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Using the derivative of the velocity, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.

Given:

Acceleration function, a(t) = 2sin(t) + 1

Initial velocity, v(0) = 0

Initial position, s(0) = 3

To find:

Velocity function, v(t)

Position function, s(t)

Average value of the position function from t = 2 seconds to t = 5 seconds

Solution:

We know that acceleration is the derivative of velocity, and velocity is the derivative of position. So we can find the velocity and position functions by integrating the acceleration function.

Velocity function:

\(v(t) = \int a(t) dt\\v(t) = \int (2sin(t) + 1) dt\\v(t) = -2cos(t) + t + C1\)

We know that the initial velocity, v(0) = 0. Substituting this value in the above equation, we get:

\(0 = -2cos(0) + 0 + C1\\C1 = 2\)

Therefore, the velocity function is:

\(v(t) = -2cos(t) + t + 2\)

Position function:

\(s(t) = \int v(t) dt\\s(t) = \int (-2cos(t) + t + 2) dt\\s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + C2\)

We know that the initial position, s(0) = 3. Substituting this value in the above equation, we get:

\(3 = 2sin(0) + 0 + 0 + C2\\C2 = 3\\\)

Therefore, the position function is:

\(s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + 3\)

Average value of the position function from t = 2 seconds to t = 5 seconds:

We can find the average value of the position function using the following formula:

\(Avg = (1/(b-a)) * \int(a,b) f(t) dt\)

Here, a = 2 and b = 5. So, substituting the values in the above formula, we get:

\(Avg = (1/(5-2)) * \int(2,5) (2sin(t) + \frac{1}{2} t^2 + 2t + 3) dt\\Avg = \frac{1}{3} * [ -2cos(t) + 1/6 t^3 + t^2 + 2t ] \eval(2,5)\\\)

\(Avg = \frac{1}{3} * [ (-2cos(5) + 1/6 (5^3) + 5^2 + 25) - (-2cos(2) + 1/6 (2^3) + 2^2 + 22) ]\\Avg = 14.5\)

Therefore, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.

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Answer:

0.2637

Step-by-step explanation:

Population size is top 15 ranking restaurants.

Number of draws = 3

Number of observed successes = 5

Probability formula :  [r . x } { n -r] [n - x]

solving the equation we get 24 / 91 which is approximately 0.2637

Answer:

f slopes was  \(\frac{3}{2}\)  ,the y intercepts was -3

g slopes was \(-\frac{1}{3}\),the y intercepts was -2

Step-by-step explanation:

g slopes :

functions g has point (0,-2) and (3,-3)

the slopes =\(\frac{-2-(-3) }{0-3} =-\frac{1}{3}\)

Answer:

2nd number is correct

Here's your solution

=> 2p(-3p^2 + 4p - 5)

=> multiple 2p with whole

=>. -6p^3 + 8p^2 - 10p

this is your answer

hope it helps

Answer:

It means if you graph the function, the line is straight.

also s p a m

Answer:

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.

Step-by-step explanation:

plzz mark brianliest i needdddd

Answer:

D. 4

Step-by-step explanation:

Use rise over run, (y2 - y1) / (x2 - x1)

Plug in the points:

(y2 - y1) / (x2 - x1)

(20 - 12) / (4 - 2)

8 / 2

= 4

So, the slope is 4.

Step-by-step explanation:

The MAD represents the average distance each data value is away from the mean. A data distribution can be described in terms of its center, spread, and shape. The center can be measured by the mean. The spread can be measured by the mean absolute deviation (MAD).

Answer:

Step-by-step explanation:

part a = 1 x 4

part b = b

Answer:

y=2x+25

the graph is B.

Step-by-step explanation:

Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x

Part B: width is 50 meters.

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that the variables are expressed as;

We then have that;

l = 2x + 10

Substitute the values

5500 = (2x + 10)(x)

expand the bracket

5500 = 2x² + 10x

2x² + 10x - 5500

x² + 5x - 2750

x² + 55x - 50x - 2750

x(x + 55) - 50(x + 55)

x = 50 meters

Length = 2(50) + 10

Length = 100 + 10 = 110 meters

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The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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The required length of the rectangle is 12/5 feet and the width is 9/5 feet.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's denote the length of the rectangle as L and the width as W.

From the problem statement, we know that:

3L = 4W (equation 1)

We also know that the perimeter P is given by:

P = 2L + 2W = 8 2/5 feet

Multiplying both sides by 5 to get rid of the fraction, we get:

10L + 10W = 42

Dividing by 2, we get:

5L + 5W = 21 (equation 2)

Now we can use equations 1 and 2 to solve for L and W.

First, we can substitute equation 1 into equation 2 to get an equation in terms of W:

5L + 15L/4 = 21

Multiplying both sides by 4, we get:

20L + 15L = 84

35L = 84

L = 84/35 = 12/5 feet

Now we can substitute the value of L into equation 1 to get the value of W:

3L = 4W

3(12/5) = 4W

W = 9/5 feet

Therefore, the length of the rectangle is 12/5 feet and the width is 9/5 feet.

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Answer:

See below.

Step-by-step explanation:

7x^2 = 343                     Divide both sides by 7

7x^2/7 = 343/7

x^2 = 49                         Take the square root of both sides.

sqrt(x^2) = sqrt(49)

x = +/- 7

Answers

I think the last two are kind of iffy. I'm not sure you can call them solutions, but the question probably assumes they are. If you use all four answers and get it wrong, them submit +7 and - 7.  

