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3 years ago

9 cm

Mathematics

1 answer:

olga2289 [7]3 years ago

4 0

Step-by-step explanation:

583,200 cubic centimeters

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Natasha places a mirror on the ground 24 ft from the base of an oak

Kamila [148]

Answer:

33 ft

Step-by-step explanation:

5.5/4 = x/24

x=33

6 0

3 years ago

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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

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

6 0

3 years ago

√secA+tanA/√secA-tanA × √cosecA-1/√cosecA+1=1

Snowcat [4.5K]

$Use:\\\\\sec A=\dfrac{1}{\cos A}\\\\\tan A=\dfrac{\sin A}{\cos A}\\\\\csc A=\dfrac{1}{\sin A}\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\---------------------------------\\\\\sec A+\tan A=\dfrac{1}{\cos A}+\dfrac{\sin A}{\cos A}=\dfrac{1+\sin A}{\cos A}\\\\\sec A-\tan A=\dfrac{1-\sin A}{\cos A}\\\\\csc A-1=\dfrac{1}{\sin A}-\dfrac{\sin A}{\sin A}=\dfrac{1-\sin A}{\sin A}\\\\\csc A+1=\dfrac{1+\sin A}{\sin A}$

$\dfrac{\sqrt{\sec A+\tan A}}{\sqrt{\sec A-\tan A}}\cdot\dfrac{\sqrt{\cos A-1}}{\sqrt{\cos A+1}}=1\\\\L_s=\sqrt{\dfrac{\sec A+\tan A}{\sec A-\tan A}\cdot\dfrac{\cos A-1}{\cos A+1}}=\sqrt{\dfrac{\frac{1+\sin A}{\cos A}}{\frac{1-\sin A}{\cos A}}\cdot\dfrac{\frac{1-\sin A}{\sin A}}{\frac{1+\sin A}{\sin A}}}\\\\=\sqrt{\dfrac{1+\sin A}{\cos A}\cdot\dfrac{\cos A}{1-\sin A}\cdot\dfrac{1-\sin A}{\sin A}\cdot\dfrac{\sin A}{1+\sin A}}\\\\\text{Everything are simplified}\\\\=\sqrt{1}=1=R_s$

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3 years ago

Find the two angles and show work!!!

USPshnik [31]

Answer:

x=23.5

Step-by-step explanation:

90=25-x/2+18

combine like terms

90=43-x/2

subtract 43 from both sides

47= -×/2

47/2= 23.5

x=23.5

90-25= 65

65-18=47

47/2=23.5

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3 years ago

14,762 is what percent of 121

Irina-Kira [14]

Answer:

12,200

Step-by-step explanation:

hope this helps!!!

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3 years ago

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