Answers
Answer:
the answer is A. g(x) = -x^2 - 4
Step-by-step explanation:
hope this helps! :)
Related Questions
!!!Please help!!!
What is the following quotient?
96
B
O 2.13
4.
2.V22
12
Answers
[infinity]
Substitute y(x)= Σ 2 anx^n and the Maclaurin series for 6 sin3x into y' - 2xy = 6 sin 3x and equate the coefficients of like powers of x on both sides of the equation to n= 0. Find the first four nonzero terms in a power series expansion about x = 0 of a general
n=0
solution to the differential equation.
У(Ñ)= ___________
Answers
Recall that
[tex]\sin(x)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex]
Differentiating the power series series for y(x) gives the series for y'(x) :
[tex]y(x)=\displaystyle\sum_{n=0}^\infty a_nx^n \implies y'(x)=\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]
Now, replace everything in the DE with the corresponding power series:
[tex]y'-2xy = 6\sin(3x) \implies[/tex]
[tex]\displaystyle\sum_{n=0}^\infty (n+1)a_{n+1}x^n - 2\sum_{n=0}^\infty a_nx^{n+1} = 6\sum_{n=0}^\infty(-1)^n\frac{(3x)^{2n+1}}{(2n+1)!}[/tex]
The series on the right side has no even-degree terms, so if we split up the even- and odd-indexed terms on the left side, the even-indexed [tex](n=2k)[/tex] series should vanish and only the odd-indexed [tex](n=2k+1)[/tex] terms would remain.
Split up both series on the left into even- and odd-indexed series:
[tex]y'(x) = \displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} + \sum_{k=0}^\infty (2k+2)a_{2k+2}x^{2k+1}[/tex]
[tex]-2xy(x) = \displaystyle -2\left(\sum_{k=0}^\infty a_{2k}x^{2k+1} + \sum_{k=0}^\infty a_{2k+1}x^{2k+2}\right)[/tex]
Next, we want to condense the even and odd series:
• Even:
[tex]\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2k+2}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2(k-1)+1}x^{2k}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2k-1}x^{2k}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty \bigg((2k+1)a_{2k+1} - 2a_{2k-1}\bigg)x^{2k}[/tex]
• Odd:
[tex]\displaystyle \sum_{k=0}^\infty 2(k+1)a_{2(k+1)}x^{2k+1} - 2\sum_{k=0}^\infty a_{2k}x^{2k+1}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2(k+1)}-2a_{2k}\bigg)x^{2k+1}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1}[/tex]
Notice that the right side of the DE is odd, so there is no 0-degree term, i.e. no constant term, so it follows that [tex]a_1=0[/tex].
The even series vanishes, so that
[tex](2k+1)a_{2k+1} - 2a_{2k-1} = 0[/tex]
for all integers k ≥ 1. But since [tex]a_1=0[/tex], we find
[tex]k=1 \implies 3a_3 - 2a_1 = 0 \implies a_3 = 0[/tex]
[tex]k=2 \implies 5a_5 - 2a_3 = 0 \implies a_5 = 0[/tex]
and so on, which means the odd-indexed coefficients all vanish, [tex]a_{2k+1}=0[/tex].
This leaves us with the odd series,
[tex]\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1} = 6\sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!}[/tex]
[tex]\implies 2(k+1)a_{2k+2} - 2a_{2k} = \dfrac{6(-1)^k}{(2k+1)!}[/tex]
We have
[tex]k=0 \implies 2a_2 - 2a_0 = 6[/tex]
[tex]k=1 \implies 4a_4-2a_2 = -1[/tex]
[tex]k=2 \implies 6a_6-2a_4 = \dfrac1{20}[/tex]
[tex]k=3 \implies 8a_8-2a_6 = -\dfrac1{840}[/tex]
So long as you're given an initial condition [tex]y(0)\neq0[/tex] (which corresponds to [tex]a_0[/tex]), you will have a non-zero series solution. Let [tex]a=a_0[/tex] with [tex]a_0\neq0[/tex]. Then
[tex]2a_2-2a_0=6 \implies a_2 = a+3[/tex]
[tex]4a_4-2a_2=-1 \implies a_4 = \dfrac{2a+5}4[/tex]
[tex]6a_6-2a_4=\dfrac1{20} \implies a_6 = \dfrac{20a+51}{120}[/tex]
and so the first four terms of series solution to the DE would be
[tex]\boxed{a + (a+3)x^2 + \dfrac{2a+5}4x^4 + \dfrac{20a+51}{120}x^6}[/tex]
Find Easy question For yall
Answers
Answer:
V = 64.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos V = adj side/ hypotenuse
cos V = 3/7
Taking the inverse cos of each side
cos ^-1 ( cos V) = cos ^-1 (3/7)
V=64.62306
Rounding to the nearest tenth
V = 64.6
Answer:
V=64.6
Step-by-step explanation:
the same thing as other guy, lol
PLEASE HELP!!
