Suppose that the power series, LaTeX: \sum c_n x^n∑ c n x n, converges when x = −4 and diverges when x = 7. Determine whether each statement is true, false or not possible to determine. (a) The power series converges when x = 10. (b) The power series converges when x = 3. (c) The power series diverges when x = 1. (d) The power series diverges when x = 6.

A. FALSE

B. TRUE

C. FALSE

D. NOT POSSIBLE TO DETERMINE

Step-by-step explanation:

(A) FALSE. since the power series ∑ has radius of convergence |-4|=4 ans 7> 4 which is beyond its radius of convergence. thus by the theorem of power series, the series diverges at 10.

(B)TRUE. since the radius of convergence of the power series ∑ must be at least |-4| = 4 and 3 lies within this radius, thus it converges at x=3

(C)FALSE the series does not diverge at x=1, since 1 is within its radius of convergence |-4| = 4

(D)NOT POSSIBLE TO DETERMINE

At x=6, it is beyond its radius of convergence but has not attain its divergence point. thus it is not possible to determine.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.