What exactly is the meaning of the del symbol with an x next to it, as seen in Equation [1]? To understand this, we will again use the analogy of flowing water to represent a vector function or vector field. In Figure 1, we have a vector function V and we want to know if the field is rotating at the point D that is, we want to know if the curl is zero. Example of a Vector Field Surrounding a Point.

Math Home Search Dr. Cannot find rigorous solution, just the obvious.

I cannot find a rigorous solution to the following: Solve for X in terms of Y only: Hi Chuck, Thanks for writing to Dr.

But let me tell you how you would be best advised to analyze this equation: First take the log of both sides: Look at the function, and you'll find that the smaller value is somewhere between 1 and e, and the larger value is bigger than e. Also, the closer the smaller value is to e, the closer the larger value is to e.

The closer the smaller value is to 1, the bigger the larger value is. But can you write out a formula for the smaller value in terms of the bigger value, or vice-versa? Well, not using any closed-form function. But you can use numerical methods to find approximate solutions for any X value.

If you have any questions about this or need more help, please write back and show me what you have been able to do, and I will try to offer further suggestions. Hi again, Chuck, It occurs to me that there is something else about this equation that you might be interested in.

The solutions you gave 2, 4 and 4, 2 are in integers. Proving that is as follows: First suppose that X and Y are positive.

Since the left side is clearly an integer, the right side has to be an integer. But if you raise a non-integer rational number to an integer power, then you don't get an integer.

If both X and Y are even, then we don't need to multiply, and we still get the same equation. So -X, -Y is a solution in positive integers. Again, if you have any questions about this or need more help, please write back and show me what you have been able to do, and I will try to offer further suggestions.A line has a slope of negative 3/4 and goes through the point 0 comma 8.

What is the equation of this line in slope-intercept form?

So any line can be represented in slope-intercept form, is y is equal to mx plus b, where this m right over here, that is of the slope of the line. The Story Equation: How to Plot and Write a Brilliant Story from One Powerful Question (Brilliant Writer Series) - Kindle edition by Susan May Warren.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading The Story Equation: How to Plot and Write a Brilliant .

Students are asked to write and solve a two-step equation to model the relationship among variables in a given scenario. The equation is nonlinear because of the square of x, but it is still a function because there is only one answer for every x.

When evaluating a function for a specific value, you place the value in the parenthesis rather than the variable.

Improve your math knowledge with free questions in "Slope-intercept form: write an equation from a word problem" and thousands of other math skills. (CONTINUED) Transforming an equation from Polar to Rectangular Form.

Example 8 on p Transform r = 4sinθto rectangular coordinates. Since x2 + y2 = r2 multiply both sides by r to get r2 on the left. r2 = 4rsinθ Substitute x2 + y2 for r2 and y for rsinθ x2 + y2 = 4y Put everything on the left to see this is an equation of a circle.

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simplify and write the trigonometric equation in terms of sine and cosine.