Indicate the method you would use to prove the two ▵‘s ≅. If no method applies, enter “none”
A. SSS
B. SAS
C. ASA
D. AAS
E. None
(I attached the triangle thing that goes with the question)
Answers
Please show work will mark you brainliest!
Answers
QUESTION:- An artist uses 200 tiles to create a tessellation design that covers a rectangle with dimensions 2 ft by 3 ft. He will cover a wall with dimensions 10 ft by 15 ft using the same design and tiles of the same size. How many tiles will he need to cover the entire wall?
ANSWER:-
CASE 1 :- NUMBER OF TILES USED -> 200AREA WHICH IS TO BE COVERED-> 2×3 ft² (given-> rectangle)CASE 2:-
AREA WHICH IS TO BE COVERED-> 10×15 ft² (given-> rectangle)NUMBER OF TILES:- TO FINDIT IS GIVEN THAT DESIGN AND SIZE OF TILES R SAME SO WE CAN CONSIDER THAT SAME NUMBER OF TILES WILL COVER SAME AREA IN BOTH CASE.
WE CAN USE UNITARY METHOD FOR SOLVING THIS:-
[tex]6ft² \: is \: covered \: using \: 200 \: tiles \\ 1ft² \: is \: covered \: using \: \frac{200}{6} \: tiles \\ 150ft² \: is \: covered \: using \: \frac{200 \times 150}{6} \: tiles \\ 150ft² \: is \: covered \: using \: \frac{200 \times \cancel{150}^{ \: \: 25} }{ \cancel6 {}^{ \: 1} } \: tiles \\ 150ft² \: is \: covered \: using \: 200 \times 25 \: tiles \\ 150ft² \: is \: covered \: using \: 5000 \: tiles[/tex]
On Fridays, Jerry stops at Steak & Taco Shack before he goes home. This week
his order was 1 steak sandwich, 2 orders of cheese fries, and 2 taco salads. He was
charged $11.50 before tax. One week ago, his order was 2 steak sandwiches, 3
orders of cheese fries, and 1 taco salad, and he was charged $15.25. Two weeks ago
he ordered 1 steak sandwich, 4 orders of cheese fries, and 1 taco salad, and was
charged $13. How much is 1 steak sandwich? How much is 1 cheese fries? How
much is 1 taco salad?
Answers
Answer:
Steak sandwich = x = 4
Cheese fries = y = 1.75
Taco salad = z = 2
Step-by-step explanation:
Let :
Steak sandwich = x
Cheese fries = y
Taco salad = z
This week:
x + 2y + 2z = 11.50 - - - - (1)
Last week :
2x + 3y + z = 15.25 - - - (2)
Two weeks ago :
x + 4y + z = 13 - - - - - (3)
Taking (1) and (2)
x + 2y + 2z = 11.50 ___(1)
2x + 3y + z = 15.25 ___(2)
Multiply (1) by 2 and (2) by 1 and subtract
2x + 4y + 4z = 23
2x + 3y + z = 15.25
_______________
y + 3z = 7.75 - - - - (4)
Taking (2) and (3)
2x + 3y + z = 15.25 - - (2)
x + 4y + z = 13 - - - - - (3)
Multiply (2) by 1 and (3) by 2 and subtract
2x + 3y + z = 15.25
2x + 8y + 2z = 26
______________
-5y - z = - 10.75 - - - - - (5)
Lets solve (4) and (5)
y + 3z = 7.75 - - - - (4) - - - multiply by 5
-5y - z = - 10.75 - - - - - (5) - - - multiply by 1
Then add the result :
5y + 15z = 38.75
-5y - z = - 10.75
____________
14z = 28
z = 28 / 14
z = 2
To find y ; put z = 2 in (4)
y + 3z = 7.75
y + 3(2) = 7.75
y + 6 = 7.75
y = 7.75 - 6
y = 1.75
From equation 3 ;
x + 4y + z = 13 - - - - - (3)
x + 4(1.75) + 2 = 13
x + 7 + 2 = 13
x + 9 = 13
x = 13 - 9
x = 4
Hence,
Steak sandwich = x = 4
Cheese fries = y = 1.75
Taco salad = z = 2
Find the Sample size for 99% confidence level with a margin of error of 4% and p unknown.
