Answer:
Step-by-step explanation:
Represent Celsius with C and Fahrenheit with F.
So, we have:
Solving (a): Represent as a linear equation
First, we calculate the slope:
This gives:
The linear equation is then calculated using:
Where
Make F the subject
Solving (b): The value of F when C = 30
Substitute 30 for C in
Answer:
sin
(
x/
2
) = -
√
3
/2
Take the inverse sine of both sides of the equation to extract x
from inside the sine.
x/
2
=
arcsin
(
−
√
3/
2
)
The exact value of arcsin
(
−
√
3
/2
) is −
π
/3
.
/x
2
=
−
π
/3
Multiply both sides of the equation by 2
.
2
⋅
x
/2
=
2
⋅
(
−
π
/3
)
Simplify both sides of the equation.
x
=
−
2
π
/3
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from 2
π
, to find a reference angle. Next, add this reference angle to π to find the solution in the third quadrant.
x
/2
=
2
π
+
π/
3
+
π
Simplify the expression to find the second solution.
x
=
2
π
/3
4
π
Add 4
π to every negative angle to get positive angles.
x
=
10
π
/3
The period of the sin
(
x
/2
) function is 4
π so values will repeat every 4
π radians in both directions.
x
=2
π
/3
+
4
π
n
,
10
π/
3
+
4
π
n
, for any integer n
Exclude the solutions that do not make sin
(
x
/2
)
=
−
√
3/
2 true.
x
=
10
π
/3
+
4
π
n
, for any integer n
Answer:
2x = y
Step-by-step explanation:
As you can see in the table, y = 2x, this is proven by the fact that if you divide any value in the y of the table by 2 you will get its corresponding x value, proving that 2x = y is the function that is used to represent this table's value.
X. 0,2,6,4,8,10
Y. 2,0,2,4,6,8
It’s how far the number is from zero
