Give that each figure shown below is a trapezoid. Find the missing values.

The coordinate vector for pP₁-0 will be (2, 0).Overall, we can use the above method to find the coordinate vectors for all the polynomials in the given set and then use these vectors to determine the near independence of the set.

We can write the basis vectors as follows:$$B = \{1, x, x^2, x^3\}$$Now, we can write each of the polynomials as a linear combination of the above basis vectors and then create a matrix from the coefficients. If the rank of this matrix is equal to the number of basis vectors, then the given set is linearly independent.

Otherwise, it is linearly dependent.The coordinate vector for a polynomial p of degree at most n is given by a list of n + 1 numbers,

where the ith number is the coefficient of xi in p.

For example, if \(p = 2 + 3x + 4x^2,\)

then the coordinate vector of p with respect to B is (2, 3, 4, 0).

Now, to write the coordinate vector for the polynomial (2-0, denoted p P₁-0, we can use the above formula to get the coordinate vector.

In this case, the degree of the polynomial is 1, so the coordinate vector will be of length 2.

Therefore, the coordinate vector for p

P₁-0 will be (2, 0).

Overall, we can use the above method to find the coordinate vectors for all the polynomials in the given set and then use these vectors to determine the near independence of the set.

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Step 1: Multiply a and c

a = 1

c = 20

a * c = 20

Step 2: Find factors of +20 that add up to +9

Factors of 20 = 1, 2, 4, 5, 10, 20

The two factors that add up to 9 are 4 and 5.

Step 3: Factor

(x + 4)(x + 5) = 0

Answer: (x + 4)(x + 5) = 0

Hope this helps!

Answer:

a1 = 4

a2 = 40

a3 = 400

a4 = 4000

Step-by-step explanation:

First substitute n with 1.

1. 4 ⋅ 10^1  - 1

4 ⋅ 10^0

4 ⋅ 1 = 4

Second substitute n with 2.

2. 4 ⋅ 10^2 - 1

4 ⋅ 10^1

4 ⋅ 10 = 40

Next substitute n with 3.

3. 4 ⋅ 10^3 - 1

4 ⋅ 10^2

4 ⋅ 100 = 400

Finally, substitute n with 4.

4. 4 ⋅ 10^4 - 1

4 ⋅ 10^3

4 ⋅ 1000 = 4000

It's simple. Just plug in 1, 2, 3, and 4 into n and solve the equation.

The frequency of the data sets is defined as the number of times the data is repeated in the given dataset. The frequency of the given data is calculated in the table below.

The frequency of the data sets is defined as the number of times the data is repeated in the given dataset.

Height (cm)              Frequency

146           --             2

147           --              1  

148           --              1                

149           --              1                  

150           --             2                  

151            --              1                      

152           --             6                                  

153           --             2                                      

154          --              3                                                  

155          --              1          

As we can see that the height of 146 cm is repeated two times so its frequency is 2. From this concept, all the frequencies are calculated above.

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The integral is L = ∫-1² √(1 + (10x+15)²) dx which is used to represents the length of curve from the point (-1,-10) to the point (2,50).

To find the length of the curve from (-1,-10) to (2,50), we need to set up an integral using the formula for arc length:

L = ∫√(1 + [dy/dx]²) dx

First, we need to find dy/dx:

y = 5x² + 15x
dy/dx = 10x + 15

Next, we need to find the limits of integration. We are given the endpoints of the curve, so we can use these to find the limits:

x1 = -1
y1 = 5(-1)² + 15(-1) = -10

x2 = 2
y2 = 5(2)² + 15(2) = 50

Now we can set up the integral:

L = ∫-1² √(1 + (10x+15)²) dx

This integral represents the length of the curve from (-1,-10) to (2,50).

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The probability is a fraction of 43/205 which is approximately 0.2098.

To calculate the probability of the next person who leaves the lecture having gray hair, we need to know the total number of people who left the lecture, as well as the number of people who have gray hair.

From the given data, we can see that there were a total of 50+40+39+33+43 = 205 people who left the lecture. We also know that there were 43 people who had gray hair.

