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MaRussiya [10]
2 years ago
10

tom had a very challenging fraction multiplycation problem to do, but his sister said it was really easy to do mentally. can you

find the answer mentally? Explain how
Mathematics
2 answers:
noname [10]2 years ago
5 0

Answer:

Step-by-step explanation:

show the picture of the problem

Veseljchak [2.6K]2 years ago
5 0

Well it's too easy if you understand

\\ \tt\hookrightarrow \dfrac{a}{b}\times \dfrac{c}{d}

  • Just multiply denominator with denominator and numerator and numerator.

\\ \tt\hookrightarrow \dfrac{ac}{bd}

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Answer: B

Step-by-step explanation:

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3 years ago
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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
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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.

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X - 2y + 2z = -22 <br> x + 3y - z = 03 <br> x + 2y + 3z = -15
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