$4\sin^2 x - 3 = 3 \sin x\\\\\implies 4\sin^2 x -3 \sin x -3 =0\\\\\implies 4u^2 -3u -3 =0~~~~~~~~~~~~~~;[\text{Set} ~ \sin x = u]\\\\\implies u = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 4 \cdot (-3)}}{2(4)}~~~~~~;[\text{Apply quadratic formula}]\\\\\\\implies u = \dfrac{3\pm\sqrt{57}}8\\\\\implies \sin x = \dfrac{3\pm\sqrt{57}}8~~~~~~;[\text{Substitute back}~ u = \sin x]\\\\\text{Now,}\\\\\sin x = \dfrac{3+\sqrt{57}}8\\\\\text{No solution for}~ x\in \mathbb{R} ~\text{Since}~ -1\leq \sin x \leq 1\\$

$\sin x = \dfrac{3 - \sqrt{57}}8\\\\\implies x = n\pi + (-1)^n \sin^{-1} \left(\dfrac{3-\sqrt{57}}8\right)\\\\\\\text{ When n = 1,2 and}~ [0,2\pi]},\\\\\\x= \pi - \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)~ \text{and} ~x = 2\pi + \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)\\\\\text{In decimal,}\\\\x= 3.75~~~~ \text{and}~~~ x =5.68$

5 0

2 years ago

The spinner at the right is divided into eight equal parts. Find the theoretical probability of

finlep [7]

Answer:

$\frac{3}{4}$ probability of landing on a number greater than 2 on the spinner.

Step-by-step explanation:

A theoretical probability is given by the number of desired outcomes divided by the number of total outcomes.

In this question:

8 possible outcomes(all numbers from 1 to 8).

6 desired outcomes(3, 4, 5, 6, 7 and 8, that is, all the numbers greater than 2). So

$p = \frac{6}{8} = \frac{3}{4}$

$\frac{3}{4}$ probability of landing on a number greater than 2 on the spinner.

4 0

3 years ago

Kayra and Mycho sell flowers on weekends to earn extra money.For every 2 flowers that Kayra sells,Mycho sells 5. If Kayra sold 6

andreyandreev [35.5K]

Answer:

We know that:

For every two flowers that Kayra sells, Mycho sells 5.

Now, in the question we have:

"If Kayra sold 6 newspapers, how many did Mycho sell?"

There is no information about newspapers, so we can't answer anything.

If we had something like:

"If Kayra sold 6 flowers, how many did Mycho sell?"

Well, in this case, we remember that for every 2 flowers that Kayra sells, Mycho sells 5, then the first thing we need to do is count how many groups of 2 flowers we have in 6 flowers, this is:

6/2 = 3 groups.

And for each one of these, Mycho will sell 5 flowers, then the total number of flowers that Mycho sold is:

3*5 = 15 flowers.

5 0

3 years ago