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julia-pushkina [17]

3 years ago

14

on a number line, the directed line segment from q to s has endpoints q at –8 and s at 12. point r partitions the directed line

segment from q to s in a 4:1 ratio.which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r?

1 answer:

Mekhanik [1.2K]3 years ago

5 0

The location of the point R will be at $R(x, y) =(\frac{-32}{5}, \frac{12}{5} )$

The midpoint formula is expressed according to the formula;

$R(x, y) = (\frac{ax_1+bx_2}{a+b},\frac{ay_1+by_2}{a+b})$

where;

a and b are the ratios

Given the coordinates Q(-8, 0) and S(12, 0) partitioned in a 4:1 ratio, the coordinate of point R will be expressed as:

$R(x, y) = (\frac{4(-8)+0}{4+1},\frac{1(12)}{4+1})\\R(x, y) =(\frac{-32}{5}, \frac{12}{5} )$

Hence the location of the point R will be at $R(x, y) =(\frac{-32}{5}, \frac{12}{5} )$

Learn more on midpoint here: brainly.com/question/5566419

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$\begin{array}{cccc}Interval&x-value&S'(x)&Verdict\\(0,2\sqrt[3]{15}) &2&-56&decreasing\\(2\sqrt[3]{15}, \infty)&6&\frac{16}{3}&increasing \end{array}$

An extremum point would be a point where f(x) is defined and f'(x) changes signs.

We can see from the table that f(x) decreases before $x=2\sqrt[3]{15}$ , increases after it, and is defined at $x=2\sqrt[3]{15}$ . So f(x) has a relative minimum point at $x=2\sqrt[3]{15}$ .

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