Let g be the function given by g(x)=limh→0sin(x+h)−sinx/h. What is the instantaneous rate of change of g with respect to x at x=π3?

The vertical asymptote of the function [tex]f(x) = \frac{x^2 + 6x + 9}{x^2 - 9}[/tex] is at x = 3.

Asymptote is a line or curve that serves as the boundary of another line or curve in mathematics.

Given, A function [tex]f(x) = \frac{x^2 + 6x + 9}{x^2 - 9}[/tex].

Factoring the numerator and the denominator we have,

[tex]f(x) = \frac{(x+3)(x+3)}{(x+3)(x-3)}[/tex]

Now, The holes of the function are at [tex]f(x) = \frac{(x+3)}{(x-3)}[/tex], x + 3 = 0, x = - 3.

And the asymptote of the function is at x - 3 = 0, x = 3.

Therefore, The asymptote will be a dotted vertical line at x = 3.

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The difference between the starting volumes is 200 milliliters, the first bucket has the larger volume.

We know that the volumes can be modeled by linear equations, and remember that a general linear equation is:

y = a*x + b

Where a is the slope and b is the initial value.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

For the first bucket we have the points (1, 2900), (10, 2000), then the slope is:

a = (2000 - 2900)/(10 - 1) = -900/9 = -100

So we can write:

y = -100*x + b

To find the value of b, we can replace the value of one of the points in the equation. I will use the first point (1, 2900)

2900 = -100*1 + b

2900 + 100 = b

3000 = b

Now for the other bucket, we have the points (1, 2725) and (10, 2050), so the slope is:

a = (2725 - 2050)/(10 - 1) = -75

So this line is:

y = -75*x + b

Again, replacing the values of one of the points we will get:

2725 = -75*1 + b

2725 + 75 = b

2800 = b

Then the difference in the starting volumes is:

3000  - 2800 = 200

The first bucket has 200 milliliters more.

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Answer:

please type your questions well

The statement about the data the points appear to be on a straight line

From the question, we have the following parameters that can be used in our computation:

Equation of a trend line: y = 0.0001x + 12

The above equation is a linear equation

This implies that the data points represented by  the equation would appear to be on a straight line

Note that: The points may or may not be on a perfect straight line depending on the correlation value

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Answer:

The measure of an exterior angle of a regular polygon with n sides is given by the formula:

360°/n

For a regular polygon with 36 sides, the measure of each exterior angle is:

360°/36 = 10°

Therefore, the measure of an exterior angle of a regular polygon with 36 sides is 10°.

Step-by-step explanation:

The collection of the like terms of the equation 5x^2 - 4x + 9x^2 + 2x  can be expressed as 14x^2 - 2x .

The concept here is collecting the like terms, Algebraic expressions can be made simpler by combining like terms. Combining similar phrases is another name for it. In order to accomplish this, we locate similar terms in an algebraic equation and combine them by either adding or subtracting.

To collect like terms, add up the quantities of the same thing. The sales of various sizes of the same article of clothing, such as a jumper, will be added up by a buyer.

5x^2 - 4x + 9x^2 + 2x

=5x^2 + 9x^2 - 4x + 2x

=14x^2 - 2x

Therefore, option C is correct.

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If we run tests that can reveal non random patterns in the time ordered data , then the four patterns that might be seen are : Points outside limits , Trend , Cycles and Bias .

The four patterns that might be seen in run tests which can reveal non-random patterns in time-ordered data are:

(i) Points outside limits: This pattern indicates that the data points fall outside of the control limits and suggests that the process is not in statistical control.

(ii) Trend: This pattern indicates that the data points are moving consistently in a particular direction, either increasing or decreasing over time.

(iii) Cycles: This pattern indicates that the data points are oscillating around a central value over time, with a repeated pattern of highs and lows.

(iv) Bias: This pattern indicates that the data points are consistently above or below the centerline over time, indicating a systematic error or shift in the process.

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Answer:

man female women man women male female measurement measurement master mysteries milkman milkmaid monk non Mr Mrs nephew nice papa

The quantity 2a 2c corresponds to the rate of change of the surface area with respect to a. So, Correct option is C.

When considering a rectangular prism with dimensions a, b, and c, there are three different measures that we can associate with the dimensions: the length, width, and height. These measures are important in determining both the volume and the surface area of the prism.

In this problem, we are given a quantity 2a 2c and asked to determine which measure of the rectangular prism it corresponds to. We can do this by considering the formulas for the volume and surface area of the prism, and taking the partial derivatives with respect to each of the three dimensions.

The volume of a rectangular prism is given by:

V = abc

Taking the partial derivative of this expression with respect to a, we get:

[tex]\frac {\partial v} {\partial a}[/tex] = bc

This is not equal to 2a 2c, so we can eliminate the possibility of the quantity corresponding to the rate of change of the volume with respect to a.

