3. Letf(x) = cos(3x). Find the 6th derivative of f(x) or f'(x). (2 marks)

GIven:

To Determine: The equivalent of the given expression

Distributing the sign outside as shown below:

Hence, the equivalent expression by distributing the sign outside the given expression is:

8.4n+1

Answer:

yes... PERIODT

Step-by-step explanation: i promise you its yes

Answer:

Yes

Step-by-step explanation:

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

Learn more about Integrate here : brainly.com/question/31744185

#SPJ11

Answer:

It is the first answer you got it right

Step-by-step explanation:

The answer is 374.625

Here,just we have to apply the formula of interest and that is Principal*time*rate/100

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

$374.63

Step-by-step explanation:

Find the interest paid by the bank per year by working out 6.75% of 1850 (1850x0.0675)

Then multiply this by 3 as it is three years, to get 374.625, then round it to 2 decimal places.

Answer:

8:31

Step-by-step explanation:

all of them are equal with 1:4 except 8:31

Answer:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Step-by-step explanation:

Answer:

6.26 yards

Step-by-step explanation:

Answer:

6.25 would be the answer :)

Step-by-step explanation:

Answer:

6.14 rounded to the nearest hundreth.

Every paralelogram equals 360º. And every oppisite angle is eqaul to each other. So by doing the math we can tell the smaller angles is 80º. Now we solve for x.

80=7x+37 minus 37 from both sides

43=7x.   then divide both side by 7 to cancel it out

6.14=x that is the answer rounded

You can check by inputing x's vaule into the equation and getting the angle measurment we solved for which is 80º.

7(6.14)+37

by doing this you get 80, the measure of the angle so the vaule for x is 6.14 rounded to the nearest hundreth.

A random sample is a sample that is drawn from a population in such a way that each member of the population has an equal chance of being selected. The mean is a measure of central tendency that represents the average value of a set of data.

In this scenario, a simple random sample of size n was drawn from a population that is normally distributed. The sample mean, X, was found to be 112, and the sample standard deviation, s, was found to be 10.

(a) To construct an 80% confidence interval about us if the sample size, n, is 13, we can use the formula:

CI = X ± t(α/2, n-1) * s/√n

where t(α/2, n-1) is the critical value for the t-distribution with (n-1) degrees of freedom and α is the level of significance. For an 80% confidence interval, α = 0.2 and t(α/2, n-1) = 1.340. Thus, the confidence interval is:

CI = 112 ± 1.340 * 10/√13
CI = (103.76, 120.24)

(b) To construct an 80% confidence interval about p if the sample size, n, is 24, we can use the formula:

CI = p ± z(α/2) * √(p(1-p)/n)

where z(α/2) is the critical value for the standard normal distribution and p is the sample proportion. Since the population is normally distributed, we can assume that the sample proportion is also normally distributed. For an 80% confidence interval, α = 0.2 and z(α/2) = 1.282. Thus, the confidence interval is:

CI = 112/24 ± 1.282 * √(112/24 * (1-112/24)/24)
CI = (0.38, 0.68)

(c) To construct a 95% confidence interval about p if the sample size, n, is 13, we can use the same formula as in (b), but with α = 0.05 and z(α/2) = 1.96. Thus, the confidence interval is:

CI = 112/13 ± 1.96 * √(112/13 * (1-112/13)/13)
CI = (0.38, 0.78)

(d) Yes, we could have computed the confidence intervals using the formulas provided, as long as the assumptions of normality and independence were met. However, if the sample size was small or the population was not normally distributed, we would need to use different methods, such as the t-distribution or non-parametric tests.

Learn more about mean here:

https://brainly.com/question/31101410

#SPJ11

The given series is divergent.

