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1 year ago

Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,−8) and (9,2)

Mathematics

1 answer:

Len [333]1 year ago

7 0

Answer: $y+3=-\frac{4}{5}(x-5)$

Step-by-step explanation:

For it to bisect the segment, we need to find the midpoint.

The midpoint is $\left(\frac{1+9}{2}, \frac{-8+2}{2} \right)=(5, -3)$

Now, for it to be perpendicular, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the given segment is $\frac{-8-2}{1-9}=\frac{5}{4}$ , so the slope of the perpendicular bisector is $-\frac{4}{5}$

Thus, the equation of the line in point-slope form is $\boxed{y+3=-\frac{4}{5}(x-5)}$

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2 years ago

Which expression is equivalent to *picture attached*

DiKsa [7]

Answer:

The correct option is;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$

Step-by-step explanation:

The given expression is presented as follows;

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )$

Which can be expanded into the following form;

$\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n$

From which we have;

$\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}$

$\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}$

Therefore, substituting the value of n = 50 we have;

$\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}$

$\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}$

Which gives;

$4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}$

$3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}$

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}$

Therefore, we have;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$ .

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2 years ago

its Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs 15/m2. (Take n=3.14) flona

Stells [14]

Step-by-step explanation:

Given diameter of table (circular) =1.6m

radius =0.8m

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Cost of polishing table top = 15×2.0096

cost = 30.14m

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2 years ago