Alright here are the answers in order!
a) Independent
b) Dependent
c) 0.9
d) 0.5
I hope this helps!
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:
114°
Step-by-step explanation:
Alternate exterior angles 1 and 7 are congruent. Angle 1 has the same measure as angle 7.
angle 1 = 114°
When you have a bunch like this, I find it easiest to graph them.
The numbers of real solutions are ...
2
0
2
1
I know you know how to use Desmos to graph these. You can also write a little spreadsheet program to compute the discriminant b^2 -4ac, or do it the hard way.
1^2 -4(-3)(12) = 145 . . . positive, so 2 solutions
(-6)^2 -4(2)(5) = -4 . . .. negative, so 0 solutions
7^2 -4(1)(-11) = 93 . . . .. positive, so 2 solutions
(-8)^2 -4(-1)(-16) = 0 . .. zero, so 1 solution