The minimum number of trips the bus will have to make to accommodate everyone is 5.

To find the minimum number of trips the bus needs to make, we divide the total number of people by the capacity of the bus.

1. Divide the total number of people (330) by the capacity of the bus (68):

  330 / 68 = 4.85 (rounded to the nearest whole number)

2. The result is approximately 4.85, which means that 4 trips will not be enough to accommodate everyone.

3. Since we can't have a fraction of a trip, we need to round up to the nearest whole number to ensure that everyone is accommodated.

4. Therefore, the minimum number of trips the bus will have to make is 5, as it will require 5 full trips to transport all 330 people.

It's important to note that on the fifth trip, the bus will not be completely full, as only 10 people will be left to transport. However, this is the minimum number of trips needed to ensure that everyone can go sight-seeing on the bus.

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Answer:

-30

Step-by-step explanation:

7 - 2 • 5 + 9 • 3

7 - 10 + 27

7 - 37

-30

\(\huge\text{Hey there!}\)

\(\mathsf{7 - 2 \times 5 + 9 \times 3}\)

\(\mathsf{= 7 - 2(5) + 9(3)}\)

\(\mathsf{= 7 - 10 + 9(3)}\)

\(\mathsf{= 7 - 10 + 27}\)

\(\mathsf{= -3 + 27}\)

\(\mathsf{= 24}\)

\(\huge\text{Therefore, your answer should be: }\)

\(\huge\boxed{\textsf{Option A. 24}}\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

The Median and the modal sales is 45 and 49 respectively.

A median simply means the middle number when the number are arranged in ascending order. The mode is the number that appears most.

Since the number of sales of cars sold from January to November are 28, 20, 49, 29, 38, 40, 45, 49, 50, 55 and 60, this will be arranged as:

20, 28, 29, 38, 40, 45, 49, 49, 50, 55, 60

Therefore, the middle number is 45 and mode is 49.

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Answer:

I do not know

Step-by-step explanation:

Answer:

The probability is  \(p(n ) = 3.18*10^{-5}\)

Step-by-step explanation:

From the question we are told that

     The population size is  N =  31

      The sample size  n =  4  

Generally the number of way by which the n  can be selected from N is mathematically represented as

          \(\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}\)

=>       \(\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}\)

=>       \(\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }\)

=>        \(\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}\)

=>        \(\left 31} \atop {}} \right. C_4 = 31465\)

The number of ways of selecting a particular sample size is  is   \(k = 1\)

Therefore the probability of each simple random sample in this​ case is mathematically evaluated as  

           \(p(n ) = \frac{1}{31465}\)  

           \(p(n ) = 3.18*10^{-5}\)

Answer:

SAS

Step-by-step explanation:

2 sides and 1 angle are congurent

Answer:

The S.A.S rule can be used to prove the following triangles congruent.

Step-by-step explanation:

The S.A.S rule is when 2 sides and the angle in that triangle are equal to the 2  sides and angle of the other triangle, then u can considere that triangle congruent.

The definition of a ray is a part of a line that has one endpoint and extends indefinitely in one direction

A ray is part of a line that has one endpoint and extends indefinitely in one direction and has the folowing properties.

So, the definition of a ray is a part of a line that has one endpoint and extends indefinitely in one direction.

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The size of the file that has been downloaded is 50 megabytes.

Given total size of the file is 244 megabytes

The percentage that completed the download till now = 18.5%

We have to determine the size of the file downloaded till now can be written as

= 18.5 % of 244

= 18.5 / 100 * 244

= 45.14 megabytes

≈ 50 megabytes

The size of the file that has been downloaded is 50 megabytes.

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6.5 pints.

3.25 x 2 = 6.5 (There are 2 pints in a quart)

Linear equations are typically organized in slope-intercept form:

\(y=mx+b\)

To determine a linear equation in slope-intercept form:

We're given:

First, find the slope of the line (m):

\(m=\dfrac{y_2-y_1}{x_2-x_1}\) where two points that fall on the line are \((x_1,y_1)\) and \((x_2,y_2)\)

⇒ Plug in the given points (-1,-4) and (5,-2):

\(m=\dfrac{-2-(-4)}{5-(-1)}\\\\m=\dfrac{-2+4}{5+1}\\\\m=\dfrac{2}{6}\\\\m=\dfrac{1}{3}\)

⇒ Therefore, the slope of the line is \(\dfrac{1}{3}\). Plug this into y=mx+b:

\(y=\dfrac{1}{3}x+b\)

Now, determine the y-intercept (b):

\(y=\dfrac{1}{3}x+b\)

⇒ Plug in one of the points and solve for b:

\(-4=\dfrac{1}{3}(-1)+b\\\\-4=-\dfrac{1}{3}+b\\\\-4+\dfrac{1}{3}=b\\\\b=-\dfrac{11}{3}\)

⇒ Therefore, the y-intercept is \(-\dfrac{11}{3}\). Plug this back into our original equation:

\(y=\dfrac{1}{3}x-\dfrac{11}{3}\)

\(y=\dfrac{1}{3}x-\dfrac{11}{3}\)

Answer:

The graph is in the pic

Step-by-step explanation:

Answer: They all have a sum of there digits that is an even number.

Step-by-step explanation:

Answer:

13/12 or 1 1/12

Step-by-step explanation:

find the common denominator

Answer:

Can you be more specific on this question?

Step-by-step explanation: