Can someone please help me with this ​

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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Answer:

The equation have no solution.

3x - 4 = 3x + 4

-4 = 4

The statement is false

Answer:

Has no solution

Step-by-step explanation:

The two vectors parallel to QP with a length of 3 are:

v1 = (2/sqrt(29), -5/sqrt(29)) and v2 = (6/sqrt(29), -15/sqrt(29)).

To find two vectors parallel to QP with a length of 3, we need to determine the direction of the vector QP and then scale it to the desired length.

The vector QP can be obtained by subtracting the coordinates of point P from those of point Q:

QP = Q - P = (3, -4) - (1, 1) = (2, -5).

To obtain a vector parallel to QP with a length of 3, we can normalize QP (divide it by its magnitude) and then scale it to the desired length.

The magnitude of QP is given by:

|QP| = sqrt((2)^2 + (-5)^2) = sqrt(29).

The normalized vector of QP, let's call it v1, is:

v1 = QP / |QP| = (2/sqrt(29), -5/sqrt(29)).

To obtain a vector parallel to QP with a length of 3, we can scale v1 by a factor of 3:

v2 = 3 * v1 = (6/sqrt(29), -15/sqrt(29)).

Therefore, the two vectors parallel to QP with a length of 3 are:

v1 = (2/sqrt(29), -5/sqrt(29)) and v2 = (6/sqrt(29), -15/sqrt(29)).

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Answer:

I think it is either a or b

Step-by-step explanation:

Answer: x is greater than or equal to 1/5

Step-by-step explanation:

The value of -3( 1 - 5x) CANNOT be negative.

Using this information we know that 1-5x is negative.

We can write:

1-5x >= 0

1>=5x

x>=1/5

The correct option is D. Saving $10 this month, plus $4 per day.

The table of values is shown below:| Day | Savings | |--------|-----------| | 1      | 14        | | 2      | 18        | | 3      | 22        | | 4      | 26        |

To find which of the given savings plans is modeled by the table of values given above, we have to look at the pattern that the table follows and then select the correct option from the given alternatives.

Let us analyze the given table: On day 1, the savings are $14On day 2, the savings are $18, an increase of $4 from the savings of day 1. On day 3, the savings are $22, an increase of $4 from the savings of day 2.On day 4, the savings are $26, an increase of $4 from the savings of day 3.

Therefore, the savings increase by $4 every day. Now, let us see which option is modeled by this pattern.

A. Saving $6 this month, plus $4 per day: The savings per day is $4, but the initial amount of savings is $6 and not $14. Hence, this option is incorrect.B. Saving $10 this month, plus $6 per day: The savings per day is $4, but the initial amount of savings is $10 and not $14.

Hence, this option is also incorrect.C. Saving $0 this month, plus $10 per day: The savings per day is $10, which is more than the amount of savings on day 1 ($14). Hence, this option is also incorrect.D. Saving $10 this month, plus $4 per day: The savings per day is $4 and the initial amount of savings is $10. This matches the pattern of the table of values given above.

Hence, the correct option is D. Saving $10 this month, plus $4 per day.

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To solve this problem, we need to first find the average number of shoppers in the new store at any time.

We know that during business hours, 90 shoppers per hour enter the store and each stays an average of 12 minutes.

To find the average number of shoppers at any time, we need to convert the time each shopper spends in the store to hours:

12 minutes = 0.2 hours

So, on average, each shopper takes up 0.2 hours in the store.

Therefore, the average number of shoppers in the new store at any time is:

90 shoppers/hour x 0.2 hours/shopper = 18 shoppers

Now we can find the percent less that the average number of shoppers in the new store is compared to the original store:

Percent less = (Original - New) / Original x 100%

Percent less = (45 - 18) / 45 x 100%

Percent less = 27 / 45 x 100%

Percent less = 60%

So the answer is A. 60.
To find the average number of shoppers in the new store at any time, we can use the formula:

Average number of shoppers at any time = (Number of shoppers per hour * Average time spent in store) / 60

For the new store:
Average number of shoppers at any time = (90 shoppers per hour * 12 minutes) / 60
Average number of shoppers at any time = 1080 / 60 = 18 shoppers

