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nika2105 [10]
3 years ago
12

Can someone break this down for me!! I'm stuck

Mathematics
1 answer:
nadya68 [22]3 years ago
4 0

Answer:

_{12}C_9=220

Step-by-step explanation:

Recall the definition for the combination symbol with the use of factorial (symbol !):

_nC_k=\frac{n!}{k!(n-k)!}

Therefore, for the case where n = 12 and k = 9, we have:

_{12}C_9=\frac{12!}{9!(3)!}\\_{12}C_9=\frac{12*11*10*9*8*7*6*5*4*3*2}{9*8*7*6*5*4*3*2(3*2)}\\\\_{12}C_9=\frac{12*11*10}{3*2}\\\\_{12}C_9=\frac{1320}{6}\\\\_{12}C_9=220

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Step-by-step explanation:

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Given vectors u = (−1, 2, 3) and v = (3, 4, 2) in R 3 , consider the linear span: Span{u, v} := {αu + βv: α, β ∈ R}. Are the vec
julia-pushkina [17]

Answer:

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Step-by-step explanation:

Let b=(b_1,b_2,b_3) \in \mathbb{R}^3. We have that b\in \text{Span}\{u,v\} if and only if we can find scalars \alpha,\beta \in \mathbb{R} such that \alpha u + \beta v = b. This can be translated to the following equations:

1. -\alpha + 3 \beta = b_1

2.2\alpha+4 \beta = b_2

3. 3 \alpha +2 \beta = b_3

Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for \alpha,\beta and check if the third equationd is fulfilled.

Case (2,6,6)

Using equations 1 and 2 we get

-\alpha + 3 \beta = 2

2\alpha+4 \beta = 6

whose unique solutions are \alpha =1 = \beta, but note that for this values, the third equation doesn't hold (3+2 = 5 \neq 6). So this vector is not in the generated space of u and v.

Case (-9,-2,5)

Using equations 1 and 2 we get

-\alpha + 3 \beta = -9

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katen-ka-za [31]

Step-by-step explanation:

we know that perimeter of triangle is equals to side + side + side

but we can see that the particular triangle is having all the sides equal so it is seen to be equal lateral triangle and formula of equilateral triangle is 3 × sides.....

So,We will take sides common.....

Perimeter of equilateral triangle= 3×Side

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Pi/6 is the reference angle for:<br><br> 3pi/6<br><br> 5pi/6<br><br> 13pi/6<br><br> 8pi/6
Elanso [62]

Answer:

\frac{5\pi}{6}, \frac{13\pi}{6}

Step by step

Remember, a reference angle is a positive acute angle that represents an angle θ of any measurement.

a)

\frac{3\pi}{6}=90^\circ, then its reference angle is \frac{\pi}{2}

b)

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c)

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d)

\frac{8\pi}{6}=240^\circ and it is in the third cuadrant, then its reference angle is 240^\circ -180^\circ=60^\circ=\frac{\pi}{3}

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3 years ago
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