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kiruha [24]
3 years ago
10

Give the simple formula for the nth term of the following arithmetic sequence. Your answer will be of the form an + b.

Mathematics
1 answer:
klasskru [66]3 years ago
6 0
14, 18, 22, 26, 30, . . . = 14, 14 + 4, 14 + 8, 14 + 12, 14 + 16, . . . = 14, 14 + 1(4), 14 + 2(4), 14 + 3(4), 14 + 4(4), . . . = 14 + 4(n - 1) = 14 + 4n - 4 = 4n + 10
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A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of
Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0
2 years ago
-4w+18w+2=10-6w <br><br> What is w?
kiruha [24]

Answer:

w = .5

Step-by-step explanation:

-4w + 18w+2=10 -6w

14w + 2 -2 = 10 -2 -6w

14w + 2w = 8 - 2w + 2w

16w = 8

16w/16 = 8/16

w = .5

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Answer:

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stellarik [79]

Answer:

x = 11/7

Step-by-step explanation:

x - 2/7 = 9/7

x = 9/7 + 2/7

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Answer:

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