A trapezoidal deck has dimensions as shown.


c. What is the longer base length if the area is 88 square feet (ft)²?

The real and imaginary parts of the three complex numbers are:

In this question we find three case of complex numbers, that is, numbers of the form z = a + i b, where a, b are real coefficients and i = √(- 1). The coefficient a corresponds to the real part of the complex number and the coefficient b is its imaginary part. Now we proceed to analyze each of the three cases:

Case 1: - 7

The number - 7 is equivalent to - 7 + i 0, where - 7 is the real part and 0 is the imaginary part.

Case 2: 5 - √(- 24)

First, we rewrite the entire expression in standard form:

5 - √(- 24)

5 - √[(- 1) · 24]

5 - √(- 1) · √24

5 - i √24

5 - i 2√6

The real part is 5 and the imaginary part is 2√6.

Case 3: (6 - i) · (6 + i)

We expand and simplify the resulting expression:

(6 - i) · (6 + i)

6 · (6 - i) + i · (6 - i)

36 - i 6 + i 6 - i²

(36 - i²)

36 + 1

37

37 + i 0

The real part is 37 and the imaginary part is 0.

To learn more on complex numbers: https://brainly.com/question/28869794

#SPJ1

Answer:

The real and imaginary parts of the three complex numbers are:Real part: - 7, Imaginary part: 0Real part: 5, Imaginary part: 2√6Real part: 37, Imaginary part: 0How to determine the real and imaginary component of a complex number.In this question we find three case of complex numbers, that is, numbers of the form z = a + i b, where a, b are real coefficients and i = √(- 1). The coefficient a corresponds to the real part of the complex number and the coefficient b is its imaginary part. Now we proceed to analyze each of the three cases:Case 1: - 7The number - 7 is equivalent to - 7 + i 0, where - 7 is the real part and 0 is the imaginary part.Case 2: 5 - √(- 24)First, we rewrite the entire expression in standard form:5 - √(- 24)5 - √[(- 1) · 24]5 - √(- 1) · √245 - i √245 - i 2√6The real part is 5 and the imaginary part is 2√6.Case 3: (6 - i) · (6 + i)We expand and simplify the resulting expression:(6 - i) · (6 + i)6 · (6 - i) + i · (6 - i)36 - i 6 + i 6 - i²(36 - i²) 36 + 137 37 + i 0The real part is 37 and the imaginary part is 0.

Step-by-step explanation: hope this helps0^0

The rate of change of the area of the right triangle at that instant is -1.5 sq km/h.

Let ABC be a right triangle, right-angled at B.

the side decreasing be, BC = x

and the increasing side be, AB = y

then, AC = z = √(x² + y²) (using Pythagoras theorem)

It is given that, dx/dt = - 5km/h and dy/dt = 14 km/h

x = 3, y= 9 at certain instant

now, the area of the triangle = 1/2 xy

A = 1/2 xy

dA/dt = 1/2 (y).dx/dt + x/2.dy/dt

at x = 3, y = 9, substituting the values,

(dA/dt) = 1/2 (9)(-5) + 3/2 (14)

= -1.5

therefore, the rate of change of the area of the right triangle at the instant when x=3 and y= 9 is -1.5 sq km/h.

know more about the area of a triangle here: https://brainly.com/question/19305981

#SPJ4

Therefore, the probability that it will be raining at the end of time is 37.5%.

A) To describe the transition matrix, we can use the following notation: R = It will rain N = It will not rain

Since it is given that if it rained yesterday, then there is a 60% chance of rain today, and if it did not rain yesterday there is an 85% chance of no rain today.

Thus, the transition matrix would be as follows:| P(R/R)  P(N/R)| P(R/N)  P(N/N)| = |0.6  0.4| |0.15  0.85|

B) If it rained Monday, then we need to find the probability that it will rain Wednesday.

We can find this by multiplying the probability of rain on Wednesday given that it rained on Monday and the probability that it rained on Monday.

Thus, the probability of rain on Wednesday, given that it rained on Monday would be:0.6 x 0.6 = 0.36So, there is a 36% chance that it will rain on Wednesday given that it rained on Monday.

