A carbohydrate, galactose is present in a. Terpenes b. Glycerophosphatides c. Glycolipids d. Phosphoinositides

Sure, here are some examples of step-by-step solutions using LaTeX: Example 1: Solving a quadratic equation using the quadratic formula Given the equation $a{x}^2+bx+c=0$, where $a,b,$ and $c$ are constants and $a\ne 0$, we can solve for $x$ using the quadratic formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ To solve the equation $2x^2-5x+3=0$ using the quadratic formula, we can substitute $a=2$, $b=-5$, and $c=3$: $\begin{array}{rl}x& =\frac{-(-5)\pm \sqrt{(-5{)}^2-4(2)(3)}}{2(2)}\\ & =\frac{5\pm \sqrt{25-24}}{4}\\ & =\frac{5\pm 1}{4}\end{array}$ Therefore, the solutions are $x=\frac{3}{2}$ and $x=1$. Example 2: Finding the derivative of a function To find the derivative of a function $f(x)$, we can use the definition of the derivative: $f^{\prime }(x)={\lim }_{h\to 0}\frac{f(x+h)-f(x)}{h}$ For example, to find the derivative of $f(x)=x^3$, we can use the power rule: $\begin{array}{rl}{f}^{\prime }(x)& =\underset{h\to 0}{\lim }\frac{(x+h{)}^3-x^3}{h}\\ & =\underset{h\to 0}{\lim }\frac{(x^3+3x^{2}h+3x{h}^2+h^3)-x^3}{h}\\ & =\underset{h\to 0}{\lim }\frac{3x^{2}h+3x{h}^2+h^3}{h}\\ & =\underset{h\to 0}{\lim }(3x^2+3xh+h^2)\\ & =3x^2\end{array}$ Therefore, $f^{\prime }(x)=3x^2$. Example 3: Solving a system of linear equations using matrices To solve a system of linear equations, we can use matrices. For example, to solve the system $\begin{array}{rl}2x+y& =5\\ x-y& =1\end{array}$ we can write the system in matrix form: $\left[\begin{array}{cc}2& 1\\ 1& -1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}5\\ 1\end{array}\right]$ To solve for $x$ and $y$, we can use matrix inversion: $\left[\begin{array}{c}x\\ y\end{array}\right]={\left[\begin{array}{cc}2& 1\\ 1& -1\end{array}\right]}^{-1}\left[\begin{array}{c}5\\ 1\end{array}\right]$ We can find the inverse of the matrix using row operations: \begin{bmatrix} 2 & 1 & 1 & 0 \\ 1 & -1 & 0 & 1 \end{bmatrix} \to \begin{bmatrix} 1 & 0 & \frac{1}{3} & \frac{1}{3} \\ 0 & 1 & -\frac