Taking the partial derivative of the volume with respect to b and c gives:

[tex]\frac {\partial v} {\partial b}[/tex] = ac

[tex]\frac {\partial v} {\partial c}[/tex] = ab

Again, neither of these expressions is equal to 2a 2c, so we can eliminate the possibilities of the quantity corresponding to the rate of change of the volume with respect to b or c.

Next, we can consider the surface area of the prism, which is given by:

A = 2ab + 2ac + 2bc

Taking the partial derivative of this expression with respect to a, we get:

[tex]\frac {\partial v} {\partial a}[/tex] = 2b + 2c

Substituting 2a 2c for 2b + 2c, we get:

[tex]\frac {\partial A} {\partial a}[/tex] = 2a 2c

This is the same expression as the given quantity, so we can conclude that the quantity 2a 2c corresponds to the rate of change of the surface area with respect to a.

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The total cost of the paving stones for building a circular patio with a diameter of 12 feet is C. $1,187.

The area of the circular patio using its diameter and pi (22/7) is determined with the formula below.

The unit cost per square foot is multiplied by the area to determine the total cost.

A = π (d/2)^2

The diameter of a circular patio = 12 feet

The area, A = π (d/2)^2

= 22/7(12/2)^2

= 113.14 ft²

The cost per square foot of paving stones = $10.50

The total cost = $1,187.97 ($10.50 x 113.14)

= $1,188

Thus, using the mathematical operation of multiplication, we can conclude that Mr. Aba's project will cost Option C.

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The correct students in their approach to solving the problem are Aditi, Erick, and Raj. Nico and Sandra's approaches are incorrect.

The following are the correct approaches to solving the equation:

Aditi: two-fifths (5 + x) = eight. five-hundredths (5) + five-hundredths x = (five-halves) 8

Erick: two-fifths (5 + x) equals eight. two-fifths (5 + x) minus 5 equals eight minus five.

Raj: two-fifths (5 + x) = eight. two-fifths (5) + two-fifths x = eight.

As a result, Aditi, Erick, and Raj are the correct students in their approach to solving the problem. The approaches of Nico and Sandra are incorrect.

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The graph of the linear equation is on the image at the end.

Here we have the following linear equation:

y = (7/3)*x + 5

To graph that line we need to find two points on the line, to get them, we need to evaluate the line in two different values of x.

if x = 0

y = (7/3)*0 + 5 = 5

if x = 3

y = (7/3)*3 + 5 = 12

Then we have the points (0, 5) and (3, 12)

Now just graph these points and connect them with a line.

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To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

How to determine the appropriate graph?

The graphs that complete the question are added as an attachment

From the attached graph, we have the following highlights:

The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....

The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....

The above means that graph B is a misleading graph

Hence, Benjamin should use graph A for his report

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Answer:

240

Step-by-step explanation:

60/ 4=15

15×5=75

b) 4+5=9

540/9=60

4×60=240

Answer: 1/52

Step-by-step explanation:

There is a 13/52 chance of drawing a hearts card and then there is a 4/52 chance of drawing a 6

(13/52)(4/52)=1/52

There is a 1/52 chance of Marlin drawing a hearts card and then a 6

Anthony and Giovani will both go to the library on the same day every 12th day.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

To find out when both Anthony and Giovani will go to the library on the same day, we need to find the smallest number that is divisible by both 4 and 6.

We can start by listing the multiples of 4 and 6 until we find a common multiple:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...

We see that 12 is the smallest common multiple of 4 and 6.

Therefore, Anthony and Giovani will both go to the library on the same day every 12th day.

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The rock will be 9 meters from ground level at a time of:

x = 5.76 seconds.

The quadratic function that models a projectile's height is given as follows:

y = -4.9t² + v(0)t + h(0)

In which:

The parameters for this problem are given as follows:

v(0) = 22, h(0) = 45.

Hence the height function is given as follows:

y = -4.9t² + 22t + 45.

The rock is 9 meters from ground level when:

9 = -4.9t² + 22t + 45.

-4.9t² + 22t + 36 = 0

4.9t² - 22t - 36 = 0.

Hence the discriminant is given as follows:

D = 22² - 4(4.9)(-36)

D = 1189.6.

The positive root, representing the time for the height of 9 meters, is given as follows:

x = (22 + sqrt(1189.6))/9.8

x = 5.76 seconds.

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Answer:

Step-by-step explanation:

Using properties of logs:

= 16 log 4

= 9.63

Answer:

7

Step-by-step explanation:

To find the mean of a set of numbers, we add up all the numbers and divide the sum by the total number of numbers.

For the given sample, we have:

10 + 6 + 8 + 6 + 5 = 35

There are 5 numbers in the sample, so we divide the sum by 5:

35 / 5 = 7

Therefore, the mean of the sample is 7.

If the measure of the intercepted arc GHJ is 180°, the measure of the inscribed angle GHJ will be mGHJ = 360° - 180° = 180°.

Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.