C) If it did not rain Friday, then we need to find the probability of rain on Monday. Using Bayes' theorem, we can write: P(R/M) = P(M/R)P(R)/[P(M/R)P(R) + P(M/N)P(N)]where, M = It did not rain Friday= 0.15 (from the transition matrix)P(R) = Probability of rain = 0.6 (given in the problem)P(N) = Probability of no rain = 0.4 (calculated from 1 - P(R))P(M/R) = Probability of it not raining on Friday given that it rained on Thursday = 0.4P(M/N) = Probability of it not raining on Friday given that it did not rain on Thursday = 0.85Substituting these values, we get: P(R/M) = 0.4 x 0.6/[0.4 x 0.6 + 0.85 x 0.4] = 0.31 So, there is a 31% chance of rain on Monday given that it did not rain on Friday.

D) The steady-state vector is the vector that describes the probabilities of being in each of the states in the long run. To find the steady-state vector, we need to solve the following equation: πP = πwhere,π = steady-state vector P = transition matrix Substituting the values from the transition matrix, we get:| π(R)  π(N)| |0.6  0.4| = | π(R)  π(N)| | π(R)  π(N)| |0.15  0.85| | π(R)  π(N)|

Simplifying this, we get the following two equations:π(R) x 0.6 + π(N) x 0.15 = π(R)π(R) x 0.4 + π(N) x 0.85 = π(N) Solving these equations, we get: π(R) = 0.375π(N) = 0.625So, the steady-state vector is:| π(R)  π(N)| = |0.375  0.625|This means that in the long run, there is a 37.5% chance of rain and a 62.5% chance of no rain.

To Know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

The difference in the means between two groups indicates the extent to which the average values of a particular variable differ between the groups.

The difference in the means between the two groups provides insight into how the average values of a specific variable vary across the groups. If the difference is positive, it means that the mean of one group is greater than the mean of the other group. Conversely, if the difference is negative, it indicates that the mean of one group is less than the mean of the other group.

Several factors can contribute to differences in means between groups. One key factor is the distribution of the variable within each group. If one group has a higher concentration of larger values compared to the other group, it is likely to have a higher mean. Additionally, differences in sample sizes between groups can impact the means, as larger sample sizes provide more reliable estimates of the true population mean.

Other factors such as sampling variability, outliers, or the presence of confounding variables can also influence the difference in means between groups. Statistical methods, such as hypothesis testing or confidence intervals, can be used to determine the significance of the difference and assess whether it is due to chance or represents a true difference in the population means.

Learn more about hypothesis here:

https://brainly.com/question/29576929

#SPJ11

The probability that a household selected at random does not have an individual under the age of 18 in Nassau County in 2000 is 0.999614.

The round-off to the nearest thousands would be 1.000.

To calculate the probability that the selected household did not have an individual under the age of 18, we must determine the number of households without individuals under 18 and divide it by the total number of households in Nassau County in 2000.

We already know that,

The total households = 447,000

The number of households with individuals under 18 = 173

Now,

Number of households without individuals under 18 =

Total households - Households with individuals under 18

Number of households without individuals under 18 = 447,000-173

= 446,827

Probability = Number of households without individuals under 18/Total number of households

Probability = 446,827/447,000

= 0.999614

∴ The probability that the selected household does not have an individual under the age of 18 is 0.999614.

The round-off to the nearest thousand would be 1.000.

To know more about probability,

brainly.com/question/25839839

#SPJ12

This whole question: There were a total of 447000 households in Nassau County in 200. If one of these households was selected at random, what is the probability that the selected household did not have an individual under age 18? (Express your answer as a decimal rounded to the nearest thousandth)

Answer:

Slope is 1

Step-by-step explanation:

(-4,-1) (-3,1)

m =  y2 - y1 / x2 - x1

Answer:

2

Step-by-step explanation:

Slope is defined as change in y over change in x

if we count, we can tell that the change in y is up 2 boxes for every 1 box you take to the right. We count 1 box right every time so we are always going in the positive direction.

Since slope is change in y over change in x, then you get 2/1 = 2.

They provide a clear and concise way to demonstrate the validity of a claim, relying on known facts and logical reasoning

Candice's proof is a direct proof because it establishes the truth of a statement by providing a logical sequence of steps that directly lead to the conclusion. In a direct proof, each step is based on a previously established fact or an accepted axiom. The proof proceeds in a straightforward manner, without relying on any other alternative scenarios or indirect reasoning.

Candice's proof likely involves stating the given information or assumptions, followed by a series of logical deductions and equations. Each step is clearly explained and justified based on known facts or established mathematical principles. The proof does not rely on contradiction, contrapositive, or other indirect methods of reasoning.

On the other hand, Joe's proof is also a direct proof for similar reasons. It follows a logical sequence of steps based on known facts or established principles to arrive at the desired conclusion. Joe's proof may involve identifying the given information, applying relevant theorems or formulas, and providing clear explanations for each step.