Answers
Answer:
za/2: Divide the confidence level by two, and look that area up in the z-table: .95 / 2 = 0.475. ...
E (margin of error): Divide the given width by 2. 6% / 2. ...
: use the given percentage. 41% = 0.41. ...
: subtract. from 1.
If we add one unit to the length (l) of a rectangle that has width (w), what is its new area (NA) in terms of its old area (A)?
NA = A x w
NA = A + w
NA = A + l
NA = A
Answers
NA = A + W
By adding one unit to length, we increase the overall area by the width of the rectangle. This is because the formula for the area of a rectangle is A = l x w. So, NA = (l + 1) x w = (l x w) + w = A + w.
A walking path across a park is represented by the equation y = -4x+10. A
new path will be built perpendicular to this path. The paths will intersect at
the point (4.-6). Identify the equation that represents the new path.
102
10
10
O A. y -**-5
B. y --4x+10
C. y - 4x-22
O D. v-**-7
Answers
first invert fraction of the slope from 4/1 to 1/4 and switch sign. then figure out the y-intercept
the algebraic approach would work like this:
-4x + 10 = 1/4x + b
plug in what you got, here: the intersection information
-4*(4) + 10 = 1/4*(4) + b
-16 + 10 = 1 + b
-6 = 1 + b
-7 = b
F(x) = x +3; G(x) = 2x^2 -4 Find (f*g)(x)
Answers
9514 1404 393
Answer:
(f·g)(x) = 2x^3 +6x^2 -4x -12
Step-by-step explanation:
The distributive property is used to find the expanded form of the product.
(f·g)(x) = f(x)·g(x) = (x +3)(2x^2 -4) = x(2x^2 -4) +3(2x^2 -4)
= 2x^3 -4x +6x^2 -12
(f·g)(x) = 2x^3 +6x^2 -4x -12
The management of a large airline wants to estimate the average time after takeoff taken before the crew begins serving snacks and beverages on their flights. Assuming that management has easy access to all of the information that would be required to select flights by each proposed method, which of the following would be reasonable methods of stratified sampling?
a. For each day of the week, randomly select 5% of all flights that depart on that day of the week.
b. Divide all flights into the following 4 groups on the basis of scheduled departure time: before 9:00 am 9:00 am to 1:00 pm. 1:00 pm to 5:00 pm, and after 5:00 pm. Randomly select 5% of the flights in each group.
c. For each crew member the airline employs, randomly select 5 flights that the crew member works.
d. Divide the airports from which the airline's fights depart into 4 regions: Northeast, Northwest Southwest and Southeast. Randomly select 5% of all flights departing from airports in each region
Answers
Answer:
The answer is "Option a, Option b, and Option d".
Step-by-step explanation:
In the given question it is used to stratifying the sampling if the population of this scenario it flights takes off when it is divided via some strata.
In option a, In this case, it stratified the sampling, as the population of planes taking off has been divided into the days of the week. In option b, It also used as the case of stratified sampling. In options c, it is systematic sampling, that's why it is wrong. In option d, It is an example of stratifying the sampling.Answer:
For each day of the week, randomly select 5% of all flights that depart on that day of the week.
Divide all flights into the following 4 groups on the basis of scheduled departure time: before 9:00 am, 9:00 am to 1:00 pm, 1:00 pm to 5:00 pm, and after 5:00 pm. Randomly select 5% of the flights in each group.
Divide the airports from which the airline's flights depart into 4 regions: Northeast, Northwest, Southwest, and Southeast. Randomly select 5% of all flights departing from airports in each region.
Step-by-step explanation:
ll sampling methods that divide the flights into a small number of mutually exclusive categories are appropriate. These methods include all flights on the basis of a characteristic that might be associated with the variable being investigated and randomly selects a proportionate number of flights from each group.