The measure of an inscribed angle in a circle is always equal to the measure of its intercepted arc. The measure of the arc intercepted by a central angle is determined by the formula, mGHJ = 360° - mJKH. Therefore, the measure of an inscribed angle in a circle with intercepted arc GHJ is equal to mGHJ = 360° - mJKH. This means that the measure of an inscribed angle in a circle can vary depending on the measure of its intercepted arc. For example, if the measure of the intercepted arc GHJ is 180°, the measure of the inscribed angle GHJ will be mGHJ = 360° - 180° = 180°.

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Answer:

Day 1: 6 inches

Day 2: 21 inches

Day 3: 9 inches

Step-by-step explanation:

First, we need to convert the total rainfall from feet to inches. Since 1 foot is equal to 12 inches, 3 feet is equal to 36 inches.

On the first day, 1/6 of the total rainfall falls, so:

(1/6) * 36 = 6 inches

On the second day, 7/12 of the total rainfall falls, so:

(7/12) * 36 = 21 inches

To find the rainfall on the third day, we can subtract the rainfall on the first and second days from the total rainfall:

36 - 6 - 21 = 9 inches

Therefore, the amount of rainfall on each day, in inches, is:

Day 1: 6 inches

Day 2: 21 inches

Day 3: 9 inches

The scenerio that represents an example of mutualism would be an ant colony living on an acacia tree and not allowing vines to grow on the bark. That is option D.

Mutualism is defined as the feeding relationship where by the both organisms which are involved work together to benefit from each other.

A typical example of mutualism is the relationship that exists between the ant and the acacia tree.Here, the ant colony living on an acacia tree and not allowing vines to grow on the bark shows that both organisms benefits from each other.

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If n is an integer and m + 5 is odd, then n must be even.

To prove this statement using contraposition, we need to show that if n is odd, then m + 5 must be even. Assume that n is odd, which means we can write n = 2k + 1 for some integer k.

Then, we can rewrite m + 5 as (2k + 1) + 5 = 2k + 6 = 2(k + 3), which is even.

Therefore, we have shown that if n is odd, then m + 5 is even.

By contraposition, we can conclude that if m + 5 is odd, then n must be even. Overall, the proof uses the fact that odd + odd = even and even + odd = odd, along with the definition of even and odd integers.

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Answer:

Veronica's attempt at ordering the hikes from least to greatest by the number of animals seen per kilometer is not correct.

To order the hikes by the number of animals seen per kilometer, we need to calculate the number of animals seen per kilometer for each hike. We can do this by dividing the number of animals seen by the length of the hike in kilometers.

Using this method, we can calculate the number of animals seen per kilometer for each hike as follows:

Rivers Edge: 8/3 = 2.67 animals/km

Wooded Marsh: 24/8 = 3 animals/km

Canyon Creek: 35/15 = 2.33 animals/km

Based on these calculations, the correct order of the hikes from least to greatest by the number of animals seen per kilometer is Rivers Edge, Canyon Creek, Wooded Marsh.

Veronica's mistake appears to be that she simply ordered the number of animals seen in each hike from least to greatest, rather than calculating the number of animals seen per kilometer.

The solution of the given system of equation is (11, 3/2) and (10, 2) is not a solution of the equations,

A mathematical statement connecting two expressions by equal sign is called an equation.

Given is a system of equations, x-2y = 8 and x + 2y = 14, we are to find the solution and determine if (10, 2) is a solution to the system,

x-2y = 8

x+2y = 14

Adding both the equations,

2x = 22

x = 11

Put x = 11 in any equation to find the value of y,

11 - 2y = 8

2y = 3

y = 3/2

Now, to determine whether (10, 2) is a solution to the system or not, put x = 10 and y = 2 and see if the value is satisfying the equation or not,

10 - 4 = 6

6≠8

Therefore, (10, 2) is not a solution of the equations,

Hence, the solution of the given system of equation is (11, 3/2) and (10, 2) is not a solution of the equations,

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The question is solved for :

Determine if (10, 2) is a solution to the system and what is a solution to a system?

x-2y = 8

x + 2y = 14

The number of different arrangements is 36,000

This is equivalent to the total number of combinations, it is given by the product between the numbers of options.

The numbers of options are:

12 for the noses

20 for the eyes

5 for the lips

30 accessories.

Then the number of different arrangements is:

N = 12*20*5*30 = 36,000

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Answer:

B

Step-by-step explanation:

Answer:

B: Distribute it to all variables by multiplying their exponents

Step-by-step explanation:

The domain of the given relation is:

D: {-3, -2, -1, 0, 1, 3}

For any relation that maps elements from one set into elements of another set, the domain is just the set of the inputs, and usually the domain is the se of the values "x"

Here the domain is the listof numbers in the left,the domain is:

D: {-3, -2, -1, 0, 1, 3}

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The graph of the function f(x)=(x-3)(x-1)(x+1) is given by the image presented at the end of the answer.

The function for this problem is defined as follows:

f(x)=(x-3)(x-1)(x+1).

The product is written as a product of it's linear factors, hence the x-intercepts are given as follows:

The y-intercept of the function is given as follows:

f(0) = -3(-1)(1) = 3.

The end behavior is given as follows:

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