Now we will find the percentage difference between the average number of shoppers in the original store (45 shoppers) and the new store (18 shoppers):

Percentage difference = ((Original store shoppers - New store shoppers) / Original store shoppers) * 100
Percentage difference = ((45 - 18) / 45) * 100
Percentage difference = (27 / 45) * 100 = 60%

So the average number of shoppers in the new store at any time is 60% less than the average number of shoppers in the original store at any time. Your answer: A. 60

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Answer:

54°

Step-by-step explanation:

If GJ is an angle bisector that the 2 angles are congruent so their measures are equal

7x -9 = 2x +36

7x -2x = 36 +9

5x = 45

x= 45/5 = 9

measure of angle FGH = 7x-9 = 7*9 -9 = 54°

The specific values of a, b, and c, or any additional conditions or constraints, it is not possible to determine the exact function f.

To provide more specific information about the function f, to the form of the function. Typically, the height of an object in free fall modeled using a quadratic function.

A common form of a quadratic function is:

f(t) = at² + bt + c

Where:

f(t) represents the height of the ball at time t.

t represents time in seconds.

a, b, and c are constants that determine the shape and position of the quadratic curve.

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The maximum height of the ball is 18.25 meters.

Given, Sarah kicked the ball in the air. The function f models the height of the ball (in meters) as a fiction if time (in seconds) after Sarah kicked it.

The height of the ball is modeled by the function f(t) where t is time in seconds after the ball is kicked .The height of the ball can be modeled as a quadratic function given by

f(t) = -5t² + 15t + 2where, f(t) is the height of the ball (in meters) and t is the time (in seconds) after Sarah kicked the ball.

Let us find the maximum height of the ball:

Maximum height of the ball is given by the vertex of the parabola.

The vertex of the parabola is given by, x = -b / 2a

Here, a = -5, b = 15

So, x = -15 / 2 (-5) = 1.5 sec

The maximum height of the ball is given by

f(1.5) = -5 (1.5)² + 15 (1.5) + 2 = 18.25 m

Therefore, the maximum height of the ball is 18.25 meters.

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The major benefit of enterprise application integration (EAI) is that it allows different applications and systems within an organization to seamlessly communicate and share data.

This integration eliminates data silos and enables real-time data exchange, leading to improved efficiency, productivity, and decision-making within the organization.

By implementing EAI, businesses can achieve the following benefits:

1. Enhanced Data Accuracy and Consistency: EAI ensures that data is synchronized and consistent across different systems, eliminating the need for manual data entry and reducing the risk of errors or discrepancies.

2. Increased Efficiency and Productivity: EAI automates the flow of information between applications, reducing the need for manual intervention and streamlining business processes.

This leads to improved efficiency and productivity as employees spend less time on repetitive tasks.

3. Improved Decision-Making: EAI provides a unified view of data from various systems, enabling better analysis and decision-making. Decision-makers have access to real-time and accurate information, allowing them to make informed and timely decisions.

4. Cost Savings: By integrating existing applications instead of developing new ones from scratch, EAI can help businesses save costs. It reduces the need for duplicate systems, minimizes data duplication, and optimizes IT infrastructure.

5. Scalability and Flexibility: EAI allows organizations to easily integrate new applications or systems as their needs evolve. It provides a flexible framework that can accommodate future growth and changes in business requirements.

Overall, the major benefit of enterprise application integration is the ability to achieve seamless connectivity and data exchange between systems, leading to improved efficiency, productivity, and decision-making in an organization.

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If chuck earns additional 40,000 of taxable income, 23.52% the marginal tax rate on this income

Chuck, a single taxpayer, earns $76,000 in taxable income and $1 in interest from an investment in city of heflin bonds.

Tax on $76,000

4,617.5 + (76,000 - 40,125) * 22% = 12,510.0

Taxable income 76,000 + 40,000 = 116,000

Tax on $116,000  

14,605.5 + (116,000 - 85,525) * 24% = 21,919.5

Marginal tax rate

(21,919.5 - 12,510) / 40,000 = 23.52%

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Answer:

Working alone, the faster pipe can do the work in 3 hrs; the slower pipe can do the work in 6 hrs.