Therefore, the probability of the next person who leaves the lecture having gray hair is:

P(gray hair) = (number of people with gray hair) / (total number of people who left the lecture)

P(gray hair) = 43/205

P(gray hair) ≈ 0.2098

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Since the test statistic (-2.24) falls outside the range of the critical values (-1.96 to 1.96), we reject the null hypothesis.

What is sign test?

The sign test is a non-parametric statistical test used to determine whether the median of a distribution is equal to a specified value. It is a simple and robust method that is applicable when the data do not meet the assumptions of parametric tests, such as when the data

The given problem can be solved using the one-sample sign test to test the null hypothesis that the mean of the population is 19.4 minutes against the alternative hypothesis that it is not 19.4 minutes.

(a) Using Table I:

Step 1: Set up the hypotheses:

Null hypothesis (H0): The mean of the population is 19.4 minutes.

Alternative hypothesis (H1): The mean of the population is not 19.4 minutes.

Step 2: Determine the test statistic:

We will use the sign test statistic, which is the number of positive or negative signs in the sample.

Step 3: Set the significance level:

The significance level is given as 0.05.

Step 4: Perform the sign test:

Count the number of observations in the sample that are greater than 19.4 and the number of observations that are less than 19.4. Let's denote the count of observations greater than 19.4 as "+" and the count of observations less than 19.4 as "-".

In the given sample, there are 5 observations greater than 19.4 (18.1, 20.3, 19.3, 19.5, and 20.0), and 15 observations less than 19.4 (18.3, 15.6, 16.8, 17.6, 16.9, 17.0, 16.5, 18.6, 18.8, 19.1, 17.5, 18.5, and 18.0).

Step 5: Calculate the test statistic:

The test statistic is the smaller of the counts "+" or "-". In this case, the test statistic is 5.

Step 6: Determine the critical value:

Using Table I, for a significance level of 0.05 and a two-tailed test, the critical value is 3.

Step 7: Make a decision:

Since the test statistic (5) is greater than the critical value (3), we reject the null hypothesis.

(b) Using the normal approximation to the binomial distribution:

Alternatively, we can use the normal approximation to the binomial distribution when the sample size is large. Since the sample size is 20 in this case, we can apply this approximation.

Step 1: Set up the hypotheses (same as in (a)).

Step 2: Determine the test statistic:

We will use the z-test statistic, which is calculated as (x - μ) / (σ / √n), where x is the observed number of successes, μ is the hypothesized value (19.4), σ is the standard deviation of the binomial distribution (calculated as √(n/4), where n is the sample size), and √n is the standard error.

Step 3: Set the significance level (same as in (a)).

Step 4: Calculate the test statistic:

Using the formula for the z-test statistic, we get z = (5 - 10) / (√(20/4)) ≈ -2.24.

Step 5: Determine the critical value:

For a significance level of 0.05 and a two-tailed test, the critical value is approximately ±1.96.

Step 6: Make a decision:

Since the test statistic (-2.24) falls outside the range of the critical values (-1.96 to 1.96), we reject the null hypothesis.

Rework Exercise 16.16 using the signed-rank test based on Table X:

To provide a more accurate solution, I would need additional information about Exercise 16.16 and Table X.

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Answer:

Not equivalent

Step-by-step explanation:

if we simplify our two equations we get 6x + 2y and 4x + 4y. Which is not equivalent to each other

Answer:

Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = \(\frac{1}{2}bh\)

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =  \(\frac{1}{2}*4*2.24 =\) 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2

For the rectangular sections of the roof, area is

A = \(lh\)

where \(l\) is the length of the rectangle = 5 ft

h is the height of the rectangle = 3 ft

A = 5 x 3 = 15 ft^2

For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2

For the bottom face, area is

A = \(lw\)

where \(l\) is the length of the house = 5 ft

w is the width of the house = 4 ft

A = 5 x 4 = 20 ft^2

Surface area of the roof of the dog kennel is

8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2

\(\displaystyle (f-g)=f(x)-g(x) =3x^3+4x^2-8x-2-(3x-5 )= \\\\ \boxed{3x^3+4x^2-11x+3}\)

The rancher has 5,280 acres left after selling off 5 quarter sections.

