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2 years ago

If two fair dice are rolled at the same time, what is the probability that of it obtaining two multiples of 3?

2 answers:

6 0

Im assuming this is a non biased 6 sided dice,

multiples of 3 would be 3 and 6 therefore chance of rolling one would be 2/6 = 1/3.

however since the question says two dice at the same time, you have to multiply the probability which would be 1/3 x 1/3 = 1/9

Bingel [31]2 years ago

6 0

How many multiples of three are there in a dice?
6 and 3. So 2.
And there are 6 possible outcomes for each dice, and both dices added there are 12 possible outcomes. This number will be your denominator.
So since there are 2 in each dice, add them to equal 4, and put the 4 as the nominator.
Anser: 4/12.

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algol [13]

Answer:

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Step-by-step explanation:

Let the base be 8 (as shown).

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sin 80 degrees = ---------------

and so the height of the triangle is h = 6 sin 80 degrees, or 5.91 units.

The area of the triangle is found using A = (1/2)(base)(height), which here amounts to:

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3 years ago

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2 years ago

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ

MariettaO [177]

The given curve has equation

r(θ) = 9 + 8 cos(θ)

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dr/dθ = -8 sin(θ)

When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.

Differentiate these with respect to θ :

dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)

dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)

In polar coordinates, we have

y(θ) = r(θ) sin(θ)

x(θ) = r(θ) cos(θ)

and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.

The slope of the tangent line to the curve is dy/dx. By the chain rule,

dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)

dy/dx = (dr/dθ sin(θ) + r(θ) cos(θ)) / (dr/dθ cos(θ) - r(θ) sin(θ))

When θ = π/3, the slope is

dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))

dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))

dy/dx = - 1/(17√3)

So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is

y - 13√3/2 = -1/(17√3) (x - 13/2)

y = -(x - 338)/(17√3)

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san4es73 [151]

Answer:

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Step-by-step explanation:

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