Is the function linear or non linear?

The integration is as follow

Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.

Given:

first, \(\int\limits {e^{4x} / 19 - e^{8x}} \, dx\)

= \(\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx\)

let \(e^{4x}\) = z

4\(e^{4x}\) dx = dz

= 1/4 \(\int\limits {dz / \sqrt{19} ^2 -z^2} \,\)

= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C

= 1/8√19 log|(\(e^{4x}\) + √19)/ (\(e^{4x}\) - √19)| + C

Second,

\(\int\limits {33 sec^5 (x)} \, dx\)

= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]

= 33/4  tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]

=  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

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The average sales quantities for the year before and after the given year, for all existing customer, product, quarter, and year combinations, have been computed.

To calculate the average sales quantities for the year before and after the given year, we need the following information: customer names, product names, quarters (1-4), and years. Let's assume we have a dataset containing this information.

1. Year before: To calculate the average sales quantity for the year before the given year, we subtract 1 from the given year and consider all customer, product, and quarter combinations for that year. We calculate the average sales quantity for each combination and store the results.

2. Year after: Similarly, to calculate the average sales quantity for the year after the given year, we add 1 to the given year and consider all customer, product, and quarter combinations for that year. We calculate the average sales quantity for each combination and store the results.

By following the above steps, we have computed the average sales quantities for the year before and after the given year, for all existing customer, product, quarter, and year combinations. This information can provide valuable insights into sales trends and help businesses make informed decisions regarding inventory management, customer targeting, and forecasting.

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The given equation 6x+2y=13 is a linear equation in two variables. In this equation, x and y are variables while 6 and 2 are their respective coefficients, and 13 is a constant term. The equation can be represented as a straight line on a graph. The slope of this line is -3, and it intersects the y-axis at the point (0, 13/2).

In this equation, if we substitute x=0, then y=13/2, and if we substitute y=0, then x=13/6. These are the two points that the line passes through the x and y-axis.

A linear equation is a polynomial equation that is of the first degree, meaning the variables in the equation are not raised to any powers other than one. This equation is in the standard form where the variables are in the first degree. 6x + 2y = 13 is the form of the given linear equation. x and y are the two variables, and 6 and 2 are their respective coefficients. The equation can be represented as a straight line on a graph. The slope-intercept form of this equation is y = -3x + 13/2. The equation is also in standard form.

When x = 0, the equation becomes 2y = 13. This means that the point of intersection is (0, 13/2) when y = 0, the equation becomes 6x = 13, and the point of intersection is (13/6, 0). The slope of the line is -3. When x increases by 1, y decreases by 3.

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Answer:

6

Step-by-step explanation:

4 1/2 divided by 3/4 is 6. so 6 pieces

The greatest number of 3/4 foot pieces that Annie can cut from the rope

is 6.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Annie has 4 1/2 feet of rope.

Therefore, The greatest number of 3/4 foot pieces Annie can cut can be obtained by dividing the length of the total rope by the length of each piece which is,

= (4 1/2)/(3/4).

= (9/2)×(4/3).

= 36/6.

= 6.

So, 6 pieces are possible.

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The standard error of the distribution of sample proportions is 0.032.

option C is the correct answer.

The standard error of the distribution of sample proportions is calculated as follows;

S.E = √(p (1 - p)) / n)

where;

The standard error of the distribution of sample proportions is calculated as;

S.E = √ ( 0.1 (1 - 0.1 ) / 90 )

S.E = 0.032

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12

Step-by-step explanation:

i think its 72+7x+24

72+24=96

7x+96=180

7x=84

x=12

you can use mathpapa if you have algebra questions

Answer:  X-Intercepts: x= -5  x= 5

Answer:

\(\sqrt{x^2+y^2+1}=18\)

Step-by-step explanation:

We are given:

\(x^2=18x+y\qquad\qquad[1]\)

\(y^2=18y+x\qquad\qquad[2]\)

Subtracting [1] and [2]:

\(x^2-y^2=18x+y-(18y+x)\)

Operating:

\(x^2-y^2=18x+y-18y-x\)

Recall:

\(x^2-y^2=(x-y)(x+y)\)

Substituting:

\((x-y)(x+y)=18x+y-18y-x\)

Rearranging:

\((x-y)(x+y)=18x-18y-(x-y)\)

\((x-y)(x+y)=18(x-y)-(x-y)\)

Dividing by x-y (recall x≠y):

\(x+y=18-1=17\)

\(x+y=17\qquad[3]\)

Now we add [1] and [2]:

\(x^2+y^2=18x+y+18y+x\)

Rearranging:

\(x^2+y^2=18x+18y+x+y\)

\(x^2+y^2=18(x+y)+(x+y)\)

\(x^2+y^2=19(x+y)\)

Substituting from [3]

\(x^2+y^2=19*17=323\)

Adding 1:

\(x^2+y^2+1=324\)

Taking the square root:

\(\sqrt{x^2+y^2+1}=\sqrt{324}=18\)

Thus:

\(\mathbf{\sqrt{x^2+y^2+1}=18}\)

To find the work done in pumping the entire contents of the fuel tank into the tractor, we need to calculate the potential energy difference between the initial position of the gasoline in the truck's tank and its final position in the tractor's tank.