Direct proofs are commonly used in mathematics to prove statements or theorems. They provide a clear and concise way to demonstrate the validity of a claim, relying on known facts and logical reasoning. By presenting a direct chain of deductions, these proofs build a solid argument that leads to the desired result, without the need for complex or indirect reasoning.

for more such question on reasoning visit

https://brainly.com/question/28418750

#SPJ8

Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

Answer:

To find when daily ticket sales peak, we need to find the maximum point of the quadratic equation N = -0.4x^2 + 9.6x + 10.

One way to do this is to use the formula for the x-coordinate of the vertex of a quadratic function, which is:

x = -b/2a

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c. In this case, a = -0.4 and b = 9.6, so:

x = -9.6 / 2(-0.4) = 12

This means that daily ticket sales will peak 12 days after the concert was first announced.

To find how many tickets will be sold that day, we can substitute x = 12 into the equation for N:

N = -0.4x^2 + 9.6x + 10 = -0.4(12)^2 + 9.6(12) + 10 ≈ 51.2

Therefore, approximately 51 tickets will be sold on the day that daily ticket sales peak, 12 days after the concert was first announced.

Step-by-step explanation:

The graph of the function y = f(x) with the given properties can be summarized as follows: The function f(x) has a domain of (-∞, 0) U (0, +∞) and exhibits an infinite discontinuity at x = -6. At x = -6, the function has a value of 3.

The limit of f(x) as x approaches -∞ is 2, and the limit as x approaches +∞ is also 2. At x = -3, the function has a value of 3. The function f(x) is left continuous but not right continuous at x = 3. Finally, the limits of f(x) as x approaches -∞ and +∞ are -∞ and +∞ respectively.

To explain the graph, let's start with the domain of f(x), which is all real numbers except 0. This means the graph will extend infinitely in both the positive and negative x-directions but will have a vertical asymptote at x = 0, creating a gap in the graph. At x = -6, the function has an infinite discontinuity, indicated by an open circle on the graph. The function approaches different values from the left and right sides of x = -6, but it has a specific value of 3 at that point.

The limits of f(x) as x approaches -∞ and +∞ are both 2, which means the graph approaches a horizontal asymptote at y = 2 in both directions. At x = -3, the function has a value of 3, represented by a filled-in circle on the graph. This point is separate from the infinite discontinuity at x = -6.

The function is left continuous at x = 3, meaning that as x approaches 3 from the left side, the function approaches a specific value, but it is not right continuous at x = 3. This indicates a jump or a discontinuity at that point. Finally, the limits of f(x) as x approaches -∞ and +∞ are -∞ and +∞ respectively, indicating that the graph extends infinitely downward and upward.

Learn more about graph of the function:

https://brainly.com/question/27757761

#SPJ11

The probability of the sets are solved and

a) n(P U Q) = 85%

b) n(P ∩ Q) = 20%

c) n(only P) = 35%

d) n(only Q) = 30%

Given data ,

P and are the subsets of universal set U

And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%

Now , we'll use the formula for the union and intersection of sets:

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(only P) = n(P) - n(P ∩ Q)

n(only Q) = n(Q) - n(P ∩ Q)

We're given that:

n(P) = 55%

n(Q) = 50%

n(P U Q)' = 15%

To find n(P U Q), we'll use the complement rule:

n(P U Q) = 100% - n(P U Q)'

n(P U Q) = 100% - 15%

n(P U Q) = 85%

Now we can substitute the values into the formulas above:

(i)

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(P ∩ Q) = 55% + 50% - 85%

n(P ∩ Q) = 20%

(ii)

n(P ∩ Q) = 20%

(iii) n(only P) = n(P) - n(P ∩ Q)

n(only P) = 55% - 20%

n(only P) = 35%

(iv)

n(only Q) = n(Q) - n(P ∩ Q)

n(only Q) = 50% - 20%

n(only Q) = 30%

Hence , the probability is solved

To learn more about probability click :

https://brainly.com/question/17089724

#SPJ1

Answer:

Here is your answer, this is how you prove it

Answer:

68,3 %

Step-by-step explanation:

Empirical rule establishes:

In a normal distribution with mean μ and standard deviation σ we have a  relation between values of the distribution and intervals describes as follows:

