Answer:
x = 35°
Step-by-step explanation:
These are corresponding angles. When a transversal crosses 2 parallel lines, 4 angles are created at each intersection, and each pair of corresponding angles between those are congruent.
These angles are congruent, so you can set them equal to each other:
Then, just solve for x:
You can check that by plugging it back into both:
Answer:
The simplified form is:
Step-by-step explanation:
To simplify the expression given we, need to open the brackets, and if there is power term. Then we need to group all the like terms and then arrange in the descending order of powers of the given expression.
Now the expression that is given to us is:
Here we will simplify it by grouping the like terms, as follows:
So this is the required simplified form.
1/-x*5y/-8
-1/x × (-5y/8)
5y/8x
Answer: function 1
Rate of change of function 1:
Following the format of y=mx+c, the rate of change should be m, so, the rate of change for function 1 = 4
To find the gradient (rate of change):
The two points the line passes through are (x1, y1) and (x2, y2), which in this case is (1, 6) and (3, 10)
(Doesn't matter which is which but you need to make sure that once you decide which is which, you stick to it)
To calculate the gradient, you substitute these values following (y1 - y2)/(x1 - x2)
Gradient of function 2 = (10 - 6)/(3 - 1)
= 2
Therefore, since 4 > 2, rate of change of function 1 > rate of change of function 2.
The full range is
(length
), so the half range is
. The half range sine series would then be given by
where
Essentially, this is the same as finding the Fourier series for the function
Integrating by parts yields
So the half range sine series for this function is simply