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3 years ago

I need help please!!

Mathematics

1 answer:

Nat2105 [25]3 years ago

7 0

Answer:

Step-by-step explanation:

sike i lied this is so easy pls try pls

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The inequality –x2 – 6 0 has critical points

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The critical point is (-30,0) I think

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Solve the equation<br> 1/2log(x-2) = 3log2-3/2log(x-2)<br> all logs are in base 5

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There are 600 students at a middle school. If 60% of the students are girls, how many students at the middle school are girls?

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Step-by-step explanation:

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find a homogeneous linear system of two equations in three unknowns whose solution space consists of those vectors in R3 that ar

Leona [35]

$\mathbf a=(1,1,1)^\top=1\,\mathbf i+1\,\mathbf j+1\,\mathbf k$
$\mathbf b=(-2,3,0)^\top=-2\,\mathbf i+3\,\mathbf j$
$\mathbf a\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\1&1&1\\-2&3&0\end{vmatrix}=-3\,\mathbf i-2\,\mathbf j+5\,\mathbf k=(-3,-2,5)^\top$

Basically, you're looking for a matrix $\mathbf A$ such that

$\mathbf A(\mathbf a\times\mathbf b)=\mathbf 0$

i.e. a matrix $\mathbf A$ whose nullspace with basis vector $\mathbf a\times\mathbf b$ .

By the rank-nullity theorem, the rank of $\mathbf A$ and the dimension of its nullspace must add up to the number of columns, so

$\mathrm{rank}\mathbf A+\underbrace{\mathrm{null}\mathbf A}_1=3\implies\mathrm{rank}\mathbf A=2$

One easy choice for a row would be $\begin{bmatrix}1&1&1\end{bmatrix}$ , since

$(1,1,1)(-3,-2,5)^\top=0$

Now you only need to find another combination such that the second row of $\mathbf A$ is independent of the first. An easy choice for this is to let the first element be 0, and the next be 1. Then the last element must be $\dfrac25$ , as

$\left(0,1,\dfrac25\right)(-3,-2,5)^\top=0$

So,

$\underbrace{\begin{bmatrix}1&1&1\\0&1&\frac25\end{bmatrix}}_{\mathbf A}\begin{bmatrix}-3\\-2\\5\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}$

is one possible solution.

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3 years ago

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puteri [66]

Answer: y= -7/8x-1 1/2

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