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

before coming to the head we have like 40 bones there

The answer choice that includes all solutions to the inequality and identifies the interval(s) containing viable completion times of machine 1 is - **x ≤ 8** (inclusive) represents all solutions to the inequality, and the interval **[0, 8]** contains viable completion times of machine 1.

To determine the solution to an inequality, we need to consider the given conditions. Let's assume the inequality is **x + 2 < 10**, where x represents completion times of machine 1.

To solve the inequality, we subtract 2 from both sides:

x + 2 - 2 < 10 - 2

x < 8

This inequality indicates that the completion times of machine 1 (represented by x) must be less than 8 in order to satisfy the condition.

Since the inequality is strict (**x < 8**), the solution does not include the value 8 itself. However, if the inequality were non-strict (**x ≤ 8**), it would include the value 8 as well.

Hence, the answer choice **x ≤ 8** includes all solutions to the inequality. Now, to identify the interval(s) containing viable completion times of machine 1, we consider the range of values for x.

In this case, the interval [0, 8] represents viable completion times for machine 1 because it includes all values from 0 to 8, inclusive. Any completion time within this interval, including the endpoints, would satisfy the inequality.

Therefore, the answer choice that includes all solutions to the inequality is **x ≤ 8**, and the interval **[0, 8]** contains viable completion times of machine 1.

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Answer:

We need a picture p-p

Step-by-step explanation:

We can solve this problem by using casework on the number of collinear points in each triangle.

If all three points are collinear, the triangle has zero area, so we want to count triangles with no more than two collinear points.

Case 1: Three points in a row (horizontal)

There are $4$ rows of points, and each row has $\binom{3}{1} = 3$ ways to choose a set of $3$ points. Therefore, there are $4 \cdot 3 = 12$ triangles with three points in a row.

Case 2: Three points in a column (vertical)

This case is the same as Case 1, so there are also $12$ triangles with three points in a column.

Case 3: Two points in a row, one point in a different row

There are $4$ rows of points, and each row has $\binom{3}{2} = 3$ ways to choose a set of $2$ points. For each choice of two points, there are two other rows that contain the third point of the triangle. Therefore, there are $4 \cdot 3 \cdot 2 = 24$ triangles in this case.

Case 4: Two points in a column, one point in a different column

This case is the same as Case 3, so there are also $24$ triangles with two points in a column.

Case 5: Two points in a diagonal, one point not on the diagonal

There are two diagonals that contain $4$ points each. Each diagonal has $\binom{4}{2} = 6$ ways to choose a set of $2$ points. For each choice of two points, there are $2$ other points that can be paired with it to form a triangle. Therefore, there are $2 \cdot 6 \cdot 2 = 24$ triangles in this case.

Case 6: All other triangles

All other triangles have one point in each of three different rows, or one point in each of three different columns. There are $\binom{4}{3} = 4$ ways to choose $3$ rows, and each row has $4$ points, so there are $4^3 = 64$ triangles with one point in each of three different rows. The same is true for triangles with one point in each of three different columns. Therefore, there are $2 \cdot 64 = 128$ triangles in this case.

Putting it all together, the total number of triangles with positive area is $12+12+24+24+128=\boxed{200}$.

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a) The set {1, 2, 3} does not represent vectors, but rather a collection of scalars. Therefore, there are no vectors in {1, 2, 3}.

b) The number of vectors in "col a" cannot be determined without additional context or information. "Col a" could refer to a column vector or a collection of vectors associated with a variable "a," but without further details, the exact number of vectors in "col a" cannot be determined.

c) Without knowing the specific context of "p" and "col a," it is impossible to determine if "p" is in "col a." The inclusion of "p" in "col a" would depend on the definition and properties of "col a" and the specific value of "p."

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We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.

PART 1

Let the probability that the marble is red be P(r).

Therefore,

This gives,

Therefore, the probability that the marble is red is:

ANSWER= 0.297

PART 2:

Let the probability of picking odd-numbered balls be P(o)

Therefore,

We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.

