Recent questions tagged sec-b

Find the maximum value of $2x^3 – 24x + 107$ in the interval $[1, 3]$.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

What is the maximum value of the function $\sin \: x + \cos x$?

asked Nov 27, 2012 by thanvigandhi_1

1 answer

At what points in the interval $[0, 2\pi]$, does the function $\sin\: 2x$ attain its maximum value?

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Find both the maximum value and the minimum value of $3x^4 - 8x^3 + 12x^2 - 48x + 25$ on the interval $[0, 3].$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Find the maximum profit that a company can make, if the profit function is given by $ p(x) = 41 - 72x - 18x^2$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

If P(A) =6 / 11 , P(B) = 5 / 11 and P(A ∪ B)= 7 /11 find (i) P(A∩B) (ii) P(A|B) (iii) P(B|A)

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If $ A = \begin{bmatrix} \frac{2}{3} & 1 & \frac{5}{3} \\ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \\ \frac{7}{3} & 2 & \frac{2}{3} \end{bmatrix} \text{ and } B = \begin{bmatrix} \frac{2}{5} & \frac{3}{5} & 1 \\ \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \\ \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{bmatrix} \text{ then compute } 3A - 5B $

asked Nov 26, 2012 by pady_1

1 answer

Let $A=\{\text{-1,0,1,2}\}$ and $B=\{\text{-4,-2,0,2}\} and $f,g: A $\rightarrow B$ be functions defined by $f(x)=x^2-x, \;x \in A$ and $g(x)=2 |x- \frac {1} {2} | -1,\; x \in A$. Are $f$ and $g$ equal?

asked Nov 26, 2012 by vaishali.a

1 answer

If $f(x) = 3x^2 + 15x + 5$, then the approximate value of $f (3.02)$ is

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(i)\;\sqrt{25.3}$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Show that $$ \begin{array}{l} (i) \qquad \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \\[0.5em] (ii) \qquad \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \end{array} $$

asked Nov 25, 2012 by pady_1

1 answer

Find $ A^2 -5A + 6I $ , if $ A = \begin{bmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer

If $ A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix} $ and $ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $ find $k$ so that $A^2 = kA - 2I$

asked Nov 25, 2012 by pady_1

1 answer

If $ A = \begin{bmatrix} 0 & -tan \frac{\alpha}{2} \\ tan\frac{\alpha}{2} & 0 \end{bmatrix} $ and $I$ is the identity matrix of order $2$, show that $ I + A = ( I - A ) \begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer

A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: $$ \text{(a) Rs 1800} \qquad \qquad \text{(b) Rs 2000} $$

asked Nov 25, 2012 by pady_1

1 answer

The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

asked Nov 25, 2012 by pady_1

1 answer

if $ A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} \text{, then verify that } $ $$ \text{ (i) } (A+B)' = A' + B' $$

asked Nov 25, 2012 by pady_1

1 answer

If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix} \text{ , then verify that } $$ \text{ (i) } (A + B )' = A' + B' \qquad \qquad $

asked Nov 25, 2012 by pady_1

1 answer

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$

asked Nov 25, 2012 by pady_1

1 answer

$ (i) A = \begin{bmatrix} cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{bmatrix}$ then verify that $A'A = I$

asked Nov 25, 2012 by pady_1

1 answer

$ (i)$ Show that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$ is a symmetric matrix.

asked Nov 25, 2012 by pady_1

1 answer

For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $ (i) (A+A') $ is a symmetric matrix.

asked Nov 25, 2012 by pady_1

1 answer

Find $ \frac{1}{2}(A + A')$ and $\frac{1}{2}(A - A')$ , when $ A = \begin{bmatrix} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer