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3 years ago

Evaluate the expression P(9,3), equivalently 9P3 Your answer is: Preview

Mathematics

1 answer:

Marina CMI [18]3 years ago

8 0

Answer:

504

Step-by-step explanation:

Using the definition

n $P_{r}$ = $\frac{n!}{(n-r)!}$

where n! = n(n - 1)(n - 2).... × 3 × 2 × 1

Thus

9 $P_{3}$ = $\frac{9!}{6!}$ ← cancel the terms of 6! on numerator/denominator, leaving

= 9 × 8 × 7 = 504

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Find an equation for the perpendicular bisector of the line segment whose endpoints are

Andrew [12]

The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + 2

Step-by-step explanation:

Let us revise the relation between the slopes of perpendicular lines

The product of the slopes of two perpendicular lines is -1
That means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$
You reciprocal the slope of one and change its sign to find the slope of the other

The mid point of a segment whose endpoints are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

The perpendicular bisector of a line is the line that intersect it in its mid-point and formed 4 right angles

∵ The end point of a given line are (9 , -3) and (-5 , -7)

∴ $x_{1}=9$ and $x_{2}=-5$

∴ $y_{1}=-3$ and $y_{2}=-7$

- Find the slope of the line by using the rule of the slope $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ $m=\frac{-7-(-3)}{-5-9}=\frac{-7+3}{-14}=\frac{-4}{-14}=\frac{2}{7}$

∴ The slope of the given line is $\frac{2}{7}$

To find the slope of the perpendicular bisector of it reciprocal it and change its sign

∴ The slope of the perpendicular bisector = $-\frac{7}{2}$

∵ The form of the linear equation is y = mx + b, where m is the

slope and b is the y-intercept

- Substitute the value of m in the equation

∴ The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + b

To find b substitute x and y in the equation by a point on the line

∵ The perpendicular bisector of the given line intersect it at

its midpoint

- Find the mid-point of the given line busing the rule above

∵ $x_{1}=9$ and $x_{2}=-5$

∵ $y_{1}=-3$ and $y_{2}=-7$

∴ The mid-point of the given line = $(\frac{9+(-5)}{2},\frac{-3+(-7)}{2})=(\frac{4}{2},\frac{-10}{2})=(2,-5)$

Point (2 , -5) is also lies on the perpendicular line

∴ x = 2 and y = -5

- Substitute them in the equation

∵ -5 = $-\frac{7}{2}$ (2) + b

∴ -5 = -7 + b

- Add 7 to both sides

∴ 2 = b

- Substitute the value of b in the equation

∴ The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + 2

The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + 2

Learn more:

You can learn more about the linear equation in brainly.com/question/11223427

#LearnwithBrainly

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