We can use the limit comparison test to determine the convergence or divergence of the given series:

First, note that for all n ≥ 1, we have: \(\frac{(n^9 + 1) }{ (n^10 + 1)}\) ≤ \(\frac{n^9 }{n^10} = \frac{1}{n}\)

Therefore, we can compare the given series to the harmonic series ∑ 1/n, which is a well-known divergent series. Specifically, we can apply the limit comparison test with the general term \(a_n = \frac{(n^9 + 1)}{(n^{10} + 1)}\) and the corresponding term \(b_n = \frac{1}{n}\):

lim (n → ∞) \(\frac{a_n }{ b_n}\) = lim (n → ∞) \(\frac{\frac{(n^9 + 1)}{(n^10 + 1)} }{\frac{1}{n} }\)

= lim (n → ∞) \(\frac{ n^{10} }{ (n^9 + 1)}\)

= lim (n → ∞) \(\frac{n}{1+\frac{1}{n^{9} } }\)

= ∞

Since the limit is positive and finite, the series ∑ \(\frac{(n^9 + 1) }{ (n^10 + 1) }\) behaves in the same way as the harmonic series, which is divergent. Therefore, the given series is also divergent.

To know more about "Harmonic series" refer here:

https://brainly.com/question/31582846#

#SPJ11

0.88 is the probability that the system functions. If the probability that c fails is 0.1 and the probability that d fails is 0.12

Let A be the probability that the system functions. Because of that, the probability that the system fails is:

P(system fails) = P(c fails or d fails) = P(c fails) + P(d fails) - P(c and d fail)

The above formula is true because of the addition rule of probability: we sum the probabilities of all the outcomes that satisfy the event, but we need to subtract the intersection (P(c and d fail)) because we would be adding it twice since it satisfies both conditions.

The given values are: P(c fails) = 0.1P(d fails) = 0.12 The intersection (P(c and d fail)) is not given, but we know that it can't be greater than either individual probability: P(c and d fail) ≤ min(P(c fails), P(d fails)) = min(0.1, 0.12) = 0.1

Then, we can calculate the probability that the system fails:

P(system fails) = P(c fails or d fails) = P(c fails) + P(d fails) - P(c and d fail)P(system fails) = 0.1 + 0.12 - 0.1 = 0.12

We know that the probability that the system functions is the complement of the probability that the system fails:

P(A) = 1 - P(system fails)P(A) = 1 - 0.12 = 0.88

We round to four decimal places: 0.88 is the probability that the system functions.  

To know more about probability visit:

brainly.com/question/29012539

#SPJ11

The equation of the hyperbola in standard form is \(\frac{(x - 1)^2}{5^2} - \frac{(y - 1)^2}{11} = 1\). This is the standard form of the equation of the hyperbola with the given characteristics.

To find the standard form of the equation of a hyperbola, we need to determine the key properties: the center, the distances from the center to the vertices (a), and the distances from the center to the foci (c).

Given the vertices (-4,1) and (6,1), we can find the center of the hyperbola by finding the midpoint between these two points:

Center: \((h, k) = \left(\frac{-4 + 6}{2}, \frac{1 + 1}{2}\right) = (1, 1)\)

Next, we can find the value of a, which is the distance from the center to the vertices. In this case, a is equal to the distance between the x-coordinates of the center and one of the vertices:

\(a = 6 - 1 = 5\)

Similarly, we can find the value of c, which is the distance from the center to the foci. In this case, c is equal to the distance between the x-coordinates of the center and one of the foci:

\(c = 7 - 1 = 6\)

Now we have all the necessary information to write the standard form of the equation of the hyperbola. The equation depends on whether the hyperbola is horizontal or vertical. Since the y-coordinates of the vertices and foci are the same, we can conclude that the hyperbola is horizontal.

The standard form of the equation of a hyperbola with a horizontal transverse axis is:

\(\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1\)

In this case, since the hyperbola is horizontal, the denominator of the y-term is b^2. We can find b using the relationship between a, c, and b in a hyperbola:

\(c^2 = a^2 + b^2\)

Substituting the values, we have:

\(6^2 = 5^2 + b^2\)

Solving for b, we get:

\(b^2 = 36 - 25 = 11\)

So, the equation of the hyperbola in standard form is:

\(\frac{(x - 1)^2}{5^2} - \frac{(y - 1)^2}{11} = 1\)

This is the standard form of the equation of the hyperbola with the given characteristics.

