Determine whether the series [infinity] cos(n) n2 n = 1 = cos(1) 12 + cos(2) 22 + cos(3) 32 + ⋯ is convergent or divergent. SOLUTION The series has both positive and negative terms, but it is not alternating. (The first term is positive, the next three are negative, and the following three are positive: The signs change irregularly.) We can apply the Comparison Test to the series of absolute values [infinity] cos(n) n2 n = 1 = [infinity] |cos(n)| n2 n = 1 . Since |cos(n)| ≤ 1 Correct: Your answer is correct. for all n, we have |cos(n)| n2 ≤ 1 n2 . We know that Σ 1/n2 is convergent p−series with p = and therefore Σ |cos(n)|/n2 is convergent by the Comparison Test. Thus the given series Σ (cos(n))/n2 is absolutely convergent and therefore convergent by this theorem.

hello :

70y^8 + 30y^6 = 2 ( 35 y^8 + 15y^6)

the lenght is : 35 y^8

the width is : 15y^6

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

the answer is  

a.

28 ft2

step-by-step explanation:

10 - 8 = -2

  8 - 6 = -2

etc, so -2 is the common difference

step-by-step explanation: