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2 years ago

Endpoint: (-9,-1), midpoint: (8,14) given the midpoint and one endpoint of a line segment, find the other endpoint.

Mathematics

1 answer:

jolli1 [7]2 years ago

7 0

Answer:

(25, 29)

Step-by-step explanation:

The midpoint formula can be solved to give an expression for one end point of a line segment in terms of the other end point and the midpoint.

<h3>Formula</h3>

The midpoint (M) of segment AB is found from ...

M = (A +B)/2

Solving for B, we get ...

B = 2M -A

<h3>Application</h3>

For A(-9, -1) and M(8, 14), we find the end point B to be ...

B = 2(8, 14) -(-9, -1)

B = (16 -(-9), 28 -(-1)) = (25, 29)

The other end point is (25, 29.

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Answer:

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Step-by-step explanation:

Given

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Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

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$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

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Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

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Representing x using interval notation, we have

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To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

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