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Dima020 [189]
3 years ago
10

CONVERGENT AND DIVERGENT SERIES PLEASE HELP

Mathematics
1 answer:
drek231 [11]3 years ago
5 0

Answer:

F.

Step-by-step explanation:

We are given a series

We can see that numerators are same

and denominators are

49 , 64 , 81 , .....

so,

7^2 , 8^2 , 9^2

We can write nth term

a_n=(n+7)^2

so, we can write as

\sum _{n=0}^{\infty }\:\frac{1}{\left(n+7\right)^2}

We can use p-series test

\frac{1}{n^p}

we can compare

and we get

p=2>1

So, this series is convergent

this is FALSE

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grandymaker [24]

Answer:

n=2m

Step by step:

total=rate of movie watching per month times months

n=2 movies per month times 'm' months, so,

n=2m

4 0
3 years ago
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Evaluate the given integral by changing to polar coordinates. 8xy dA D , where D is the disk with center the origin and radius 9
BabaBlast [244]

Answer:

0

Step-by-step explanation:

∫∫8xydA

converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.

So,

∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ

So we integrate r from 0 to 9 and θ from 0 to 2π.

∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ

= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ

= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ

= 8[6561/4]∫(cosθsinθ)dθ

= 13122∫(cosθsinθ)dθ

Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2

Substituting this we have

13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ

= 13122/2[-cos2θ]/2 from 0 to 2π

13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]

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= -13122/4[1 - 1]

= -13122/4 × 0

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5 0
2 years ago
Gavin and Caleb go to the movie theater and purchase refreshments for their friends. Gavin spends a total of $22.25 on 2 bags of
gavmur [86]

Answer:

Drinks = 6.75

Popcorn= 1

Step-by-step explanation:

Let the popcorn = P

Let the drink = D

2*P + 3*D = 22.25         multiply this equation by 6

12*P + 4D = 39.00

<u>12P + 18D = 133.5</u>          Subtract these two equations

- 14D = - 94.50               Divide by -14

-14D/-14 = -94.5/-14        Do the division

D = 6.75

=========================

12P  +  4D = 39            Substitute for D

12P + 4*6.75 = 39        Combine

12P + 27 = 39               Subtract 27 from both sides

12P + 27-27=39-27      Collect like terms

12P = 12                        Divide by 12

12P/12 = 12/12

P = 1                               Answer

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mash [69]
A bc it makes the most sence
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Find the gradient of the line segment between the points (-1,3) and (1,-2).
RideAnS [48]

The answer is -5/2, hope this helps you!

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2 years ago
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