$\sin(2x) = 2 \sin(x) \cos(x) \\ 9( 2 \sin(x) \cos(x) ) \sin(x) = 9 \cos(x) \\ 18 { \sin}^{2} (x)9 \cos(x) - 9 \cos(x) = 0 \\ 9 \cos(x) (2{ \sin}^{2} (x) - 1) = 0 \\ 9 \cos(x) = 0 \: or \: 2{ \sin}^{2} (x) - 1 = 0 \\ \sin(x) = \pm \frac{1}{ \sqrt{2} } \\ \cos(x) = 0 \\ x = { \cos}^{ - 1} (0) \\ x = \frac{ \pi}{2} = 90 \degree \\ x = \frac{ \pi}{2} + 2\pi \: n \: \forall \: n \: \in \: \Z \\ = 90 \degree + 360\degree\: n \: \forall \: n \: \in \: \Z \\ = \pm\frac{ \pi}{4} \pm2\pi \: n \: \forall \: n \: \in \: \Z \\ x = \pm45\degree \pm 360\degree\: n \: \forall \: n \: \in \: \Z$

8 0

2 years ago

If the first term in an arithmetic sequence is –3 and the tenth term is 15, what is the common difference?

Triss [41]

Given that the First term of the Arithmetic sequence = -3

⇒ a = -3

We know that nth term of a Arithmetic sequence is : Tn = a + (n - 1)d

where a is the first term and d is the common difference

Given that 10th term is 15

⇒ T₁₀ = -3 + (10 - 1)d

⇒ -3 + (10 - 1)d = 15

⇒ 9d = 18

⇒ d = 2

⇒ Common difference of given Arithmetic Sequence is 2

6 0

3 years ago

The Montanez family is a family of four people. They have used 3,485.78 gallons of water so far this month. They cannot exceed 7

il63 [147K]

Answer:

x ≤ 3764.72

Step-by-step expl anation:

The Montanez family cannot use more than 7250.50 gallons, this means that they can use less than or equal to 7250.50 gallons, this tells you which sign to use. The variable x can be used to describe how much water they have left to use and then you add 3,485.78 gallons to x.

x + 3485.78 ≤ 7250.50 This inequality means that the amount of water the family has yet to use added to 3485.78 gallons cannot exceed 7250.50 gallons.

Next, you simplify the inequality using the property of inequalities.

x ≤ 7250.50 - 3485.78

x ≤ 3764.72

5 0

3 years ago