Question

Hello

$\frac{\frac{1}{|\sin x|}+\frac{1}{|\cos x|}}{2}\geq\sqrt{\frac{1}{|\sin x\cos x|}}$

Find the range ​

Answer 1

$\: \: \: \: \:{\large{\pmb{\sf{\underline{ Here's \: your \: required \: solution!! }}}}}$

$\sf :\implies \purple {\dfrac{\dfrac{1}{|\sin x|}+\dfrac{1}{|\cos x|}}{2}\geq\sqrt{\dfrac{1}{|\sin x\cos x|}}}$

$\sf :\implies \dfrac{1}{|\sin x|}+\dfrac{1}{|\cos x|}\geq\dfrac{2}{\sqrt{|\sin x\cos x|}}$

$\sf :\implies f(x)\geq\dfrac{2}{\sqrt{\dfrac{|\sin(2x)|}{2}}}$

$\sf :\implies f(x)\geq\dfrac{2\sqrt2}{\sqrt{|\sin(2x)|}}$

Now,to get minimum value of $\sf \pink {f(x),}$ denominator of RHS should be maximum. So, we need to take $\sf \pink {\sin(2x)=1}$ i.e., its maximum value.

$:\sf \implies f(x)\geq2\sqrt2$

Then, the range will be :-

$\sf :\implies \red {\underline{f(x)\in\left[2\sqrt2,\ \infty\right)}}$

Answer 2

Answer:

noah is designing a set for a school theater production. he has 150 carboard bricks. he needs to use some of the bricks to make a chimney and 4 times as many bricks to make an arch. he also saves 15 bricks in case some breaks . how many can he use

Step-by-step explanation:

Thnk u