Help ASAP 100 PTS!!!!
Describe how to determine the average rate of change between x = 1 and x = 3 for the function f(x) = 3x3 + 1. Include the average rate of change in your answer. Please show all work and explain it thourougly.

A physical quantity with both magnitude and direction is called a vector quantity.

A vector quantity is a physical quantity that has both magnitude and direction. One example of a vector quantity is velocity, which is defined as the rate of change of an object's position with respect to time. Velocity is a vector quantity because it has both a magnitude (speed) and a direction (the object's motion). For instance, if an object is moving with a speed of 20 meters per second to the north, its velocity would be 20 meters per second north. If the object's direction changes to east, its velocity would become 20 meters per second east. Therefore, velocity is a vector quantity because its value depends not only on the speed of the object but also on the direction in which it is moving.

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Complete Question

Write down a vector quantity and explain your response.

Answer:

90

Step-by-step explanation:

It is proved that the join of A and B is a convex set when the join of A and B is the set of all \($\vec x$\) such that \($\vec x$\) lies on a line segment with one endpoint in A and the other in B.

Let \(p_1\) and \(p_2\) belong to the join of A and B.

Let q = x\(p_1\) + (1 − x) \(p_2\) with x ∈ [0,1].

There exist \(a_1\) ∈ A and \(b_1\) ∈ B and \(r_1\) ∈ [0,1] with

\(p_1\)= \(r_1\) \(a_1\) + (1 − \(r_1\)) \(b_1\)

There exist \(a_2\) ∈ A and \(b_2\) in B and \(r_2\) ∈ [0,1] with

\(p_2\) = \(r_2\) \(a_2\) + (1 − \(r_2\)) \(b_2\).

Since A and B are convex, we have

A⊃{c \(a_1\) + (1−c) \(a_2\) : c∈[0,1]}

and B⊃{d \(b_1\)+(1−d) \(b_2\) : d∈[0,1]}.

So if we can find c, d, e ∈ [0,1] such that

q = e[c \(a_1\) + (1−c) \(a_2\)] + (1 − e)[d \(b_1\) + (1−d) \(b_2\) ]      -------(1)

then q belongs to the join of A and B.

Now q = x \(p_1\) + (1−x) \(p_2\) = x[\(r_1\) \(a_1\) + (1−\(r_1\)) \(b_1\)] + (1−x) [\(r_2\) \(a_2\)+(1−\(r_2\)) \(b_2\)].

Similarly, we can show that there do exist c, d, e∈[0,1] such that

x \(r_1\) = ec

(1 − x) \(r_2\) = e (1−c)

x(1− \(r_1\)) \(b_1\) = (1−e)d

(1 − x)(1 − \(r_2\)) = (1 − e)(1 − d).

Then equation 1 is satisfied.

Hence, proved that the join of A and B is a convex set.

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Answer:

Question 1: 131.25 Question 2: 83.33 Question 3. 133.33

Step-by-step explanation:

1. 131.25% x 150

2. Trial and error

3. 60 ÷ 45%

y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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Answer:

(a) $878.24

(b) $848.30

(c) Amy would pay less for the golf clubs if she gets them directly from the distributor

Step-by-step explanation:

Part (a)

The wholesale price is $499. When the pro shop gets them from the distributor, it has to pay a mark-up of 10%. 10% expressed as decimal is 10/100 = 0.10

10% of 499 = 0.10 x 499 = 49.90

So total cost including markup for the pro shop is 499 + 49.90 = $548.90

We can compute this directly without computing mark-up cost using the formula

Cost = 499(1+0.10) = 499 x 1.1 = 548.90

The pro shop puts a mark up of 60% which in decimal is 60/100 = 0.6 on the above cost

So the price Amy pays = 548.90(1+0.6) = 548.90 (1.6) = $874.28

Part (b)

Wholesale price = $499

If Amy purchases directly from distributor there is a 70% markup on the wholesale price. 70% = 70/100 = 0.7

So the price Amy would have to pay = 499(1+0.7) = 499 x 1.7 = $848.30

Part (c)

Since the cost of purchasing directly from distributor is less than the cost of purchasing from pro shop the answer is

Amy would pay less for the golf clubs if she gets them directly from the distributor

Answer:

\( \sqrt[4]{ {x}^{3} } \)

Step-by-step explanation:

\( \sqrt{x} \times \sqrt[4]{x} \\ = {x}^{ \frac{1}{2} } \times {x}^{ \frac{1}{4} } \\ = {x}^{ \frac{1}{2} + \frac{1}{4} } \\ = {x}^{ \frac{3}{4} } \\ = \sqrt[4]{ {x}^{3} } \)

Answer:

50/33 is the answer that needs to written. Yes this is the simplest form.

