A cyclist leaves New York traveling at an average speed of 9 miles per hour. 4 hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 21 miles per hour. How many hours after the car leaves New York will the car catch up to the cyclist?

According to given function the final value is [tex]$f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$[/tex]

[tex]$$f(x+i y)=\sum_{k=1}^{\infty} \frac{1}{k}(x+i y)$$[/tex]

[tex]$$f(x+i y)=\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}$$[/tex]

Divide both sides by [tex]$x+i y ; \quad x \neq-i y$[/tex]

[tex]\frac{f(x+i y)}{x+i y}=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y} ; \quad x \neq-i y$$[/tex]

Simplify

[tex]\frac{f(x+i y)}{x+i y}=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y}$$[/tex]

Simplify[tex]$\frac{f(x+i y)}{x+i y}: f$[/tex]

Simplify [tex]$\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y}: \frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2}$[/tex]

[tex]f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$$[/tex]

[tex]f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$$[/tex]

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

To learn more about function visit:https://brainly.com/question/12431044

#SPJ1

Given:

The function

Required:

Find the equation of the tangent at f(x) at x=0.

Explanation:

The slope of f(x),

Now, the slope of function at x = 0 is f'(x) = 2.

The line with slope m = 2 and passing through (0, 0).

Answer:

Equation of tangent of the function at x = 0, f(x) = 2x.

Answer: A) x^2+y^2 B) x^3+y^3 C) a^2b^2c^2 D) c^2/d^2

Step-by-step explanation:

For A, you add all the powers. This is because the bases are the same. Any number or letter without a visible power on top most likely means that is has a power of 1. Because this is a multiplication question, you have to add the powers. (Example n*n = n^2 or n^3*n^7 = n^10)

This is same for B.

For C, you multiply abc by abc so it's a*a, b*b, c*c. This is because they are inside a bracket. Anything inside the bracket that has a power outside the bracket is multiplied by itself.

For D, you multiply c and d so it's c*c, d*d. This is the same as C.

The use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values will be:

1. 5 × 6 + 7 = 37

2. 5 + 6 - 7 = 4

3. 5 + 6 + 7 = 18

Addition simply means the sum of the numbers that are given. It should be noted that addition is represented by the sign +.

In this case, we are told to use 5, 6 and 7 to create different values. These are represented above. The addition of 5, 6, and 7 gives 18.

Learn more about addition on:

brainly.com/question/24536701

#SPJ1

Answer:

106 seconds

Step-by-step explanation:

14.36-8=$6.36 $6.36=636 cents so 636/6=106 so 106 seconds

Answer: A = 452.16 ft²

Step-by-step explanation:

      This gives us the formula to solve for the area.

                     A = πr²

      The radius (r) is the same as the diameter divided by 2.

                     24 ft / 2 = 12 ft

      We will input these given values and solve.

A = πr²

A = (3.14)(12)²

A = 452.16 ft²

Answer:

452.16 ft²

Step-by-step explanation:

To find the radius, you divide the diameter (24) by 2, which equals 12. The area of a circle formula is πr². To find area, you do 12² * 3.14. That equals 144 * 3.14, which equals 452.16.

The three statement true about the the distance of a dog from a post are-

For the given graph in the question,

Function f gives the distance of a dog from a post, in feet, as a function of time, t in seconds, since its owner left.

The time is denotes on the x axis and the distance covered by the dog on the y axis.

This can be described using the function as.

f(t) = d

Consider values from graph.

When, t = 0, d = 1.5 feet

Function notation ; f(0) = 1.5    ......statement 1

When t = 60, d = 4 feet

Function notation ; f(60) = 4   ......statement 2

Now, the maximum value is 5.

Thus, f(t) < 5    .....statement 3

Therefore, the three statement are formed.

To know more about the function notations, here

https://brainly.com/question/12110934

#SPJ13

The correct question is -

Write three statement that are true about this situation. Use function notations.

Function f gives the distance of a dog from a post, in feet, as a function of time, t in seconds, since its owner left.

Use the = sign in at least one statement and < sign in another statement.

In linear equation, 864 is distance the flowerbed from the hive .

