Find fx(8, 0) and fy(8, 0) and interpret these numbers as slopes for the following equation. 1. f( x, y) = sqrt(537-x^2-4y^2)
2. fx(8, 0) =
3. fy(8, 0) =
Illustrate with either hand-drawn sketches or computer plots. (Do this on paper. Your instructor may ask you to turn in this work.)

  and  

Step-by-step explanation:

Given that:

The objective is to determine

Let determine the partial derivative of the function f with respect to x and y, differentiate partially with respect to x. we have:

Thus,

Differentiate partially with respect to y, we have:

Thus,

Now, substitute 8 for x and o for y into the function

Also, substitute 8 for x and 0 for y into the function

Therefore,   and  

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4