Learn more about hyperbola here

https://brainly.com/question/30281625

#SPJ11

We need to identify the function among the given options which is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0,4].What is the Extreme Value Theorem? The extreme value theorem says that a function on a closed interval must have a maximum and a minimum value.

The correct option is-C

In other words, there is an absolute maximum and an absolute minimum value. It is an important theorem in calculus. Let's check the given options for the absolute maximum on the interval [0,4]:a. y=tan⁡x As the function

f(x)=tanx is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4]. Therefore, option a is incorrect .b

. y=tan⁻¹xAs the function

f(x)=tan⁻¹x is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4].

Therefore, option b is incorrect. c.

y=x²−16/x²+x−20 Let's check the critical points of the function

f(x)=x²−16/x²+x−20 by finding its derivative and equating it to zero:

f '(x)= (2x(x² - 20) + (x² - 16)(2x + 1))/ (x² + x - 20)²=0On solving this equation,

we get x=-4, 0, and 4. Now we will check the function values of these critical points as well as at the endpoints of the given interval:[0,4]. We get: f(0) = -4 and

f(4) = 4/3 Since f(4) is greater than all other values, the absolute maximum of f(x) is at

x=4.Therefore, option c is correct .d. y=1/e^x-1As the function f(x)=1/e^x-1 is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4].

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

The expression to represent the perimeter of the triangle is 3.6x - 24

The value of x when perimeter of the triangle equals 12 is 10.

An equilateral triangle has all its sides equal to each other.

The perimeter of a figure is the sum of all its sides. A triangle has three sides.

Therefore,

perimeter = 1.2x- 8 + 1.2x - 8 + 1.2x - 8

perimeter = 3.6x - 24

If the triangle has a perimeter of 12 the value of x can be found below:

12 = 3.6x - 24

12 + 24 = 3.6x

3.6x = 36

divide both sides by 3.6

3.6x / 3.6 = 36 / 3.6

x = 10

read more: https://brainly.com/question/9248401?referrer=searchResults

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

To know more about deviation visit:

https://brainly.com/question/31835352

#SPJ11

Answer:

6 1/5

Step-by-step explanation:

six and one fifth girl no cap

and that's on mary had a lil lamb

Answer:

\(51 \frac{1}{5} ~ laps\)

Step-by-step explanation:

\(\frac{laps}{hours} =\frac{x}{1}=\frac{12\frac{4}{5} }{\frac{1}{4} }\)

\(x=\frac{\frac{64}{5} }{\frac{1}{4} }\)

\(x=\frac{64}{5}*\frac{4}{1}\)

\(x=\frac{256}{5} =5 \frac{1}{5}\)

------------------------------

hope it helps..

have a great day!!

= 816,480 arrangements.

To keep TH together we have do arrangements of : M, A, TH, E, M, A, T, I, C, S, so there are 10 objects to be arranged.We will make arrangements of these 10 and then substract cases where THE exists.Number of arrangements of above 10 objects = 10!/(2!*2!) = 907,200 ( We have divided by 2! twice because two copies of M and A are present). Number of arrangements where THE is together = 9!/((2!*2!) =  90,720.So Number of arrangements = 907,200 - 90,720 = 816,480

You can learn more about this through the link below:

https://brainly.com/question/20730359#SPJ4

Answer:

18 tables: $143

t tables: $35 + $6t

Step-by-step explanation:

35 + 6t

35 + 6(18) = 35 + 108 = 143

According to the area of the rectangle, the dimensions of each pen will be 15.5 feet by 15.5 feet​

Area of rectangle:

Basically, the area of the rectangle refers the region occupied by a rectangle within its four sides or boundaries.

Given,

Here we need to find the dimensions of the rectangular dog park split into two pens (sharing a fence) of the same size producing the greatest enclosed area given 240 ft of fencing

Let us consider the length of the rectangle is l and the width of the rectangle is w.

Here in the given question, the length and width of the will be same.