There are different ways to approach this problem, but one possible method is to convert all the sections and subsections to acres and then subtract the number of acres sold.

One section is equal to 640 acres (1 mile x 1 mile)

One-half section is equal to 320 acres (1/2 mile x 1 mile)

The one-quarter section is equal to 160 acres (1/2 mile x 1/2 mile)

The rancher owns:

8 full sections x 640 acres/section = 5,120 acres

3 half sections x 320 acres/half section = 960 acres

Total = 6,080 acres

The rancher sells off:

5 quarter sections x 160 acres/quarter section = 800 acres

The number of acres left is:

6,080 acres - 800 acres = 5,280 acres

Therefore, the rancher has 5,280 acres left after selling off 5 quarter sections.

Answer: There are 5,280 acres left.

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Every year, 1800 units crossover point. The process focus is less expensive for volumes over 1800.

When all tax credits have been used up by a limited partnership and the limited partners are left with a tax burden, that moment is known as the crossover point.

When both projects have positive values, the crossover point is formed by the intersection of two IRR curves.

The weighted average cost of capital, also known as the crossover rate, is the rate of return at which the net present values (NPV) of two projects are equal.

The rate of return at which the net present value profiles of two projects cross each other is what this term denotes.

So, annual crossover sales are 1800 units.

Process emphasis is less expensive and less important for volumes under 1800 units; repeated manufacturing concentration is less expensive and less important for volumes exceeding 1800 units.

Fixed cost ÷ variable cost

$90000÷50 =$1800

$9,000÷5=$1800

Therefore, every year, 1800 units cross over. The process focus is less expensive for volumes over 1800.

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Correct question:

A product is currently made in a process-focused shop, where fixed costs are $9,000 per year and variable costs are $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacturing. The new process would have fixed costs of $90,000, and variable costs of $5. The cross over is at 1800 units annually. for volumes over 1800, the process focus is cheaper.

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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To measure an overbought or oversold market level, a technical analyst would typically c)use one or more price oscillators.

When assessing whether a market is overbought or oversold, technical analysts often turn to price oscillators. Price oscillators are technical indicators that provide insights into the momentum and potential reversal points in a market. These indicators are derived from price data and offer a visual representation of the relationship between current prices and historical price movements.

Price oscillators, such as the Relative Strength Index (RSI), Stochastic Oscillator, or Moving Average Convergence Divergence (MACD), measure the speed and magnitude of price changes. They help identify when a market has moved too far in one direction, signaling potential reversal or exhaustion. An overbought condition indicates that prices have risen too steeply and may be due for a pullback, while an oversold condition suggests that prices have declined excessively and could potentially rebound.

By analyzing the readings and patterns of these price oscillators, technical analysts can identify overbought or oversold levels. This information helps traders make more informed decisions, such as entering or exiting positions, adjusting risk management strategies, or looking for potential trading opportunities based on anticipated market reversals. However, it is important to note that technical analysis is just one approach to market analysis, and it should be used in conjunction with other forms of analysis and risk management techniques.

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Answer: 11

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

because 40 devided by 5 equals 8 so thats how many hours in the afternoon

x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1

x = -1, y = 6, z = 1 is the solution.

Ax = \(\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right]\) \(\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\)

and b = \(\left[\begin{array}{ccc}6\\14\\30\end{array}\right]\)

the augmented matrix is [A:B] = \(\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right]\)

we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.

operating R₂→R₂-R₁ , R₃→R₃-R₁

[A:B] = \(\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right]\)

operating, R₃→R₃-3R₃

~  \(\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right]\)

which is the row echelon, form of the matrix [A:B]

we have rank of [A:B] = the number of the non zero rows in echelon form = 2

also by the same elementary transformation we get,

A ~ \(\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right]\)

∴ rank of A = 2

since rank A = rank  [A:B] = 2 < number of unknowns

therefore, the given equation are consistent and will have an infinite number of solutions.

