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OverLord2011 [107]
3 years ago
10

14. In the following figure, M is the midpoint of

Mathematics
1 answer:
timama [110]3 years ago
3 0

Answer:

angle OAM and OBM are right angles because tangents form right angles with radii.

AO=BO and MA=MB

Quadrilateral MAOB =360 degrees

so angles AOB and AMB=90 degrees each

angle MBF=90 degrees

M is the midpoint of FA so MA=MF

MB=MF

Triangle MBF is a right triangle because angle BMF is 90 degrees and  MB=MF

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Can you tell me how to calculate R for below Matrix ?
scoray [572]

Answer:

The rank of the matrix is 3.

Step-by-step explanation:

Consider the prided information.

x=\begin{bmatrix}x_1\\ x_2\\ x_3\end{bmatrix}=\begin{bmatrix}9&2&6&5&8\\ 12&8&6&4&10\\ 3&4&0&2&1\end{bmatrix}

Reduce the matrix in row echelon form as shown:

R_1\:\leftrightarrow \:R_2\begin{bmatrix}12&8&6&4&10\\ 9&2&6&5&8\\ 3&4&0&2&1\end{bmatrix}\\

R_2\:\leftarrow \:R_2-\frac{3}{4}\cdot \:R_1\ and\ R_3\:\leftarrow \:R_3-\frac{1}{4}\cdot \:R_1\\\\\begin{bmatrix}12&8&6&4&10\\ 0&-4&\frac{3}{2}&2&\frac{1}{2}\\ 0&2&-\frac{3}{2}&1&-\frac{3}{2}\end{bmatrix}

R_3\:\leftarrow \:R_3+\frac{1}{2}\cdot \:R_2\\\begin{bmatrix}12&8&6&4&10\\ 0&-4&\frac{3}{2}&2&\frac{1}{2}\\ 0&0&-\frac{3}{4}&2&-\frac{5}{4}\end{bmatrix}

R_2\:\leftarrow \:R_2-\frac{3}{2}\cdot \:R_3\ and\ R_1\:\leftarrow \:R_1-6\cdot \:R_3\\\begin{bmatrix}12&8&0&20&0\\ 0&-4&0&6&-2\\ 0&0&1&-\frac{8}{3}&\frac{5}{3}\end{bmatrix}\\R_2\:\leftarrow \:-\frac{1}{4}\cdot \:R_2\ , \ R_1\:\leftarrow \:R_1-8\cdot \:R_2\ and\ \:R_1\:\leftarrow \frac{1}{12}\cdot \:R_1\\\begin{bmatrix}1&0&0&\frac{8}{3}&-\frac{1}{3}\\ 0&1&0&-\frac{3}{2}&\frac{1}{2}\\ 0&0&1&-\frac{8}{3}&\frac{5}{3}\end{bmatrix}

The rank of a matrix is the number of non zeros rows.

Thus, the rank of the matrix is 3.

6 0
3 years ago
12 and 3000 as decimals full equation
ICE Princess25 [194]

Answer:

12=0.12x100

3000=0.3x10000

3 0
2 years ago
What does y mean in math
Georgia [21]

Answer: There are many uses for the variable* y in math: it is often used as a variable and the y axis of a coordinate plane (the line that is vertical.)  

* = Variable: any unknown number in algebra, is usually replaced with letters, such as x or y.

4 0
4 years ago
Type the correct answer in the box. assume π = 3.14. and round your answer to the nearest hundredth. at the rate of $2.00 per sq
spin [16.1K]

The cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.

<h3>How to find the area of the composite figures?</h3>

To find area of the composite figures,

  • Separate the figure.
  • Calculate the are of the each figure by which the composite figure is made of.
  • Add the area of all the individual figures to get the total area of composite figures.

The dimentions of the rectangle is 3 by 4 foot. The area of the rectangle is,

A_r=3\times4\\A_r=12\rm \;ft^2

The radius of the semicircle is 1.5 m. The area of the semicircle is,

A_{sc}=\dfrac{1}{2}\pi\times(1.5)^2\\A_{sc}=\dfrac{1}{2}(3.14)\times(1.5)^2\\A_{sc}=3.5325\rm\; ft^2

The area of the composite figure is,

A=12+3.5325\\A=15.5325\rm\;ft^2\\

The rate of  painting is $2.00 per square foot. Thus the cost to paint the figure is,

A=15.5325\times2\\A=31.065

Hence, the cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.

Learn more about the area  of composite figures here;

brainly.com/question/15981553

8 0
3 years ago
Angela chooses between having $1,000 now, and investing it in a savings account so that she can have $1,050 a year from now, wha
natka813 [3]

Answer:

it is called interest

6 0
3 years ago
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