Therefore,

The probability of picking odd-numbered balls is

ANSWER = 0.5

PART 3:

Let the probability of picking a red or odd-numbered ball be P(r U o)

Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).

p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.

Therefore,

This implies that,

Hence, the probability of picking a red or odd-numbered ball is

ANSWER = 0.648

PART 4:

Let the probability of picking a blue or even-numbered ball be P(b U e)

Therefore,

From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,

p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.

p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls

Therefore,

Therefore, the probability of picking a blue or an even ball is:

ANSWER = 0.852

Answer:

y=19

Step-by-step explanation:

First you have to find x.

1. 3x+22=4x-6.    do this because 3x+22 and 4x-6 are the same

2. x-6=22.  you have to subtract 3x from both sides and 4x minus 3x is just x

3. x=28.     you have to add 6 to 22

4. 5y+11=3(28)+22. They are the same and now put 28 for x

5. 5y+11=106. you added everything up on the right

6.5y=95 subtracted 11 from 106

7. y=19. divided 5 by 95

Answer:

Answer:

y=19

Step-by-step explanation:

First you have to find x.

1. 3x+22=4x-6.    do this because 3x+22 and 4x-6 are the same

2. x-6=22.  you have to subtract 3x from both sides and 4x minus 3x is just x

3. x=28.     you have to add 6 to 22

4. 5y+11=3(28)+22. They are the same and now put 28 for x

5. 5y+11=106. you added everything up on the right

6.5y=95 subtracted 11 from 106

7. y=19. divided 5 by 95

Step-by-step explanation:

Answer:

[-8, 6]

Step-by-step explanation:

Domain is the x values. Look at the smallet x value, in this case -8, and the largest, in this case 6, and write them like a point using [] not (). You use [ or ] for numbers and ( or ) for infinity signs.

Answer:

Answer is 34.

Step-by-step explanation:

I hope it's helpful!

Answer:

34

Percentage Calculator: What is 40 percent of 85? = 34.

Answer:

$12.90/ 12.9

Step-by-step explanation:

divide 15 % by 86

Answer:

0

Step-by-step explanation:

A six-sided die has the numbers 1, 2, 3, 4, 5, and 6, not 7. And even is 7 was on there the probability would be 1/6 whihc is approximently 0.167 which is about 0.2 so the probability is 0.

The probability of rolling a seven is 0.

The probability of an event occurring is defined by probability.

The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given:

A single six-sided die is rolled.

So, the Sample space is= (1, 2, 3, 4, 5, 6}

As, there is no possibility of getting number 7 on the dice.

Hence, the probability of rolling a seven is 0.

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Answer:

41.44

the tax is 2.88$

the tip is 5.88$

bill is 32.68

add equals 41.44$

It appears that from graph that the function is increasing in the interval (-∞,-1) and (1,∞). Also the function is decreasing in the interval (-1,1) and (0.0.5).The function is not constant anywhere.

To check if this is correct, we will find the relative extrema of the function,

f(x) = x³-x²-2x+3

Find it derivative f'(x) = 3x²-2x-2

f'(x) = 0

⇒ x = 2 ± √(4+24)/3

      = 3.77 , -1.1

Find the second derivative f''(x) = 6x -2

f''(3.77) = 20.62>0

So the function has a relative minimum at x = 3.77.

f''(-1.1) = -8.6<0

So the function has a relative maximum at x = -1.1

Now we can conclude with the intervals where the function is increasing is before the relative maximum and after the relative minimum.

i.e., the intervals (-∞,-1) and (3.5,∞) [rounding to the nearest 0.5 unit]

So the interval in which the function is decreasing is between the relative maximum and minimum. i.e.,  the interval (-1, 3.5)

The function is nowhere constant.

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Answer:

20

Step-by-step explanation:

Total no of plants in a garden = 36

The ratio of tomato plants to cucumber plants to be 4:5.

Let tomato plants are 4x and cucumber plants is 5x.

ATQ,

4x+5x=36

9x = 36

x = 4

For cucumber plant, 5x = 5(4) = 20

So, there are 20 cucumber plants will be in Reggie's garden