For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. what is the number of variations in sign for the sequence 1, –3, 2, 5, –4, –6 ?

The no. of variations in sign is 3

Step-by-step explanation:

Variation in sign occurs when every single time a negative product is produced by a pair of consecutive terms.

Therefore, the determination of the number of changes in sign in the given sequence is must.

Therefore, we take the product of the pair of consecutive terms as:

= - 3, variation in sign

= - 6,  variation in sign

= 10,  no sign variation

= - 20,  variation in sign

= 24, no sign variation

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.