Answer: x = 11 / 3
Step-by-step explanation:
Multiply the numbers
−
1
⋅
2
3
=
3
x
−
1
⋅
2
3
=
3
x−1⋅32=3
−
2
3
=
3
x
−
2
3
=
3
x−32=3
2
Add
2
3
2
3
32
to both sides of the equation
3
Simplify
The correct answer is D, 6x
Step-by-step explanation:
The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
How to determine the value of sin(2x)
The cosine ratio is given as:
\cos(x) = -\frac 14cos(x)=−
4
1
Calculate sine(x) using the following identity equation
\sin^2(x) + \cos^2(x) = 1sin
2
(x)+cos
2
(x)=1
So we have:
\sin^2(x) + (1/4)^2 = 1sin
2
(x)+(1/4)
2
=1
\sin^2(x) + 1/16= 1sin
2
(x)+1/16=1
Subtract 1/16 from both sides
\sin^2(x) = 15/16sin
2
(x)=15/16
Take the square root of both sides
\sin(x) = \pm \sqrt{15/16
Given that
tan(x) < 0
It means that:
sin(x) < 0
So, we have:
\sin(x) = -\sqrt{15/16
Simplify
\sin(x) = \sqrt{15}/4sin(x)=
15
/4
sin(2x) is then calculated as:
\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)
So, we have:
\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗
4
15
∗
4
1
This gives
\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
9514 1404 393
Answer:
false
Step-by-step explanation:
The conjecture shown in this problem statement does not follow from the examples offered. They support the notion that ...
1/x ≤ x . . . . for x ≥ 0 (<u>not x ≤ 0</u>)
There are several possible counterexamples showing the conjecture is FALSE.
- 1/0 is undefined
- 1/(-5) > -5 . . . . . . . . a case for x < 0
If the intended domain is x ≥ 0, then the conjecture can also be demonstrated to be false for 0 < x < 1:
- 1/(1/5) > 1/5