar.
4 × 3 = 12
Answer: 12 cups of sugar
o estimate efficiency of a drug for weight loss, the clinical trial was performed. The results are presented in the table below. Weight before trial, Patient number kg Weight after trial, kg 1 83.5 2 78.1 85.2 79.6 75.8 76.2 3 4 5 73.2 74 90.2 87 91 6 89.8 7 79.9 82 81.7 8 78.5 9 64 10 67.3 68.4 70 11 65.1 67.8 70 12 64.6 13 14 74 66.8 60 94 88.2 58.6 92.9 15 16 88 Investigate the claim that the drug affects the weight. Using a=0.01 Which is the value Lower limit of the proper 2 sided confidence interval, for this analysis? Use 3 decimal digits
Answers
The lower limit of the proper 2-sided confidence interval for this analysis, investigating the claim that the drug affects weight loss, is [71.594, 78.856].
What is the lower limit of the 2-sided confidence interval for investigating the claim about the drug's effect on weight loss?In statistical analysis, confidence interval provides a range of plausible values for a population parameter, such as the effect of a drug on weight loss.
The confidence interval is calculated based on the sample data and is accompanied by a confidence level, which represents the percentage of times the interval would contain the true population parameter if the study were repeated multiple times.
In this case, the objective is to investigate the claim that the drug affects weight. The clinical trial results, including the weights of the patients before and after the trial, are provided. The next step is to calculate a confidence interval to estimate the true effect of the drug on weight loss.
Using a significance level (α) of 0.01, which corresponds to a 99% confidence level, the lower limit of the 2-sided confidence interval is found to be 71.594. This means that with 99% confidence, we can expect the true effect of the drug on weight loss to be at least 71.594 units.
The confidence interval provides valuable information for interpreting the results. Since the lower limit is above zero, it suggests that the drug has a positive effect on weight loss.
However, it is important to note that the upper limit of the confidence interval is not provided in the question, and it would give us the upper bound of the expected effect. Comparing the interval to specific thresholds or hypothesized values can further assess the claim and make more informed conclusions.
It's important to understand that a confidence interval provides an estimate of the population parameter, in this case, the drug's effect on weight loss, and it takes into account both the sample data and the chosen level of confidence.
It gives a range of plausible values rather than a single point estimate, allowing for uncertainty and variability in the data.
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find the radius of convergence of the taylor series around x = 0 for ex.
Answers
The radius of convergence of the Taylor series for the exponential function, e^x, centered at x = 0, is infinite.
The Taylor series expansion for the exponential function, \(e^x\), around x = 0 is given by the formula:
\(e^x = 1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + ...\)
This series converges for all values of x because the terms in the series decrease in magnitude as the exponent increases. This means that as x approaches infinity or negative infinity, the terms in the series approach zero.
The convergence of a power series is determined by the ratio test or the root test. In the case of the exponential function, both tests yield a radius of convergence of infinity. This indicates that the series converges for all values of x. Therefore, the Taylor series expansion of e^x around x = 0 is valid for all real numbers x.
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The point (rote 3, -1)is on the terminal side of the an angle theta. Find sin theta
Answers
We have that the angle is 330°
Now
\(\sin (330)=-\frac{1}{2}=-0.5\)
find cos ∅
A. 8/17
B. 8/15
C. 15/8
D. 15/17
Answers
Answer:
I think its c hope this helps I may be wrong