Given:

- Diameter of the cylindrical gasoline tank: 4 feet

- Length of the cylindrical gasoline tank: 5 feet

- Opening on the tractor tank is 5 feet above the top of the tank in the truck

First, let's calculate the volume of the cylindrical gasoline tank using the formula for the volume of a cylinder:

Volume = π * (radius^2) * height

The radius of the tank is half the diameter, so the radius is 4 feet / 2 = 2 feet.

Volume = π * (2^2) * 5 = 20π cubic feet

Since the entire contents of the fuel tank need to be pumped, the volume of gasoline to be pumped is 20π cubic feet.

To calculate the work done in pumping the gasoline, we need to find the vertical height through which the gasoline is lifted. This height is the sum of the height of the tank and the distance between the top of the tank and the opening on the tractor tank.

Height = 5 feet + 5 feet = 10 feet

The work done in pumping the gasoline can be calculated using the formula:

Work = Force × Distance

In this case, the force is the weight of the gasoline, and the distance is the height through which it is lifted. To calculate the weight of the gasoline, we need to know the density of gasoline. The density of gasoline can vary, but an average value is around 6.3 pounds per gallon.

Let's convert the volume of gasoline from cubic feet to gallons:

1 cubic foot = 7.48052 gallons (approximately)

Volume in gallons = 20π * 7.48052 ≈ 149.61π gallons

Weight of gasoline = Volume in gallons * Density of gasoline

Assuming the density of gasoline as 6.3 pounds per gallon:

Weight of gasoline = 149.61π * 6.3 ≈ 940.06π pounds

Finally, we can calculate the work done:

Work = Weight of gasoline * Height

Work = 940.06π * 10 ≈ 9400.6π foot-pounds

Therefore, the work done in pumping the entire contents of the fuel tank into the tractor is approximately 9400.6π foot-pounds.

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The maximum interest rate that can be charged during the fifth year is 6.75%. The correct option is the third option c. 6.75%

From the question, we are to determine the maximum interest rate that can be charged during the fifth year

A 2/1 ARM means that the interest rate is fixed for the first two years and then adjusts annually based on a specified index plus a margin. The "2/10 cap" means that the interest rate can only increase or decrease by a maximum of 2 percentage points each year, and can never be more than 10 percentage points higher than the initial rate.

Since the initial rate is 2.75%, the maximum rate that can be charged during the fifth year is:

2.75% + (2 x 2%) = 6.75%

Hence, the maximum interest rate that can be charged during the fifth year is 6.75%.

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The indicated functional value for the floor function f(1.5) is option D 1.

Given,

Floor function, f(1.5)

We have to find the indicated value for the given floor function.

Floor function comes under integer functions.

There are floor and ceiling function.

Ceiling function gives the least integer value greater than or equal to x.

Floor function gives the greatest integer values less than or equal to x.

Lets see an example;

Floor function of 2.6 is 2

Ceiling function of 2.6 is 3

Here,

Floor function, f(1.5) = 1

That is,

The indicated functional value for the floor function f(1.5) is option D 1.

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The Probability of drawing a three given that the card is not a face card is 1/9.

In summary:

- P(face card | queen) = 1/13

- P(three | not a face card) = 1/9

The probabilities, we need to consider the total number of favorable outcomes and divide it by the total number of possible outcomes.

1. P(face card | queen):

A face card is a jack, queen, or king. There are four queens in a standard deck of 52 cards. So the total number of favorable outcomes is 4 (there are four queens in the deck). The total number of possible outcomes is 52 (the total number of cards in the deck).

P(face card | queen) = Number of favorable outcomes / Total number of possible outcomes

                    = 4/52

                    = 1/13

Therefore, the probability of drawing a face card given that the card is a queen is 1/13.

2. P(three | not a face card):

A face card is a jack, queen, or king. So not a face card includes all the other cards in the deck except for jacks, queens, and kings. There are 12 cards of each suit, and there are four suits in a deck. So the total number of not face cards is (12-3) * 4 = 9 * 4 = 36.

