The equation for qr is 5y=-4x+41. is qr tangent to circle o at r

The equation of the given tangent is: . This can be rewritten as: (by dividing both sides by 5).

Therefore, the slope of the above equation is -0.8. Let us denote it by . Thus,

Now, the equation of the line from the origin, (0,0) and the point (4,5) can be found as:

or,

The above is the equation of the radius of the given circle what passes through the same point (4,5) from where the tangent passes.

The slope of the radius line is 1.25. Let us depict it by . Therefore, .

Now, we know that "the tangent lines are always perpendicular to a circle's radius at the point of intersection". And we also know that for perpendicular lines the product of their slopes is always -1.

Thus, in our case the product of and should be -1.

When we multiply and we indeed get -1

()

Therefore, we have concluded that is tangent to the circle at R because the radius is perpendicular to the tangent at R.

Thus, out of the given options, the last option is the correct option.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: