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
Answer:
One of the angles in the triangle might be 50.
AND
The length of the third side must be 11cm or smaller.
Step-by-step explanation:
-The triangle might be an equilateral triangle (having all the same sides and angles). False, since the triangle sum theorem states that all angles inside of a triangle must add up to 180, so an equilateral triangle would need to have all three angles at 60 degrees.
-One of the angles in the triangle must be 120 (false; it can be anything above 90, which is not only 120)
-The length of the third side must be 11cm or smaller. (True, Triangle Inequality Theorem)
-One of the angles in the triangle might be 50 (possibly, so very much true)
Given:
The height h of an object after t seconds is
The height of a neighboring 50-foot tall building is modeled by the equation h=50.
The time (t) when the object will be at the same height as the building is found to be t = –2 and t = 5.
To find:
The statement which describes the validity of these solutions.
Solution:
We have,
Here, t is the time in seconds.
For t=-2,
For t=5,
So, the value of h is 50 at t=-2 and t=5.
We know that time is always positive so it cannot be negative value. It means t=-2 is not possible.
The solution t = 5 is the only valid solution to this system since time cannot be negative.
Therefore, the correct option is C.
15x + 11x + 8x+5 = 180
34x + 5 = 180
34x = 180-5
34x = 175
x = 5.147
by substitution each value by of x by 5
75 + 55 + 45 = 175
The volume of a cylinder is given by the product of its base area (i.e. the area of a circle) and its height:
Solving for r, we have
Plugging the numbers, we have
