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ON THE FIRST SET OF QUESTIONS, IS THERE ANYWAY TO SHOW ME THE STEPS OF PROBLEMS 1,4,6,7, AND 9? GREAT WORK BY THE WAY

Customer:replied 9 months ago.

Variation is a great example of how mathematics is used to model and solve real-world problems. Many fields of study contain examples of the three different kinds of variation:

Direct variation (for example, y = kx)

Inverse variation (for example, y = k/x)

Joint variation (for example, z = kxy)

Definition of Joint Variation

Joint variation is the same as direct variation with two or more quantities.

"That is:

Joint variation is a variation where a quantity varies directly as the product of two or more other quantities.

Let’s first understand direct variation.

Direct variation occurs when two quantities change in the same manner.

That is:

Increase in one quantity causes an increase in the other quantity.

Decrease in one quantity causes a decrease in the other quantity.

For example:

The cost of a pencil and the number of pencils you buy.

Buy more pay more….Buy less pay less.

Direct variation between variables xand ycan be expressed as:

y = kx, where ‘k’ is the constant of variation and k ≠ 0.

y = kxz represents joint variation.Here, y varies jointly as x and z.

More Examples on Joint Variation

y = 7xz, here y varies jointly as x and z.

y = 7x^{2}z^{3}, here y varies jointly as x^{2} and z^{3}."

Math Dictionary

The variable is in the bottom of a fraction or in the denominator. (The Opposite of Direct Variation) In an inverse variation, the values of the two variables change in an opposite manner - as one value increases, the other decreases.

For example, a biker traveling at 8 mph can cover 8 miles in 1 hour. If the biker's speed decreases to 4 mph, it will take the biker 2 hours (an increase of one hour), to cover the same distance.

Please start by addressing one or more of the following topics to get the discussion going:

How would you describe the difference between direct variation and joint variation in words? Use examples to help illustrate.

Pick a field of study of interest to you and give an example of variation in that field. Some possible areas to consider are: Economics, Finance, Geometry and Physics. Example: If your hourly pay rate is $15/hour, then your weekly pay p is given by the formula p=15h where h is the number of hours worked in a week. So, your weekly pay varies directly as the number of hours worked in a week with the constant of variation = 15.

Most formulas are actually examples of variation. Pick a well-known formula and describe the type of variation as well as the constant of variation, k. Example: The area A of a triangle with base b and height h is given by the formula A=½bh. So, the area of a triangle varies jointly as the base and height (both direct) with the constant of variation = ½.

Give an example from real life where composite functions are utilized. For ideas, you may look it up on the internet or find examples in the book.

if it doesn't cost extra. I am trying to understand

Customer:replied 9 months ago.

Can you solve these with steps included and I will give you a big tip. I just can't afford another $60.00

Find the vertex of the parabola f(x) = x^{2 }- 16x + 63.

Find the x- and y-intercepts of the cubic function f(x) = (x+4)(2x-1)(x-1).

If f(x) = x^{2}-2x-24 and g(x) = x^{2}-x-30, find (f-g)(x).

If f(x) = x+4 and g(x) = 2x^{2}-x-1, evaluate the composition (g o f)(2).

If f(x) = x+4 and g(x) = 2x^{2}-x-1, find the composition (f o g)(x).

Write the following sentence as an equation: y varies directly as x.

Write the following sentence as an equation: x is directly proportional to y and is inversely proportional to the cube of z.

What are the zeros of the parabola: f(x) = x^{2} - 7x + 10 (that is, what are the x-intercepts or the points where the graph crosses the x-axis)?

What is the vertical asymptote of the rational function f(x) = 3x / (2x - 1)?

What is the horizontal asymptote of the rational function f(x) = 3x / (2x - 1)?

How would you describe the difference between direct variation and joint variation in words? Use examples to help illustrate.

Pick a field of study of interest to you and give an example of variation in that field. Some possible areas to consider are: Economics, Finance, Geometry and Physics. Example: If your hourly pay rate is $15/hour, then your weekly pay p is given by the formula p=15h where h is the number of hours worked in a week. So, your weekly pay varies directly as the number of hours worked in a week with the constant of variation = 15.

Most formulas are actually examples of variation. Pick a well-known formula and describe the type of variation as well as the constant of variation, k. Example: The area A of a triangle with base b and height h is given by the formula A=½bh. So, the area of a triangle varies jointly as the base and height (both direct) with the constant of variation = ½.

Give an example from real life where composite functions are utilized. For ideas, you may look it up on the internet or find examples in the book.

I am going to have more work and wanted to see if I could request you.

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