Then the it can be calculated as,

=> 240 = s²

=> s = √240

=> s = 15.5

Therefore, the dimension is 15.5 feet by 15.5 feet.

To know more about Area of rectangle here.

https://brainly.com/question/20693059

#SPJ1

Answer:

-8g+16-12t is the answer

Step-by-step explanation:

multiply everything by 4

Answer:

D. 3x^2y(9 – 14y)​

Step-by-step explanation:

To factor the expression 27x^2y - 42x^2y^2 completely using the greatest common factor (GCF) method, we need to find the largest common factor that can be factored out from both terms.

First, let's identify the common factors of the coefficients 27 and 42. The prime factorization of 27 is 3 * 3 * 3, and the prime factorization of 42 is 2 * 3 * 7. The common factor between them is 3.

Next, let's look at the variables. We have x^2 and y as common variables in both terms. The lowest exponent of x is 2, and the lowest exponent of y is 1.

Therefore, the GCF of 27x^2y and 42x^2y^2 is 3x^2y.

Now, we can factor out the GCF from the expression:

27x^2y - 42x^2y^2 = 3x^2y(9 - 14y)

Thus, the factored form of the expression using the GCF is 3x^2y(9 - 14y).

Answer:

x=-7

Step-by-step explanation:

Translate into an equation.

“A number” + -2 = -9

Assign “a number” to be “x”

X+-2=-9

Add 2 on both sides to even it out and get x

X-2+2=-9+2

X=-7

The number is -7. :)

Answer:

-7

Step-by-step explanation:

Let's put this into an equation with x being the unknown number. Then use the reversed order of operations to find the value of x.

x + -2 = -9

   + 2   + 2

x = -7

Pls mark Brainliest with the crown

Answer:

-30

Step-by-step explanation:

Simplifying:

2x + 30 = x

Reorder the terms:

30 + 2x = x

Solving:

30 + 2x = x

Solving for variable 'x'

Move all the terms containing x to the left, all the others to the right

Add '-1x' to each side of the equation

30 + 2x + -1x = x + -1x

Combine like terms: 2x + -1x = 1x

30 + 1x = x + -1x

Combine like terms: x + -1x = 0

30 + 1x = 0

Add '-30' to each side of the equation

30 + -30 + 1x = 0 + -30

Combine like terms: 30 + -30 = 0

0 + 1x = 0 + - 30

1x = 0 + -30

Combine like terms: 0 + -30 = -30

1x = -30

Divide each side by '1'

x = -30

Simplifying:

x = -30

Hope this helps :)

Pls brainliest...

At the end of 2018, the world population was approximately 7.53 billion people. This figure is calculated by taking the total population at the end of 2017, 7.4 billion people, and multiplying it by the population growth rate of 1.07%..

This means that the world population increased by approximately 130 million people in 2018. This population growth rate is consistent with the average growth rate of the world population over the last decade. While the population growth rate has been decreasing over the past few decades, it is still relatively high at 1.07%.

The high population growth rate is primarily due to high fertility rates in developing countries and a longer life expectancy in developed countries. This means that more people are born and fewer people die each year. As a result, the total population of the world increases each year.

know more about population here

https://brainly.com/question/27991860#

#SPJ11

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

To know more about values visit :

https://brainly.com/question/30145972

#SPJ11

x = 6 is not a solution to the equation x + 13 = 18.

Hence, Option C) No, because 6 + 13 = 18 is not true. is the correct answer.

Given the equation;  x + 13 = 18.

We plug x = 6 into the equation

x + 13 = 18

6 + 13 ≠ 18

6 + 13 is not 18

x = 6 is not a solution to the equation x + 13 = 18.

Hence, Option C) No, because 6 + 13 = 18 is not true. is the correct answer.

Learn more about equations here: brainly.com/question/14686792

#SPJ1

Answer:

3

Step-by-step explanation:

Answer:

0,1,2,3,4

Step-by-step explanation:

trustttttt meee

Answer:

Every dog will receive 1/15 bag of dog food

Step-by-step explanation:

1/5 = 3/15

3/15 : 3 = 1/15