We see that the given system of equations is equivalent to the matrix equation

\(\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right]\)  \(\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\)  =  \(\left[\begin{array}{ccc}6\\8\\0\end{array}\right]\)

which gives the equations x + y + z = 6 ........(1)

and y + 2z = 8 .......(2)

from (2), y = 8 - 2z, putting the value of y in (1) we get,

x = 6 - y - z = 6 (8 - 2z) z = z - 2

taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,

if k = 1

x = -1, y = 6, z = 1 is the solution.

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Answer:

What does the "+8" mean in the expression 2x + 8?

The +8 is the 8 more advertisement orders received on Friday.

It's 8 more than x.

How many more advertisements were ordered on Friday than Thursday

8

The number of days

2

The number of advertisement ordered on Friday

x + 8

The total number of advertisement on both days

2x + 8

Answer:

A

Step-by-step explanation:

I took the test

Answer:

36 inches = 0.000568182 miles

there is a horizontal asymptote at y = 0 (the x-axis).

After finding the asymptotes and plotting some points, we can sketch the curve of the function.

The curve approaches the asymptotes but never touches them.

The curve is also symmetric with respect to the y-axis since the function is even.

its graph is as follows: Graph of y = x / (x² - 9)

Firstly,

to sketch the curve of the function y = x / (x² - 9) for the values given,

we can follow these steps:

Replace x by the values given in the domain to obtain their corresponding images.

In this case, the domain is D = {x | x ≠ -3 and x ≠ 3}, because x cannot be -3 or 3 for the function to be defined.

For example, for x = 1, we have y(1) = 1 / (1² - 9) = -1/8.

Therefore, the point (1, -1/8) belongs to the curve.

Repeat the previous step for some more values of x, for instance x = -2, -1, 0, 2, 4, 5, 6, etc.

We can also find the horizontal and vertical asymptotes of the function.

To find the vertical asymptotes, we set the denominator equal to zero, that is x² - 9 = 0.

Solving this equation, we obtain x = ±3.

Thus, there are vertical asymptotes at x = 3 and x = -3.

To find the horizontal asymptote, we need to compare the degrees of the numerator and denominator of the function. In this case, both have degree 1, so we can find the horizontal asymptote by dividing the leading coefficients of both polynomials.

That is:

y = 1 / x.

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Step-by-step explanation:

|4x + 8| > 2

Therefore 4x + 8 > 2 or 4x + 8 < -2.

When 4x + 8 > 2, 4x > -6, x > -1.5.

When 4x + 8 < -2, 4x < -10, x < -2.5.

Hence, x < -2.5 or x > -1.5.

Answer:

x= -3/2

4x < -6

x = -3/2

.............

Answer:

36

Step-by-step explanation:

The wavelength of the wave is 0.125 m.

A periodic wave's wavelength is its spatial period, or the length over which its shape repeats. It is a property of both traveling waves and standing waves as well as other spatial wave patterns. It is the distance between two successive corresponding locations of the same phase on the wave, such as two nearby crests, troughs, or zero crossings.

A sinusoidal waveform's wavelength (λ) is determined by the equation

λ= ν/f,

where ν denotes the wave's phase speed (or magnitude of the phase velocity) and f denotes its frequency.

According to the given information,

Speed of transverse wave, ν = 25 m/s

Frequency, f = 200 Hz

We know the formula, λ= ν/f

By substituting the values, we get

λ = 25/200

λ = 0.125m

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This question is related to Physics.

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

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Answer:

Copy this onto a piece of graph paper

Step-by-step explanation:

when graphing you want to make sure  that the slope is correct and the y-intercept is the same

The estimated values of f '(0), f '(1/2), f '(2), f '(3), and f '(4) are approximately 0, positive, greater, greater, and greater, respectively, based on the graph of f(x) = \(x^{3}\)

By analyzing the graph of f(x) = x^3, we can estimate the values of the derivatives f '(0), f '(1/2), f '(2), f '(3), and f '(4) by zooming in on the graph using a graphing device.

When x is close to 0, the slope of the graph of f(x) is also close to 0. Therefore, we can estimate that f '(0) is approximately 0.

Similarly, when x is close to 1/2, the slope of the graph of f(x) is positive and relatively steep. Hence, we can estimate that f '(1/2) is a positive value.