The operations manager of a company that manufactures tires wants to determine whether there are any differences in the quality of work among the three daily shifts. She randomly selects 300 tires and carefully inspects them. Each tire is either classified as perfect, satisfactory, or defective, and the shift that produced it is also recorded. The two categorical variables of interest are "shift" and "condition of the tire produced". The p-value of the Chi-Squared test of independence is 0.073. Does the data provide sufficient evidence at the 5% significance level to infer that there are differences in quality among the three shifts?
Answers
The operation manager is responsible to identify whether there are errors in quality of the tires manufactured.
There are three different shifts and each shift has different team of workers who manufacture tires. For this we test hypothesis as;
H0 ; Quality of tire manufactured is independent on shifts
Ha ; Quality of tires manufactured is dependent on shifts.
The p value of chi squared test is greater than the significance level therefore we reject the null hypothesis.
This hypothesis reach to conclusion that quality of tires is dependent on shifts, which means there are differences in quality among the three shifts.
Learn more at https://brainly.com/question/24365931
2+4? I am omisha please give me answer
Answers
Answer:
6
Step-by-step explanation:
2+4 = 6
..............
Answer:
Here is your answer omisha
2+4=6
ko dung may tinh hay so sanh
3√7 vs 7√3
Answers
Answer:
what this makes bi sense haha
Step-by-step explanation:
but ok
37. The trip between 2 towns is exactly 90 miles. You have gone 40% of this distance. How far have
you gone?
Answers
Answer:
36 miles
Step-by-step explanation:
We want to find 40% of 90 miles
40% * 90
.40 * 90
36 miles
We have to find travelled distance inorder to find this we have to find 40℅ of 90miles
[tex]\\ \Large\sf\longmapsto 90\times 40\℅[/tex]
[tex]\\ \Large\sf\longmapsto 90\times \dfrac{40}{100}[/tex]
[tex]\\ \Large\sf\longmapsto 9\times 4[/tex]
[tex]\\ \Large\sf\longmapsto 36miles [/tex]
Tuition. The tuition at a community college increased from $2,500 to $2,650 per semester. What was the percent of increase in the tuition?
Answers
Answer:
6 percent increase
Step-by-step explanation:
2650 divided by 2500 gives you 1.06 which means if 2500 is 100 percent 2650 would be 106 percent so the answer is a 6 percent increase
Answer:
6%
Step-by-step explanation:
another way of doing this type of calculation is...
NEW-OLD = 2650-2500 = 150 = .06 = 6%
OLD 2500 2500
Please help me with this
Answers
Answer:
[tex]\frac{121}{14} = 8\frac{9}{14}[/tex]
Step-by-step explanation:
If $500 were deposited into an account paying 5% interest, compound monthly, how much would be in the account in 4 years?
Please show me proper work and a good explanation on how you got said answer.
Answers
Answer:
610.48
Step-by-step explanation:
The formula for compound interest is
A = P(1+r/n) ^nt where
A is the amount in the account
P is the principle
r is the interest rate
n is the number of times the interest is compounded per year
t is the time in years
A = 500(1+.05/12) ^12*4
A = 500(1+.0041666666) ^48
A = 500(1.0041666666) ^48
A = 500*1.220895355
A =610.4476775
Rounding to the nearest cent
A = 610.48
please help me with this question!
Answers
Answer:
12 miles
Step-by-step explanation:
Let the amount of hours it takes Leroy to catch up to Kevin equal x. Since speed multiplied by time is distance, Leroy would have run a total of 6x miles(6*x). Kevin already had a head start of 24 minutes, which is the same as 2/5 of an hour. In 2/5 an hour, Kevin ran 2 miles as 2 is 2/5 *5. For the next x hours his distance would be a total of 5x(5*x). This means, after x hours, Kevins distance is 5x + 2. In this case, catching up to someone is the same as having the same distance value. This means we can set the two expressions equal to each other, and solve:
6x = 5x + 2
x = 2
The time it took Leroy to catch up is 2 hours, but we are looking for the distance, which is represented by 6x. We substitute in 2 to get:
6(2) = 12
This means Leroy had to run 12 miles.
4 times a certain number less two times that's the same number is 10 what is the number
Answers
Answer:
The number is 5
Step-by-step explanation:
Let the number be x,
Four times the number= 4x
two times the same number= 2x
So we have ,
4x – 2x = 10
2x = 10
x = 5
Therefore the number is 5
What is the area of this figure?
