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
90+30=120
180-120=60
The measurement for angle G is 60 degrees.
And for angle J is the same as 90+30 which equals 120 degrees.
Answer:
an =7+4(n-1)
Step-by-step explanation:
an =a1+ d(n-1) is the equation for an arithmetic sequence
When n=4 an =19
19 =a1 + d(4-1)
19 =a1 + d(3)
When n =6 an =27
27 = a1 +d*(6-1)
27 = a1 +d*5
Now we have 2 equations and 2 unknowns
19 =a1 + d(3)
27 = a1 +d*5
Subtract them to eliminate a1
27 = a1 +d*5
-19 =a1 + d(3)
-----------------------
8 = 2d
Divide by 2
8/2 = 2d/2
4 =d
The common difference is 4
Now we need to find a1
27 = a1 +d*5
27 = a1 + (4) *5
27 = a1+ 20
Subtract 20 from each side
27-20 =a1 +20-20
7 =a1
The initial term is 7
an = a1+ d(n-1)
an =7+4(n-1)
- Yes, the height, h(t) of a ball t seconds after it's dropped from the third floor of a building is a function.
- No, table B is not a function because no function can have the same y-values (5) for different x-values (1 and 8).
- Yes, table C is a function because it has different y-values for same x-values.
- Yes, graph D is a function because it has different y-values for same x-values.
<h3>What is a function?</h3>
A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.
<h3>The types of function.</h3>
In Mathematics, there are different types of functions and these include the following;
- Piece-wise defined function.
For this exercise, we would indicate whether or not each of the above mathematical relation represents a function:
- Yes, the height, h(t) of a ball t seconds after it's dropped from the third floor of a building is a function.
- No, table B is not a function because no function can have the same y-values (5) for different x-values (1 and 8).
- Yes, table C is a function because it has different y-values for same x-values.
- Yes, graph D is a function because it has different y-values for same x-values.
In conclusion, we can infer and logically deduce that a function maps every x-value in a valid domain to a single y-value only.
Read more on domain here: brainly.com/question/17003159
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since the 2 is the 5th digit after the decimal, scientific notation will be 2*10^-5 thus choosing
Thus choice A is the correct answer.