U(x) = f(x).(gx)
v(x) = f(x) / g(x)
Use chain rule to find u(x) and v(x).
u '(x) = f '(x) g(x) + f(x) g'(x)
v ' (x) = [f '(x) g(x) - f(x) g(x)] / [g(x)]^2
The functions given are piecewise.
You need to use the pieces that include the point x = 1.
You can calculate f '(x) and g '(x) at x =1, as the slopes of the lines that define each function.
And the slopes can be calculated graphycally as run / rise of each graph, around the given point.
f '(x) = slope of f (x); at x = 1, f '(1) = run / rise = 1/1 = 1
g '(x) = slope of g(x); at x = 1, g '(1) = run / rise = 1.5/ 1 = 1.5
You also need f (1) = 1 and g(1) = 2
Then:
u '(1) = f '(1) g(1) + f(1) g'(1) = 1*2 + 1*1.5 = 2 + 1.5 = 3.5
v ' (x) = [f '(1) g(1) - f(1) g(1)] / [g(1)]^2 = [1*2 - 1*1.5] / (2)^2 = [2-1.5]/4 =
= 0.5/4 = 0.125
Answers:
u '(1) = 3.5
v '(1) = 0.125
3x + 6 = 48 (alternate angles are equal)
- 6
3x. = 42
÷3
x = 14 degrees
180-48 - 2y + 5y-9 =180
123 + 3y = 180
-123
3y = 57
÷3
y = 19 degrees
Explanation:
To find the last angle on the top straight line, do:
180 - (the 2 given angles).
So, 180 - (3x + 16, which is 48 due to alternate angles being equal). Then, minus the 2y.
(180 - 48 - 2y) & simplify => 132 - 2y
This gives you the equation for the missing angle on our top straight line.
Thus, co-interior angles add to 180. So, we add the new equation (132 - 2y) to 5y - 9.
Simplify
=> 123 + 3y (because - 2+5 =3)
and put it equal to 180. Solve for y
Hope this helps!
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<span>How many miles are in 400 kilometers
248.548
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