Find the circumcenter of a triangle with vertices o(0, 0), v(0, 26), and w(−10,0).

Circumcenter is .

Step-by-step explanation:

Given:

The three vertices of triangle OVW are .

Circumcenter is a point inside the triangle which is equidistant from each of the vertices of the triangle.

Let be the circumcenter.

Distance between two points and  is given as:

So, as per the definition of circumcenter, distance of point from point is equal to distance of point from point .

So, OC = VC

or

.

Similarly, distance of point from point is equal to distance of point from point .

or

.

Therefore, the circumcenter of the triangle with the given vertices is .

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week