$\dfrac{2}{\sqrt3\cos x+\sin x}=\sec\left(\dfrac{\pi}{6}-x\right)\\\\\dfrac{2}{\sqrt3\cos x+\sin x}=\dfrac{1}{\cos\left(\dfrac{\pi}{6}-x\right)}\ \ \ \ \ (*)\\----------------\\\\\cos\left(\dfrac{\pi}{6}-x\right)\ \ \ \ |\text{use}\ \cos(x-y)=\cos x\cos y+\sin x\sin y\\\\=\cos\dfrac{\pi}{6}\cos x+\sin\dfrac{\pi}{6}\sin x=\dfrac{\sqrt3}{2}\cos x+\dfrac{1}{2}\sin x=\dfrac{\sqrt3\cos x+\sin x}{2}\\------------------------------$

$(*)\\R_s=\sec\left(\dfrac{\pi}{6}-x\right)=\dfrac{1}{\cos\left(\dfrac{\pi}{6}-x\right)}=\dfrac{1}{\dfrac{\sqrt3\cos x+\sin x}{2}}\\\\=\dfrac{2}{\sqrt3\cos x+\sin x}=L_s$

6 0

3 years ago

Read 2 more answers

Tamika makes a 5.5% commission selling electronics. How much commission does she make if she sells a flat-screen TV for $10,000?

strojnjashka [21]

Answer: She makes $550

Step-by-step explanation:

This is because to find the answer you do 10000t imes 5.5%

And 5.5% is 0.055

So you do 10000 times 0.055

Which is 550

7 0

3 years ago

Read 2 more answers

Find the values of the mode when median is given to be 5 and mean is 7.

Reil [10]

Answer:

Mode = 1

Step-by-step explanation:

Relation between the Central Measures of Tendency

Mean, Median, and Mode are commonly referred to as the Central Measures of Tendency
The formula between the three is given by :
⇒ Mode = 3Median - 2Mean or Mode + 2Mean = 3Median

Solving

We know that :

Median = 5
Mean = 7

Therefore,

Mode = 3(5) - 2(7)
Mode = 15 - 14
Mode = 1

5 0

3 years ago

Read 2 more answers