What are a definition and an example of a linear equation?

a) The equation is so called "time equation"

      D%2F12 + 16*60 + D%2F8 = 19*60 seconds

(b) To determine the distance D, solve the equation

D%2F12 + D%2F8 = 19*60 - 16*60 = 3*60,

multiply both sides by 24

2D + 3D = 3*60*24

5D = 4320

D = 4320/5 = 864

Learn more about linear equation

brainly.com/question/11897796

#SPJ13

The system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased is b + s = 9 and 10s + 12s = 100

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the small box be represented as s.

Let the big box be represented as b.

Each small box has 10 granola bars and each large box has 12 granola bars. The The camp bought a total of 9 boxes that have 100 granola bars altogether.

The equation will be:

b + s = 9

10s + 12s = 100

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:

​10x + 12y = 100

x + y = 9

Step-by-step explanation:

Define Variables:

Let x = the number of small boxes purchased

Let y = the number of large boxes purchased

Each small box has 10 granola bars, so small boxes have 10x granola bars.

Each large box has 12 granola bars, so large boxes have 12y granola bars. Therefore, the total number of granola bars 10x + 12y equals 100:

10x + 12y = 100

Since a total of 9 boxes were purchased, we know x + y must equal 9.

x + y = 9

Answer:

the answer is 2

The graph of the defined piece-wise function is sketched at the end of the answer.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

In the context of this problem, the function has three definitions, as follows:

For the first definition, to the left of x = -3, the function assumes a constant value of 3, hence it is an horizontal line at y = 3.

For the second definition, between x = -3 and x = 4, the function is a increasing linear function, with intercept 1 and slope 2, due to the rule y = 2x + 1.

For the third definition, to the right of x = 4, the function assumes a constant value of -2, hence it is an horizontal line at y = -2.

With each of these definitions, the graph of the function is given at the end of the answer.

More can be learned about piece-wise functions at https://brainly.com/question/19358926

#SPJ1

Answer:

find search bar

Step-by-step explanation:

see answer

The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism

The law of syllogism is defined as a type of logical argument using deductive reasoning.

Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:

(1) If a , then b .

(2) If b , then c .

Then we can derive a third true statement:

(3) If a , then c .

Now, applying that law to our question, we see that;

1) If I'm a student, then I go to school.

2) If I go to school, then I learn.

Then we can derive a third true statement:

3)  If I'm a student, then I learn.

Read more about Law of Syllogism at; https://brainly.com/question/28560796

#SPJ1

Answer:

Step-by-step explanation:

Plot the points, we see it is a rectangle.

Side lengths are:

The perimeter is:

The perimeter of polygon RSTU is

A straight line connects any two places with the smallest distance possible. The distance formula can be used to get this distance. It is possible to define the distance between two positions (x 1, y 1) and (x 2, y 2) as d=√(x2-x1)² + (y2 - y1)².

Distance between R and S is;

√(2+4)² + (2 - 2)²= 6 units

Distance between S and T is;

√(2-2)² + (-2 - 2)²= 4 units

Distance between T and U is;

√(-4+-2)² + (2 - 2)²= 6 units

Distance between T and U is;

√(-4+4)² + (2 + 2)²= 4 units

The total perimeter is of polygon is:

6+4+6+4 = 20 units

To know more about perimeter visit here:

https://brainly.com/question/6465134

#SPJ13

Answer:

72.5%

Step-by-step explanation:

Hello!

We can find the percentage by dividing the sale price by the original price, then multiplying that by 100.

The percentage is 72.5%.

Answer: 1.33

Step-by-step explanation:

0.8 divided by 0.6= 1.33333333333

3 is in the hundredths place and 3 is in the thousandths place.

Since the digit in the thousandths place (3) is less than 5, the digit in the hundredths place (3) does not change.

The digits to the right of the hundredths place are dropped.

1.33333333 rounded to the nearest hundredth (two decimal places) = 1.33.

Answer:

1/4

Step-by-step explanation:

Hope this helps!

The amount of insurance that Travis will have to pay for the year is of:

$47.3.

He is renting the apartment, in which the belongings are worth $11,000, hence the insurance will be paid over that amount.

The number of hundredths in $11,000 is given by:

11000/100 = 110.

He pays an insurance of $0.43 for each $100 in belongings, hence the total insurance is of:

0.43 x 110 = $47.3.

There is no information regarding the value of the building, hence we are going to consider that he does not pay insurance for the building.

This insurance was taken from the table, as the apartment is in the city (downtown), and all brick, hence the coefficient is of 0.43.

The table with the rates is given by the image at the end of the answer.