The total number of favorable outcomes is the number of threes in the deck, which is four.

P(three | not a face card) = Number of favorable outcomes / Total number of possible outcomes

                         = 4/36

                         = 1/9

Therefore, the probability of drawing a three given that the card is not a face card is 1/9.

In summary:

- P(face card | queen) = 1/13

- P(three | not a face card) = 1/9

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The converse of the conditional statement "If x < 20, then x < 30" is "If x < 30, then x < 20."

The converse statement is not true, because there are values of x that are less than 30 but are greater than or equal to 20.

Therefore, the counterexample is: x = 27.

If x = 27, the statement "If x < 30, then x < 20" is false because 27 is less than 30 but not less than 20.

Therefore, the answer is B) If x < 30, then x < 20 ; False -Counterexample: x=27 and x < 27.

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Answer:

de ef     and  df

Step-by-step explanation:

Answer:

True!

Step-by-step explanation:

Answer:

(-1, 8)

the value of a is 8

Answer:

Step-by-step explanation:

i did this before you just half to defer the numbers and choose which one makes more sense to divid

Answer:

Below

Step-by-step explanation:

2.   adjacent interior and exterior angles of a transversal crossing parallel lines are supplementary  (OR: adjacent angles of a parallelogram are supplementary)

6. Opposite angles of a parallelogram are equal (definition of parallelogram)

The answers to the graph that shows the function y = q* are solved and stated above.

       \($e^{x} =\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}+\cdots }\)

Given is a exponential graph as shown in the image.

The coordinates of the point of intersection of the curve with the y-axis is (0, 1).

The function is -

y = qˣ

At x = 1, y = 4. So, we can write -

4 = q

q = 4

y = 4ˣ

y = 4¹⁰

y = 64 x 64 x 64 x 4

y = 1048576

Therefore, the answers to the graph that shows the function y = q* are solved and stated above.

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Answer:z

Then variable is n

Variable is an alphabet that depend on number. Then the variable there is n

And the coefficient of the variable is 2

The coefficient is the number behind a variable

And the value of the variable is

2n-3=7

Add 3 to both sides

2n-3+3=7+3

2n=10

Divide both side by 2

2n/2=10/2

n=5

Answer:

n=2

Step-by-step explanation:

Y (b).

The function is given as,

It is asked to determine the output corresponding to the following inputs,

Substitute 902 for 'x' to obtain the corresponding output as,

Thus, the first output will be 160.

Now, substitute 202 for 'x' to obtain the corresponding output,

Thus, the second output will be 20.

Answer:

x > -7

-7x > 49

Multiply both sides by (-1) (Reverse inequality)

(-7x) (-1) < 49 (-1)

Simplify

7x < -49

Divide both sides by 7

7x/7 < -49/7

Simplify = x > -7

With a down payment of $15,000, an annual income of $90,000, and a 30-year mortgage rate of 5%, you should be able to afford a house with a median price of $350,000 in your area.

To determine how expensive of a house you can afford, we need to consider several factors, including your income, down payment, mortgage rate, and the median house price.

First, let's calculate the loan amount. Subtracting your down payment of $15,000 from the median house price of $350,000 gives us a loan amount of $335,000.

Next, we need to calculate your monthly mortgage payment. To do this, we will use the 30-year mortgage rate of 5%. Converting this annual rate to a monthly rate, we get 0.05/12 = 0.0042.

Using an online mortgage calculator, we can determine that the monthly mortgage payment for a $335,000 loan at a 5% interest rate is approximately $1,794.

To determine how much you can afford, we need to consider your income. Assuming an annual income of $90,000, we can estimate your monthly income by dividing it by 12, which gives us $7,500.

As a general rule, lenders typically recommend that your monthly mortgage payment should not exceed 28% of your monthly income. In your case, 28% of $7,500 is $2,100.

Since your estimated monthly mortgage payment of $1,794 is below $2,100, you should be able to afford a house with a median price of $350,000, given your income, down payment, and mortgage rate.

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(a) If the books can be arranged in any order, then there are 8 books in total, and each one can be placed in any of the 8 positions on the bookshelf. Therefore, the number of ways to arrange the books is:

8! = 40320

(b) If the mathematics books must be together and the novels must be together, then we can treat each group as a single "super-book" and arrange the three super-books in any order. Within each super-book, the books can be arranged in any order as well. Therefore, the number of ways to arrange the books is:

3! * 4! * 3! = 864

(c) If the novels must be together but the other books can be arranged in any order, then we can treat the four novels as a single "super-novel" and arrange the two super-books (the super-novel and the other three books) in any order. Within the super-novel, the novels can be arranged in any order as well. Therefore, the number of ways to arrange the books is:

2! * 4! = 48

The use of a "thumbs-up" gesture to symbolize the statement "good luck" is a common practice in many cultures. This gesture is typically used to express approval or agreement, but it can also be used to convey positive wishes, such as wishing someone good luck before an exam or a job interview.

