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Brilliant_brown [7]
3 years ago
14

Determine whether the

Mathematics
1 answer:
blagie [28]3 years ago
6 0

Answer:

B.

Step-by-step explanation:

If n = 1 ,  a1 = 9^1^2 +3 = 12

a2 = 9*2^2 + 3 = 39

a3 = 9*3^2 + 3 = 84

The differences are 39 - 12 = 27 and 84 - 39 = 45   so it is not arithmetic as an arithmetic series ad a common difference.

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Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with
skad [1K]

Parameterize S by the vector function

\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle

The integral of the field over S is then

\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv

\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv

\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}

8 0
2 years ago
Mrs. Reid is going on a trip. She has 9 book that she hasn't ready yet, but she wants to bring only 3 on the trip.
Karo-lina-s [1.5K]
The way you work this out is by thinking about the odds of each singular event, then finding the overall odds based on the individual odds.

The number of different books Mrs. Reid can choose is 9, so the first number is 9.

Mrs. Reid has picked one book so far, so now she has (1 - 9) = 8 books to choose from.
The of different books Mrs. Reid can choose now is 8, so your second number is 8.

Mrs. Reid has picked 2 book thus far, so now there are (2 - 9) = 7 books to choose from.
The of different books Mrs. Reid can choose now is 7, so your second number is 7.

To get the total number of different choices, multiply all the singular events together:

7*8*9=504\ different\ ways\ to\ bring\ 3\ books
7 0
3 years ago
Your parents purchase a computer for $1,257.00 plus 6% sales tax. They decide to finance it through the store’s 0% program for 6
Katena32 [7]

Answer:

$111.59

Step-by-step explanation:

The total amount of the purchase was the cost of the computer plus the sales tax:

$1,257*1,06= $1,332.42

Now, to determine the interest that they will have to pay, you have to consider that the interest rate is 16,75% APR that is the annual percentage rate but as only 6 month have passed, the interest rate at this point that they have to pay is 8.375%:

$1,332.42*8.375%= $111.59

The interest that they will be charged is  $111.59

5 0
3 years ago
Solve y=3x-4 and y=2/5x 9
mojhsa [17]
I need the sign between the (2/5)x and the 9
5 0
3 years ago
Write the equation of each ellipse in standard form with the given characteristics.
Eddi Din [679]

Answer:

Step-by-step explanation:

The foci are horizontally aligned.

horizontal ellipse:

(x-h)²/a² + (y-k)²/b² = 1

center (h,k)

vertices (h±a,k)

length of minor axis = 2b

foci (h±c,k), c² = a²-b²

Apply your data and solve for h, k, a, and b.

foci (±3√19, 6)

h = 0

k = 6

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b = 5

foci (h±3√19, 6)

c = 3√19

c³ = a² - b²

171 = a² - 25

a²  = 196

x²/196 + (y-6)²/25 = 1

6 0
2 years ago
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