Learn more about insurance at https://brainly.com/question/28944215

#SPJ1

By using a reflection over the y-axis, the coordinates of the image of the triangle are (- 3, - 3), (- 6, 3) and C'(x, y) = (- 3, 3).

Rigid transformations are transformations applied on geometric loci such that the form of the construction is not altered. Reflections over the y-axis are examples of rigid transformations. In this problem we need to apply this kind of transformation on the three vertices of the triangle: A(x, y) = (3, - 3), B(x, y) = (6, 3), C(x, y) = (3, 3).

The reflection over the y-axis is described by the following formula:

P'(x, y) = P(x, y) + (- 2 · p, 0)

Where:

If we know that A(x, y) = (3, - 3), B(x, y) = (6, 3) and C(x, y) = (3, 3), then the image of the vertices of the triangle:

A'(x, y) = (3, - 3) + (- 6, 0)

A'(x, y) = (- 3, - 3)

B'(x, y) = (6, 3) + (- 12, 0)

B'(x, y) = (- 6, 3)

C'(x, y) = (3, 3) + (- 6, 0)

C'(x, y) = (- 3, 3)

Now we present the picture of the two triangles.

The coordinates of the image of the triangle are A'(x, y) = (- 3, - 3), B'(x, y) = (- 6, 3) and C'(x, y) = (- 3, 3).

To learn more on rigid transformations: https://brainly.com/question/1761538

#SPJ1

Answer:

5/8

Step-by-step explanation:

Slope = rise/run

In this problem:

rise = 5

run = 8

Therefore, Slope = 5/8

Answer: (B) Multiply by 2

Step-by-step explanation:

For every ounce of flour, 2 cupcakes can be made.

Answer:

The answer is d

Step-by-step explanation:

2/11 has a numerator of 2 but cant be reduced

Answer:

Step-by-step explanation:

I misunderstood the question. So, please disregard this answer. Thank you.

The researcher makes use of stratified sampling method to select a random sample from each of the three groups mentioned.

It is given to us that -

A researcher separated the people in a population into three political categories:

Democrat

Republican

or, Independent.

It is also mentioned that she then selected a random sample from each of these three groups.

We have to determine the kind of sample she selected.

In this case, stratified sampling is used by the researcher to select a random sample.

Stratified sampling is a type of probability sampling method where the total population is segmented into homogenous groups to successfully complete the sampling technique.

Here we see that the researcher has separated the total population into homogenous groups of democrat, republican, or independent.

From these homogenous groups, she selected random samples.

Thus, the kind of sample selected by the researcher is stratified sampling.

To learn more about stratified sampling visit https://brainly.com/question/20544692

#SPJ4

Answer: [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex]

Step-by-step explanation:

If the numbers have at least one 2 and at least one 5, then they are multiples of 10 (since [tex]10=2 \times 5[/tex]).

So, these numbers are [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex].

The fact that Maria runs of a mile every 8 minutes means that we runs faster.

The speed is measured as the distance with respect to the time. This will be illustrated thus:

Maria runs of a mile every 8 minutes. Althea runs 2 miles every of an hour. It should be noted that an hour is 60 minutes. That means the she runs 1 mile in (60 / 2) = 30 minutes.

In this case, Maria runs faster. This is because of her speed.

Learn more about speed on:

brainly.com/question/4931057

#SPJ1

Answer:

It is arithmetic, the common difference is 5

Step-by-step explanation:

What an arithmetic sequence has to have is a common difference meaning you are adding or subtracting the same number each time, in this case you are adding 5 every time so it is arithmetic

The output of the linear function is -n+3 when the input is n.

A linear equation is given by ,

f(x) = mx+ c   ---(1)

From the table,

x value increases by 1

y value decreases by 1

Substituting slope m = - 1 in (1)

f(x) = -x+ c  ---(2)

Substitute  (1, 2) in (2)

2 = -1 +c

c = 2 + 1

c = 3

Substitute slope m and c in (2)

f( x ) = - x + 3

When input is n output is given by,

f(n) = - n + 3

The output of the linear function is -n+3 when the input is n.

To learn more about slope, refer:

https://brainly.com/question/3493733

#SPJ13

Answer:

7358.84

Step-by-step explanation:

Step 1

An improper fraction is a fraction in which the numerator(top number) is greater than or equal to the denominator ( the bottom number)

Step 2

Conclude based on step 1

Hence

Therefore the right answer is an improper fraction