Find the coordinates of P so that partitions ab in the ratio 5:1 with A(2,4) and B(8,10)

Mathematics

1 answer:

julsineya [31]3 years ago

8 0

Answer:

The answer would be (7,9).

Step-by-step explanation:

If you partition that line by 6 you'd get (3,5), (4,6), (5,7), (6,8), and (7,9) in the middle of the two points. And the ratio of 5:1 would be seen at point (7,9).

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Number 16 a b and c please

zlopas [31]

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3 years ago

For what values of x is f(x) = |x + 1| differentiable? I'm struggling my butt off for this course

pav-90 [236]

By definition of absolute value, you have

$f(x) = |x+1| = \begin{cases}x+1&\text{if }x+1\ge0 \\ -(x+1)&\text{if }x+1$

or more simply,

$f(x) = \begin{cases}x+1&\text{if }x\ge-1\\-x-1&\text{if }x$

On their own, each piece is differentiable over their respective domains, except at the point where they split off.

For x > -1, we have

(x + 1)' = 1

while for x < -1,

(-x - 1)' = -1

More concisely,

$f'(x) = \begin{cases}1&\text{if }x>-1\\-1&\text{if }x$

Note the strict inequalities in the definition of f '(x).

In order for f(x) to be differentiable at x = -1, the derivative f '(x) must be continuous at x = -1. But this is not the case, because the limits from either side of x = -1 for the derivative do not match:

$\displaystyle \lim_{x\to-1^-}f'(x) = \lim_{x\to-1}(-1) = -1$