What is the value of x in the equation x – y = 30, when y = 15?
2 answers:
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Answer:
sin θ =
Step-by-step explanation:
Given that,
cos θ =
From the trigonometric functions,
cos θ =
⇒ adjacent = , and the hypotenuse = 3
Let the opposite side be represented by x, applying the Pythagoras theorem we have;
=
+
=
+
9 = 3 +
= 9 - 3
= 6
x =
Thus, opposite side =
So that,
sin θ =
=
Therefore,
sin θ =
To determine the maximum value of a quadratic function opening downwards, we are going to find the vertex; then the y-value of the vertex will be our maximum.
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form
we'll use the vertex formula: 
, and then we are going to replace that value in our original function to find k.
So, in our function
, 
and 
.
Lets replace those values in our vertex formula:
Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:
We just prove that the vertex of
is (2,1), and for the graph we can tell that the vertex of 
is (-2,4). The only thing left is compare their y-coordinates to determine w<span>hich one has the greater maximum value. Since 4>1, we can conclude that </span> has the greater maximum.
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form
So, in our function
Lets replace those values in our vertex formula:
Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:
We just prove that the vertex of