Make a sketch of a linear relationship with slope 3 that is not a proportional relationship show how you know hay slope is 3 wri
1 answer:
Answer:
A proportional relationship is something like:
y = k*x
Where k is the constant of proportionality
And a linear relationship is something like:
y = a*x + b
Is easy to see that if:
a = k, and b = 0, this would be a proportional relationship.
Then if we want to have a slope equal to 3, but this must not be a proportional relationship, we must only have b different than 0.
This could be something like:
y = 3*x + 1
The graph of this is:
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Recall the angle sum identities:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
sin(a + b) = sin(a) cos(b) + sin(b) cos(a)
sin(a - b) = sin(a) cos(b) - sin(b) cos(a)
Notice that adding the first two together, and subtract the last from the third, we get two more identities:
cos(a + b) + cos(a - b) = 2 cos(a) cos(b)
sin(a + b) + sin(a - b) = 2 sin(b) cos(a)
Let a = 4x and b = x. Then
cos(5x) + cos(3x) = 2 cos(4x) cos(x)
sin(5x) - sin(3x) = 2 sin(x) cos(4x)
Now,
as required.
First calculate the missing angle 
. By knowing all angles in triangle have a sum of 180°.
Now we required to use angle functions in a right triangle. The cosine of
is equal to the relation of side 
and hypotenuse 
.
Now we solve this for hypotenuse.
Now put in the numbers.
So we know the length of hypotenuse and length of side therefore side 
can be calculated using Pythagorean theorem: 
.
Solve for side.
So there you go. If you have any questions feel free to ask.
r3t40
Now we required to use angle functions in a right triangle. The cosine of
Now we solve this for hypotenuse.
Now put in the numbers.
So we know the length of hypotenuse and length of side
Solve for side
So there you go. If you have any questions feel free to ask.
r3t40