( μ ± σ )  contains  68.3 % of all values of the distribution

( μ ± 2σ )  contains 95,4 %       and

( μ ± 3σ )  contains 99.7 %

In our particular case we have that

( μ ± σ )   ⇒    (  70  ±  5 )   ⇒   ( 65 , 75 )

( μ ± 2σ ) ⇒    ( 70   ±  10 ) ⇒   ( 60 , 80 )     and

( μ ± 3σ ) ⇒    ( 70  ±  15  )  ⇒   ( 55 , 85

As we can clearly see 68,3 % of values fall between values going from 65 up to 75 inches

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

To know more about root click here

brainly.com/question/16880173

#SPJ11

The value of the Discriminant is 0 so we have equal roots  = b/2a = 6/2 = 3

The given equation is a quadratic equation.

x^2+6x+9 = 0.

To tell the nature of the roots we have to understand how to find the root of a quadratic equation.

The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f(α) = 0, then x = α is a root of the quadratic equation f(x).

The term Discriminant is used in quadratic equations.

The discriminant of a quadratic equation is the expression \((b^2 - 4ac)\) in the quadratic formula. A quadratic equation's discriminant shows the nature of roots.

Discriminant important thing is that it is used to find the nature of roots.

x^2+6x+9 = 0. a =1, b = 6, c=9

discriminant d = b^2 - 4*a*c = 36-4*1*9 = 36-36 = 0

So the value of the discriminant is 0 so we have equal roots  = b/2a = 6/2 = 3

To know more about roots of quadratic equation here:

https://brainly.com/question/26926523

#SPJ4

On solving the provided question, we can say that The maximum rank of a matrix is 2 and The maximum rank is min (5,2)=2.

A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.

The maximum rank of a matrix is 2.

The maximum rank is min (5,2)=2.

Option c with the biggest rank is min(m,n).

To know more about matrix visit:

https://brainly.com/question/29995229

#SPJ4

it seems that it starts from 4 then every time it gets multiplied by 3 so F(n)=4*3^n-1

Answer:

option 1 and option 2 should be correct

Let Sn = So + X₁ (n ≥ 1) ΣX; i=1 be a simple random walk starting in the random variable So. That is, X1₁, X2,. of i.i.d. random variables independent of So such that = P[X₁ +1]: = p and P[X₁] = q = 1 - p.

A random process, X₁, X₂,... is a simple random walk beginning at So if:It starts at So.Xn = So + X₁+ X₂+ ...+ Xn and that n ≥ 1.It is a Markov process. That is, for all integers n > 1 and So, the distribution of Xn depends only on Xn - 1 and So; it is independent of the history X1, X2,..., Xn - 2.The increments X1, X2,... are independent and identical in distribution.

The random variable Xn represents the amount by which the random walk shifts from n-1 to n. Since the increments X1, X2,... are independent and have the same distribution, the probability distribution of Xn does not depend on n. Consequently, the mean of Xn is 0. The variance of Xn is σ^2, the variance of X1.The generating function of a random variable X is given by its probability distribution function. It's given byGx (z) = E(z^X).The distribution of Xn is obtained by the convolution of the distribution of Xn-1 and the distribution of X1.

Therefore, the generating function of Xn is given byGn (z) = Gn-1 (z) . G1 (z).The generating function of the sum of n independent and identical random variables is given byGn (z) = G (z) ^ n.Gn (z) = G (z) ^ n is obtained by induction. G1 (z) = E(z^X) is the generating function of the increment X1 of the random walk.Considering the generating function of the stationary distribution, we haveG (z) = z^k . (pq) / (1 - pz)If we differentiate G (z) with respect to z, we getdG (z) / dz = k z^k-1 . (pq) / (1 - pz)^2 + z^k . (pq) / (1 - pz)^2 + z^k . p (1 - q) / (1 - pz)^2

This means we havek z^k . pq / (1 - pz)^2 + k z^k . (1 - p) q / (1 - pz)^2 = 0which simplifies to k = p / (1 - p)Consequently, the stationary distribution of the simple random walk is given byPn = (pq)^(n-k) . p / (1 - p).ConclusionThe simple random walk has a stationary distribution given byPn = (pq)^(n-k) . p / (1 - p). The generating function of this distribution isG (z) = z^k . (pq) / (1 - pz) where k = p / (1 - p).

To know more about stationary distribution visit:

brainly.com/question/23858250

#SPJ11

The surface area of the solid formed by the triangular prism and cube will be 598.33 square inches.

A prism is a closed solid that has two parallel bases connected by a rectangle surface.

The height of a right triangular prism is 11/6 inches.

