Science, asked by thapaavinitika6765, 7 months ago

Solve : foci\:\frac{\left(x-1\right)^2}{9}+\frac{y^2}{5}=100

Answers

Answered by LastShinobi
1

Answer:

dividing by a fraction is the same as multiplying by the reciprocal of the fraction.

In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,

x2+3x

x+3

has a quadratic binomial in the numerator and a linear binomial in the denominator. We have to apply the different factorisation methods in order to factorise the numerator and the denominator before we can simplify the expression.

x2+3x

x+3

=

x(x+3)

x+3

=x(x≠−3)

If x=−3 then the denominator, x+3=0 and the fraction is undefined.

Explanation:

Hope it will help

Answered by XxMrGlamorousXx
0

\begin{gathered}\mathrm{Rank}\:\begin{pmatrix}2&1&6\\ 3&4&5\end{pmatrix}=2\end{gathered}

Rank(

2

3

1

4

6

5

)=2

\begin{gathered}\mathrm{Reduce\:matrix\:to\:reduced\:row\:echelon\:form}\:\begin{pmatrix}1\:&\:\cdots \:&\:b\:\\ 0\:&\ddots \:&\:\vdots \\ 0\:&\:0\:&\:1\end{pmatrix}\end{gathered}

Reducematrixtoreducedrowechelonform

1

0

0

0

b

1

\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_2\:\mathrm{\:by\:performing}\:R_2\:\leftarrow \:R_2-\frac{2}{3}\cdot \:R_1CancelleadingcoefficientinrowR

2

byperformingR

2

←R

2

3

2

⋅R

1

\begin{gathered}=\begin{pmatrix}3&4&5\\ 0&-\frac{5}{3}&\frac{8}{3}\end{pmatrix}\end{gathered}

=(

3

0

4

3

5

5

3

8

)

\begin{gathered}\mathrm{Reduce\:matrix\:to\:reduced\:row\:echelon\:form}\:\begin{pmatrix}1\:&\:\cdots \:&\:b\:\\ 0\:&\ddots \:&\:\vdots \\ 0\:&\:0\:&\:1\end{pmatrix}\end{gathered}

Reducematrixtoreducedrowechelonform

1

0

0

0

b

1

\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_1\:\mathrm{\:by\:performing}\:R_1\:\leftarrow \:R_1-4\cdot \:R_2CancelleadingcoefficientinrowR

1

byperformingR

1

←R

1

−4⋅R

2

\begin{gathered}=\begin{pmatrix}3&0&\frac{57}{5}\\ 0&1&-\frac{8}{5}\end{pmatrix}\end{gathered}

=(

3

0

0

1

5

57

5

8

)

\mathrm{Multiply\:matrix\:row\:by\:constant:}\:R_1\:\leftarrow \frac{1}{3}\cdot \:R_1Multiplymatrixrowbyconstant:R

1

3

1

⋅R

1

\begin{gathered}=\begin{pmatrix}1&0&\frac{19}{5}\\ 0&1&-\frac{8}{5}\end{pmatrix}\end{gathered}

=(

1

0

0

1

5

19

5

8

)

\bf{The\:rank\:of\:a\:matrix\:is\:the\:number\:of\:non\:all-zeros\:rows}Therankofamatrixisthenumberofnonall−zerosrows

=2=2

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