Answers
Answer:
22
Step-by-step explanation:
(5x2) + (3x2) + (3x2)
22 square units
Answer from Gauthmath
The graph f(x)=x^5 is transformed to form a new function, g(x). Which set of transformations takes f(c) to g(x) in the correct order?
- translation 2 units to right,vertical stretch by a factor 1/3, translation 1 unit up
-translation 2 units to the right, vertical stretch by a factor of 3, translation 1 unit up
-translation 2 units to the right,translation 1 unit up,vertical stretch by a factor of 1/3
-translation 2 units to the right,translation 1 unit up,vertical stretch by a factor of 3
Answers
Answer:
Translation 2 units to the right
Vertical stretch by a factor of 3
Translation 1 unit up
Step-by-step explanation:
Correct on plato :}
2 balloons and 3 cakes cost £29.
6 balloons and 4 cakes cost £52.
Find the cost of one of each.
1 balloon is £
1 cake is £
Answers
Answer:
1 balloon is 4/ 1 cake is 7
Step-by-step explanation:
2 balloons is 8/ 3 cakes are 21 add together you get 29.
18 Geometry question: Use an algebraic equation to find the measure of each angle that is representative in terms of X
Answers
Answer:
12x - 28° = 116°
7x + 32° = 116°
Step-by-step explanation:
12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.
Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:
12x - 28° = 7x + 32°
Collect like terms
12x - 7x = 28 + 32
5x = 60
Divide both sides by 5
5x/5 = 60/5
x = 12
✔️12x - 28°
Plug in the value of x
12(12) - 28
= 144 - 28
= 116°
✔️7x + 32°
7(12) + 32
= 84 + 32
= 116°
a) Show that 4x² -6x+9 is positive for all values real numbers x.
Answers
Answer:
(4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75
(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x
Step-by-step explanation:
a) Use the formula a²-2ab+b²= (a-b)² (You need to make squared expression because it is always positive)
Consider 4x² as a² and -6x=-2ab
4x²=a² a=2x ab=3x 2x*b=3x
b=1.5
Express 4x² -6x+9= (4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75
(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x
Please help
What are the roots (zeros) of the polynomial f(x)=x^3+3x^2-9x+15
Answers
9514 1404 393
Answer:
{-5.2555, 1.1278 ± 1.2579i}
Step-by-step explanation:
Descarte's rule of signs tells you there are 0 or 2 positive real roots and 1 negative real root. A graph shows you the negative roots is irrational, and the positive roots are complex.
There are formulas for solving equations of this sort. The method you use will depend on whether you need an exact result or just a numerical approximation. Exact results can be obtained in terms of radicals or in terms of trig functions.
The first attachment is from a freely available solver. It gives 4 decimal places, which is sufficient for many purposes.
The second attachment is the graph, along with the quadratic that results from dividing f(x) by the factor that gives the real root. While the values shown on the graph are to 3 decimal places, the calculator can be used to find them to greater precision. (We have used Newton's Method iteration to find the real root to 12 significant figures.)
The sum of the two numbers is 66. The larger number is 10 more than the smaller number. What are the numbers?
Answers
Answer:
28 and 38
Step-by-step explanation:
a+b = 66
a + 10 = b
using substitution, a + (a+10) = 66
2a = 56
a = 28
28 + 10 = 38
b = 38
-27
Which of the following is equivalent to
نان-۴
?
N
O
(197)
NI
12
22
(22)
2².2
Answers
Answer:
3rd option
Step-by-step explanation:
(1/2)^-2t
= (2^-1)^-2t
= 2^2t
= (2^2)^t
Answered by GAUTHMATH
A 90% confidence interval is (35 45). What is the margin of error?
A. 5
B.4.5
C.9
D.10
Answers
Answer:
option A 5
I hope it's correct
.....
An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes.
Required:
Let x̄ be the sample average lifetime of 64 Duracell and ȳ be the sample average lifetime of 64 Eveready Energizer batteries. What is the mean value of x̄- ȳ(i.e., where is the distribution of -centered)?
Answers
Answer:
The mean is of -0.4 hours.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Mean of the sample of 64 Duracell:
By the Central Limit Theorem, 4.1 hours.
Mean of the sample of 64 Eveready:
By the Central Limit Theorem, 4.5 hours.
Mean of the difference?
Subtraction of normal variables, so we subtract the means.
4.1 - 4.5 = -0.4
The mean is of -0.4 hours.
