Maths

13. sin 765°

We know that value of sun x repeats after an interval of 2π or 360°.

Sin (765°) = sin (2*360°+45°)

= sin 45°

= 1/√2.

12. Kindly go through the solution

22. Given f(x) = $\{\begin{array}{ll}\frac{sinx}{x},\hfill & if x<0.\hfill \\ x+1,\hfill & if x\ge 0.\hfill \end{array}$

For x = c < 0,

f(c) = $\frac{sinc}{c}$

$\underset{x\to c}{lim}$ f(x) = $\underset{x\to c}{lim}$ $\frac{sinx}{x}=\frac{sinc}{c}=f(c)$

So, f is continuous for x < 0

For x = c > 0

f(c) = c + 1

$\underset{x\to c}{lim}$ f(x) = $\underset{x\to c}{lim}$ x + 1 = c + 1 = f(c)

So, f is continuous for x > 0.

For x = 0.

L.H.L. = $\underset{x\to 0^{-}}{lim}f(x)=\underset{x\to 0^{-}}{lim}\frac{sinx}{x}=1.$

R.H.S. = $\underset{x\to 0^{+}}{lim}f(x)=\underset{x\to 0^{+}}{lim}x+1=0+1=1$

And f(0) = 0 + 1 = 1

L.H.L = R.H.L. = f(0)

So, f is continuous at x = 1.

Hence, discontinuous point of x does not exit.

11. Kindly go through the solution

10. Kindly go through the solution

9. Kindly go through the solution

8. Kindly go through the solution

It is given that,

IQ = $\frac{\mathrm{MA}}{CA}*100$…. (1)

and 80 $\le$ IQ $\le$ 140 $\Rightarrow -3-4$ ……. (2)

Putting (1) in (2) we get,

$8\mathrm{0,}$
$\frac{MA}{CA}*10\mathrm{0,}140.$

Let x be the mental age for chronological age 12, then we can write,

$8\mathrm{0,}$
$\frac{x}{12}*10\mathrm{0,}140.$

$\Rightarrow 80*\frac{12}{100}\le \frac{x}{12}*100*\frac{12}{100}\le 140*\frac{12}{100}$  (multypling by 12/1200 throughout)

$\Rightarrow 9.6\le x\le 16.8.$

$\therefore x\in [9.6,16.8]$

Thus, the required metal age for 12 yes old children is from 9.6 to 16.8.