Each side of the triangular base measures 10 inches, and the height of the base is 26/3 inches.

The triangular prism is placed at top of a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.

Then the surface area of the prism will be

\(\rm Surface \ area = 5 \times (10 \times 10) + 0.5 \times 10 \times \dfrac{26}{3} + 3 \times 10 \times \dfrac{11}{6}\\\\\\Surface \ area = 598.33\ in^2\)

More about the prism link is given below.

https://brainly.com/question/12649592

Answer:

i would reword this to 6x+7=61

Step-by-step explanation:

So.  

move the 7 to the right side of the equation but as an opposite number so in this case its gonna be a negative

61-7=54

then you divide the number and get your missing numbers

54/6=9

d=9

plug it in

6(9)+7=61

Answer:

Step-by-step explanation:

For every 4 pounds of sugar you get 20 cups of coffee. 4:20

For every packet of seeds you get 10 plants  1:10

The probability that the average tail length of the sample is between 3.8 and 3.9 feet is approximately 0.2417.

We have,

First, we need to find the mean and standard deviation of the sample distribution of the mean tail length:

The mean of the sample distribution is equal to the mean of the population, which is 3.75 feet.

The standard deviation of the sample distribution is equal to the standard deviation of the population divided by the square root of the sample size:

σ/√n = 0.6/√36 = 0.1 feet

Now we can use the standard normal distribution to find the probability:

z1 = (3.8 - 3.75) / 0.1 = 0.5

z2 = (3.9 - 3.75) / 0.1 = 1.5

Using a standard normal table or calculator, we can find the probability that z is between 0.5 and 1.5:

P(0.5 ≤ z ≤ 1.5) = P(z ≤ 1.5) - P(z ≤ 0.5) = 0.9332 - 0.6915 = 0.2417

Therefore,

The probability that the average tail length of the sample is between 3.8 and 3.9 feet is approximately 0.2417.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ11

The right answer is B. It is not applicable when data are continuous, is not a characteristic of the standard deviation.

The statement "It is not applicable when data are continuous" is not a characteristic of the standard deviation.

The standard deviation is a measure of the dispersion or variability of a dataset. It quantifies how spread out the values are from the mean. Explanation for other parts are as follows:

A. It can be calculated when the data contain negative or zero values:

This is true. The standard deviation can be calculated for datasets that contain negative or zero values. It considers the deviations from the mean, regardless of their sign.

C. It is always the square root of the variance:

This is true. A quadrilateral with exactly two sets of congruent following sides is called a kite. The variance is the average of the squared deviations from the mean.

D. Its physical interpretation is not as easy as the MAD:

This is a subjective statement. The physical interpretation of the standard deviation depends on the context and the familiarity of the user with the concept. However, it is often considered a more widely used and understood measure of dispersion compared to the Mean Absolute Deviation (MAD).

The statement "It is not applicable when data are continuous" is incorrect. The standard deviation can be calculated for both discrete and continuous data. The other options provided (A, C, and D) correctly describe characteristics of the standard deviation.

To know more about Standard Deviation, visit

brainly.com/question/475676

#SPJ11

The first three nonzero terms of the Maclaurin series for the function f(x) = (2 sin x) ln(1 + x) are: 2x - (2/3)x^3 + (4/45)x^5. The Maclaurin series converges absolutely for all values of x within the interval -1 < x ≤ 1.

To find the Maclaurin series for f(x), we need to express the function as a power series centered at x = 0. We can do this by using the known Maclaurin series expansions for sin x and ln(1 + x).

The Maclaurin series expansion for sin x is:

sin x = x - (1/3!)x^3 + (1/5!)x^5 - ...

The Maclaurin series expansion for ln(1 + x) is:

ln(1 + x) = x - (1/2)x^2 + (1/3)x^3 - ...

Multiplying these two series, we obtain the Maclaurin series expansion for f(x):

f(x) = (2 sin x) ln(1 + x) = 2x^2 - (2/3)x^3 + (4/45)x^5 - ...

The first three nonzero terms of the Maclaurin series for f(x) are: 2x - (2/3)x^3 + (4/45)x^5.

To determine the values of x for which the series converges absolutely, we need to consider the interval of convergence. In this case, the Maclaurin series converges absolutely for all values of x within the interval -1 < x ≤ 1.

To learn more about  Maclaurin series  Click Here: brainly.com/question/31745715

#SPJ11

Answer:

4 sq ft is the answer to your question

b and c are the answers i think....