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3 years ago

Select the correct answer from each drop-down menu.

Mathematics

1 answer:

Nesterboy [21]3 years ago

4 0

Answer:

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Step-by-step explanation:

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Evaluate the expression when x = 3.<br>7) 4.5x

iren2701 [21]

Answer: 13.5

Step-by-step explanation: You would plug 3 in for x. The expression would then be 3(4.5). This is equivalent to 13.5 when simplified.

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3 years ago

Help me with this please!!!!!!

castortr0y [4]

Answer:

$\huge\mathcal\red{here's \: your \: solution..} \\ \\ \cos = base \div hypotenuse \: \\ \\ \cos(60) = 1 \div 2 \\ \\ \cos = a \div 14 \\ \\ a \div 14 = 1 \div 2 \\ \\ a = 14 \div2 \\ \\ a = 7 \: cm \\ \\ \huge\mathfrak\green{hope \: it \: helps..}$

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3 years ago

Find a formula for the least squares solution of ax=b when the columns of a are orthonormal1 .

neonofarm [45]

Let $\mathbf A$ be a rectangular $m\times n$ matrix with column vectors $\mathbf a_1,\ldots,\mathbf a_n$ , i.e.

$\mathbf A=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}$

Then we have

$\mathbf A^\top=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}^\top$

and the product of the two is

$\mathbf A^\top\mathbf A=\begin{bmatrix}\mathbf a_1\cdot\mathbf a_1&\mathbf a_1\cdot\mathbf a_2&\cdots&\mathbf a_1\cdot\mathbf a_n\\\mathbf a_2\cdot\mathbf a_1&\mathbf a_2\cdot\mathbf a_2&\cdots&\mathbf a_2\cdot\mathbf a_n\\\vdots&\vdots&\ddots&\vdots\\\mathbf a_n\cdot\mathbf a_1&\mathbf a_n\cdot\mathbf a_2&\cdots&\mathbf a_n\cdot\mathbf a_n\end{bmatrix}$

Because the columns of $\mathbf A$ are orthonormal, we have

$\mathbf a_i\cdot\mathbf a_j=\begin{cases}1&\text{for }i=j\\0&\text{for }i\neq j\end{cases}$

which means $\mathbf A^\top\mathbf A$ reduces to an $n\times n$ matrix with ones along the diagonal and zero everywhere else, i.e.

$\mathbf A^\top\mathbf A=\begin{bmatrix}1&0&\cdots&0\\0&1&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&0&\cdots&1\end{bmatrix}=\mathbf I_n$

where $\mathbf I$ denotes the identity matrix. This means the solution to $\mathbf{Ax}=\mathbf b$ is given by

$\mathbf A^\top(\mathbf{Ax})=\mathbf A^\top\mathbf b\implies(\underbrace{\mathbf A^\top\mathbf A}_{\mathbf I})\mathbf x=\mathbf A^\top\mathbf b\implies\mathbf x=\mathbf A^\top\mathbf b$

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3 years ago

How do you show the work for 1162 divided by 4

Blizzard [7]

You would solve, so 1162/4. Show the steps of you dividing it down on notes of paper

6 0

3 years ago

The product of 3 and a number increased by 8 is -48<br> what is the number?

Alekssandra [29.7K]

You just have to reverse the operations
1. -48-8= -56
2. -56/3= -18.66

ANSWER = -18.66

4 0

4 years ago