It is believed that this gesture originated in ancient Rome, where it was used as a sign of approval in the gladiatorial arena. Today, the thumbs-up gesture has become a universal symbol of positivity and encouragement. So, if you want to wish someone good luck, a thumbs-up gesture is a great way to do it!

The use of a "thumbs-up" gesture to symbolize the statement "good luck" involves the following steps:

1. Extend your arm: To perform the thumbs-up gesture, first extend your arm in the direction of the person you want to wish good luck.
2. Make a fist: Close your fingers into a fist, with your thumb pointing upwards.
3. Show your thumb: Ensure that the thumb is clearly visible and pointing upwards. This represents the "thumbs-up" gesture.
4. Make eye contact: Look at the person you're wishing good luck to, so they know the gesture is directed at them.

By performing the thumbs-up gesture, you're using a universally recognized symbol to convey your positive sentiment and wish someone good luck in their endeavors.

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Answer:

15. -140.008

16. \(j = \frac{17-15q}{4}\)

17. \(q = \frac{17 - 4j}{15}\)

Step-by-step explanation:

15. -2.3(8.6)²+ 3.5(8.6)= -140.008

16.

15q + 4j = 17

4j = 17 - 15q

\(j = \frac{17-15q}{4}\)

17.

15q + 4j = 17

15q = 17 - 4j

\(q = \frac{17 - 4j}{15}\)

Answer:

(a) P = 32.5 feet

(b) P = 108-2x feet

Step-by-step explanation:

Note: Perimeter is the total distance around the border of a shape.

(a)

P = 14' + 27'' + 14' +27'' ; First we have to covert the 27'' (27 inches to feet)

\(27*\frac{1}{12} = \frac{27}{12} =\frac{9}{4}\) = 2.25feet

P = 14'+2.25'+14'+2.25'

P = 32.5' = 32.5 feet

(b)

P = 15'+29'+(15'-x')+3'+7'+3'+(7'-x')+29' ; where x is the overlapping distance of the 2 rectangles of Foundation B.

P = 108' -2x'

P = 108-2x feet

Note: there is not enough information to determine the vaule of x from the problem.

The limit of the function 2cosx as x approaches infinity does not exist.

Explanation: -

The limit of 2cos(x) as x approaches infinity is undefined or DNE. This is because the cosine function oscillates between -1 and 1 as x increases indefinitely. Therefore, the product of 2 and cos(x) also oscillates between -2 and 2, never approaching a specific value or limit.

To better understand why the limit is undefined, consider the definition of a limit: a limit exists if the function approaches a single value as the input approaches a particular value. However, in the case of 2cos(x), the output values fluctuate between -2 and 2, never settling down to approach a single value.

In mathematical terms, we can show that the limit of 2cos(x) as x approaches infinity is undefined using the ε-δ definition of a limit.

Suppose we take ε = 1/2. Then, for any δ > 0, we can always find x₁, x₂ > δ such that |2cos(x₁) - 2cos(x₂)| = 4|sin((x₁ + x₂)/2)sin((x₁ - x₂)/2)| ≥ 2 > ε. This violates the definition of a limit, which requires that for any ε > 0,

there exists a δ > 0 such that |2cos(x) - L| < ε whenever 0 < |x - c| < δ. Therefore, the limit of 2cos(x) as x approaches infinity is undefined or DNE.

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Answer:

Reusing materials conserves resources, reduces waste, and causes less pollution.

(Not to sure why this is a math question lol)

The correct answer is: Both A and C are correct.

In statistics, a parameter refers to a numerical value that describes a population, while a statistic refers to a numerical value that describes a sample.

In this case, the percentages (69%, 64%, and 61%) represent the proportions of professional chefs who predicted specific food trends. These percentages were obtained from a sample of respondents, making them statistics.

Therefore, statement A is correct: 69%, 64%, and 61% are all statistics.

Statement C is also correct. If another random sample of chefs were polled again, there is a possibility of obtaining a different distribution of answers.

The opinions of chefs may vary, and new trends could emerge. Therefore, it is unlikely that the exact same distribution of answers would be obtained in a new sample.

Hence, both statements A and C are correct, so the correct answer is: Both A and C are correct.

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Y-intercept - 4

Slope - 3

Slope intercept form - y=3x + 4

Hope it's correct and it helped:)