Answer:

50/33

Here you go

The statement which best describes Gary’s error is; Gary did not use the greatest common factor in the equation.

This is the largest positive integer or polynomial that is a divisor of several different numbers. For instance, the greatest common divisor of 66, 30 and 18 is 6.

Gary's work:

66 + 36

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

66 + 36

= 3 (22 + 12)

Gary did not use the greatest common factor in the equation.

The correct answer:

66 + 36

= 6(11 + 6)

Therefore, Gary did not use the greatest common factor in the equation.

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The correct statement regarding the end behavior of the functions is given by:

As x→∞, f (x)→∞ and g(x)→0.

It is given by the limits of f(x) as x goes to infinity.

In this problem, the function f(x), the limits are given as follows:

For function g(x), the limit is given as follows, as it is not defined for negative values:

\(\lim_{x \rightarrow \infty} f(x) = 0\).

Hence the correct statement is:

As x→∞, f (x)→∞ and g(x)→0.

As it considers both positive infinity and negative infinity just as infinity.

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Answer:

1. 10$

2. 24,59$

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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It's the same question and has an answer to it...

Explanation:

We have y = f(x) where x is the input and y is the output.

Any point is of the form (x,y)

Writing f(-2) means x = -2 is plugged into f(x), which results in an output of -4 because f(-2) = -4.

So we have (x,y) turn into (-2, -4)

Answer:

76%

Step-by-step explanation:

57/75

(57 X 100)/ 75

5700/75

1900/25

76/1

76

The correct expression is  \($(150 \cdot 1.15)^7$\) (Choice A).

The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).

To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.

If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.

Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.

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Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

68?

Step-by-step explanation:

multiples of 5 end in 5 or 0

_ _ _

last digit has 2 choices ( 5 and 0 )

1,3,5,7,9 are odd

so tens digit has 5 choices but we see that 5 is repeated so we split into more cases

when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40

when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28

40+28=68

Explanation:

Make a graph with interval -2 ≤ x ≤ 2

Then graph the function: f(x) = x + 3

Table:

\(\begin{array}{| c | c | }\cline{1-2} \sf x & \sf y \\\cline{1-2} -2 & 1 \\\cline{1-2} -1 & 2 \\\cline{1-2} 0 & 3 \\\cline{1-2} 1 & 4 \\\cline{1-2} 2 & 5 \\\cline{1-2}\end{array}\)

Plot these coordinates and draw a smooth line through these coordinates.

Explanation

a line that passes throught the origin (0,0) is a line in the form

where k is the constant , rate of change or slope

so

Step 1

find the constant of the line:

to do that, check any coordiante and replace

a) pick up a coordinate from the line

Let

P(4,2)

so

replace

therefore, rewriting the function would be

I hope this helps you

Answer:

The result can be shown in multiple forms.

Exact Form:

log (48)

Decimal Form:

1.68124123…

Step-by-step explanation:

A multiple of a number is the product of that number and any other whole number. Zero is a multiple of every number.

Answer:

exact form is log( 48)

decimal form will be 1.68124123

but for short it will be 1.7 because you can round the 6 to a 7 if you have to do that

Step-by-step explanation:

Answer:

6. = >  7. = 3√ 45, 63/16, -2/9 PI, -0.09, -√ 15

Step-by-step explanation:

Sorry if im wrong

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Answer:

Hitting a tennis ball over a net.

Step-by-step explanation:

B,C,D are non-rigid

Answer:

y = 2x - 1

Step-by-step explanation:

To get slope:

m = y2 - y1 / x2 - x1

m = 13 - 7 / 7 - 4

m = 6 / 3

m = 2

To get y-intercept:

y = mx + b

13 = 2(7) + b

13 = 14 + b

13 - 14 = b

-1 = b

Put it together:

y = 2x - 1