Instead of typing it all on here, I included my explanations with the work.
Answer:
Step-by-step explanation:
To find an equation of a line in point slope form when given the slope and a point we use the formula
From the question we have the final answer as
Hope this helps you
Answer: £225
Step-by-step explanation:
Let Sarah's amount be represented by x.
Since Caroline gets three times as much as Sarah, Caroline will get: 3x
Bridget gets twice as much as Caroline, therefore Bridget will get: 2 × 3x = 6x
Sarah = x
Caroline = 3x
Bridget = 6x
Total = x + 3x + 6x = 10x
Caroline's faction is 3/10. We then multiply the fraction by £750. This will be:
= 3/10 × £750
= 0.3 × £750
= £225
Caroline will get £225
Answer:
(f⁻¹)'(b) = 1/f'(f⁻¹(b)) = 1/f'(a)
Step-by-step explanation:
The function f⁻¹(x) is the reflection of the function f(x) across the line y=x. Every point (a, b) that is on the graph of f(x) is reflected to be a point (b, a) on the graph of f⁻¹(x).
Any line with slope m reflected across the line y=x will have slope 1/m. (x and y are interchanged, so m=∆y/∆x becomes ∆x/∆y=1/m) Since f'(x) is the slope of the tangent line at (x, f(x)), 1/f'(x) will be the slope of the tangent line at (f(x), x).
Replacing x with f⁻¹(x) in the above relation, you get ...
... (f⁻¹)'(x) = 1/f'(f⁻¹(x)) will be the slope at (x, f⁻¹(x))
Putting your given values in this relation, you get
... (f⁻¹)'(b) = 1/f'(f⁻¹(b)) = 1/f'(a)