As x increases, the slope of the graph of f(x) becomes steeper. Therefore, we can estimate that f '(2) is greater than f '(1/2) and f '(3) is greater than f '(2).

Finally, as x gets larger, the slope of the graph of f(x) continues to increase but at a decreasing rate. Hence, we can estimate that f '(4) is greater than f '(3) but less than f '(2).

By zooming in on the graph of f(x) using a graphing device, we can obtain more accurate estimations for the values of f '(0), f '(1/2), f '(2), f '(3), and f '(4).

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The distance of closest approach of an alpha particle to the center of a lead-208 nucleus is about 7.2 x 10^-15 m, which is in good agreement with the given value of 7 x 10^-15 m.

To calculate the distance of closest approach of an alpha particle to the center of the nucleus, we can use the classical formula for the minimum distance of approach of a charged particle to a point charge:

r = k * (q1 * q2 / E)

where r is the distance of closest approach, k is Coulomb's constant, q1 and q2 are the charges of the two particles, and E is the kinetic energy of the alpha particle.

For an alpha particle (which is a helium nucleus) approaching a nucleus, we can assume that the nucleus is a point charge with charge Z e, where Z is the atomic number and e is the elementary charge. The charge of the alpha particle is 2 e.

The kinetic energy of the alpha particle can be related to its velocity v as:

E = 1/2 * m * v^2

where m is the mass of the alpha particle.

Now, let's plug in the values and calculate the distance of closest approach:

r = k * (q1 * q2 / E)

= k * (2 e * Z e / (1/2 * m * v^2))

= k * (2 * Z * e^2 / m * v^2)

Plugging in the values of the constants:

k = 8.99 x 10^9 N m^2 / C^2

e = 1.6 x 10^-19 C

m = 6.64 x 10^-27 kg (mass of alpha particle)

v = 2.2 x 10^6 m/s (typical velocity of alpha particles in radioactive decay)

Z = atomic number of the nucleus (let's assume Z = 82 for lead-208, which is a common target for alpha decay)

r = 8.99 x 10^9 N m^2 / C^2 * (2 * 82 * (1.6 x 10^-19 C)^2 / (6.64 x 10^-27 kg * (2.2 x 10^6 m/s)^2))

= 7.2 x 10^-15 m

Therefore, the distance of closest approach of an alpha particle to the center of a lead-208 nucleus is about 7.2 x 10^-15 m, which is in good agreement with the given value of 7 x 10^-15 m.

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The vector function r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). is
(a) r'(t) = 3ti - 3j + 15t²k

(b) r"(t) = 3i + 15tk

(c) r'(t) · r"(t) = 9t - 45t²

(d) r'(t) x r"(t) = -90t²i - 45tj - 9k

To find the derivatives of the vector function r(t) = 3²³i - 3tj + 5t³k, we differentiate each component of the vector with respect to t.

(a) To find r'(t), we differentiate each component separately:

r'(t) = (d/dt)(3²³i) - (d/dt)(3tj) + (d/dt)(5t³k)

= 0i - 3j + 15t²k

= 3ti - 3j + 15t²k

(b) To find r"(t), we differentiate each component of r'(t) with respect to t:

r"(t) = (d/dt)(3ti) - (d/dt)(3j) + (d/dt)(15t²k)

= 3i + 0j + 15tk

= 3i + 15tk

(c) To find r'(t) · r"(t), we take the dot product of r'(t) and r"(t):

r'(t) · r"(t) = (3ti - 3j + 15t²k) · (3i + 15tk)

= 9t - 45t²

(d) To find r'(t) x r"(t), we take the cross product of r'(t) and r"(t):

r'(t) x r"(t) = (3ti - 3j + 15t²k) x (3i + 15tk)

= -90t²i - 45tj - 9k

In summary, r'(t) = 3ti - 3j + 15t²k, r"(t) = 3i + 15tk, r'(t) · r"(t) = 9t - 45t², and r'(t) x r"(t) = -90t²i - 45tj - 9k.

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Answer:

D should be right

Step-by-step explanation: