User:Hakeem.gadi/philtl

$$\mathrm{d}(\mathbf{V_{x}},\mathbf{V_{y}}) = \sqrt{(f_{y1}-f_{x1})^2 + (f_{y2}-f_{x2})^2 + (f_{y3}-f_{x3})^2} $$

$$\mathrm{d_{\sigma}}(\mathbf{V_{x}},\mathbf{V_{y}}) = \sqrt{\left(\frac{f_{y1}-f_{x1}}{\sigma_1}\right)^2 + \left(\frac{f_{y2}-f_{x2}}{\sigma_2}\right)^2 + \left(\frac{f_{y3}-f_{x3}}{\sigma_3}\right)^2} $$

$$\sigma_{f_{c1}} = \sqrt{ \frac{(f_{c1_1}-E(V_{c1}))^2+(f_{c1_2}-E(V_{c1}))^2+\dots+(f_{c1_{20}}-E(V_{c1}))^2}     {n}        } $$

$$\sigma_{f_{c1}} = \sqrt{ \frac{(2-2.15)^2+(2-2.15)^2+(2-2.15)^2+(2-2.15)^2+(3-2.15)^2+(2-2.15)^2+(2-2.15)^2+\dots+(2-2.15)^2}     {20}        } $$

$$\sigma_{f_{c1}} = \sqrt{ \frac{(-0.15)^2+(-0.15)^2+(-0.15)^2+(-0.15)^2+(0.85)^2+(-0.15)^2+(-0.15)^2+\dots+(-0.15)^2}     {20}        } $$

$$\sigma_{f_{c2}} = \sqrt{ \frac{(f_{c2_1}-E(V_{c2}))^2+(f_{c2_2}-E(V_{c2}))^2+\dots+(f_{c2_{20}}-E(V_{c2}))^2}     {n}        } $$

$$\sigma_{f_{c2}} = \sqrt{ \frac{(1-1.15)^2+(1-1.15)^2+(1-1.15)^2+(1-1.15)^2+(1-1.15)^2+(1-1.15)^2+(1-1.15)^2+\dots+(1-1.15)^2}     {20}        } $$

$$\sigma_{f_{c3}} = \sqrt{ \frac{(f_{c3_1}-E(V_{c3}))^2+(f_{c3_2}-E(V_{c3}))^2+\dots+(f_{3_{20}}-E(V_{c3}))^2}     {n}        } $$

$$\mathrm{d_{\sigma}}(\mathbf{E(V_{c})},\mathbf{V_{new}}) = \sqrt{\left(\frac{f_{new1}-E(V_{c1})}{\sigma_{f_{c1}}}\right)^2 + \left(\frac{f_{new2}-E(V_{c2})}{\sigma_{f_{c2}}}\right)^2 + \left(\frac{f_{new3}-E(V_{c3})}{\sigma_{f_{c3}}}\right)^2} $$

$$\mathrm{d_{\sigma}}(\mathbf{E(V_{z})},\mathbf{V_{new}}) = \sqrt{\left(\frac{f_{new1}-E(V_{z1})}{\sigma_{f_{z1}}}\right)^2 + \left(\frac{f_{new2}-E(V_{z2})}{\sigma_{f_{z2}}}\right)^2 + \left(\frac{f_{new3}-E(V_{z3})}{\sigma_{f_{z3}}}\right)^2} $$

$$sum=\frac{1.0}{0.5}+\frac{1.1}{1.5}+\frac{1.2}{2.5}+\frac{1.3}{3.5}+\frac{1.4}{4.5}+\dots+\frac{2.0}{10.5} $$

$$Class(f_1,f_2,f_3,f_4,f_5,f_6) = \begin{cases} C_1 & \text{if } 0 \leq Prog_i(f_1,f_2,f_3,f_4,f_5,f_6) < 10000 \\ C_2 & \text{if } 10000 \leq Prog_i(f_1,f_2,f_3,f_4,f_5,f_6) < 20000 \\ C_3 & \text{if } 30000 \leq Prog_i(f_1,f_2,f_3,f_4,f_5,f_6) < 40000 \\ C_4 & \text{if } 40000 \leq Prog_i(f_1,f_2,f_3,f_4,f_5,f_6) < 50000 \end{cases}$$

c exams
$$y = \begin{cases} 3x-7 & \text{if } x=-3 \\ 5x^2 & \text{if } x=2 \text{ or } x=5 \\ x-4x^3 & \text{if } x=-4 \text{ or } x=4 \end{cases}$$

$$ \mathbf{A} = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{13} \\ a_{31} & a_{32} & a_{33} \\ \end{bmatrix} $$

$$y=\frac{1}{1!} + \frac{2}{2!} + \frac{3}{3!} + \cdots+\frac{n}{n!} $$

$$f(n)=\sum_{i \mathop =1}^n n^{\frac{1}{i}} $$

$$f(N)=\prod_{i \mathop =1}^N 7^{\frac{1}{i}}=7\times7^{\frac{1}{2}}\times7^{\frac{1}{3}}\times7^{\frac{1}{4}}\times \cdots\times7^{\frac{1}{N}} $$