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dimulka [17.4K]
3 years ago
15

9. A stock's price has been continuously declining at a rate of 5% per week. If the stock started at a price of

Mathematics
1 answer:
WARRIOR [948]3 years ago
4 0

Answer:

After 13.6 weeks the price per share will be $20.

Step-by-step explanation:

The stock's price has been continuously declining at a rate of 5% per week.

Now, if the stock's price is $62.50 per share at the start, then after w weeks the price will be 62.5(1 - \frac{5w}{100} ) dollars.

Hence, we have to find the value of w if the after w week price per share is $20.

So, 62.5(1 - \frac{5w}{100} ) = 20

⇒ 1 - \frac{w}{20} = \frac{20}{62.5} = 0.32

⇒ \frac{w}{20} = 0.68

⇒ w = 13.6 weeks

Therefore, after 13.6 weeks the price per share will be $20. (Answer)

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Answer:

4. The equation of the perpendicular bisector is y = \frac{3}{4} x - \frac{1}{8}

5. The equation of the perpendicular bisector is y = - 2x + 16

6. The equation of the perpendicular bisector is y = -\frac{3}{2} x + \frac{7}{2}

Step-by-step explanation:

Lets revise some important rules

  • The product of the slopes of the 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} (reciprocal m and change its sign)
  • The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
  • The formula of the slope of a line is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}
  • The mid point of a segment whose end points are (x_{1},y_{1}) and (x_{2},y_{2}) is (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})
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4.

∵ The line passes through (7 , 2) and (4 , 6)

- Use the formula of the slope to find its slope

∵ x_{1} = 7 and x_{2} = 4

∵ y_{1} = 2 and y_{2} = 6

∴ m=\frac{6-2}{4-7}=\frac{4}{-3}

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = \frac{3}{4}

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = (\frac{7+4}{2},\frac{2+6}{2})

∴ The mid-point = (\frac{11}{2},\frac{8}{2})=(\frac{11}{2},4)

- Substitute the value of the slope in the form of the equation

∵ y = \frac{3}{4} x + b

- To find b substitute x and y in the equation by the coordinates

   of the mid-point

∵ 4 = \frac{3}{4} × \frac{11}{2} + b

∴ 4 = \frac{33}{8} + b

- Subtract  \frac{33}{8} from both sides

∴ -\frac{1}{8} = b

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5.

∵ The line passes through (8 , 5) and (4 , 3)

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∵ 4 = -2 × 6 + b

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6.

∵ The line passes through (6 , 1) and (0 , -3)

- Use the formula of the slope to find its slope

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∴ The mid-point = (\frac{6}{2},\frac{-2}{2})

∴ The mid-point = (3 , -1)

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∵ y = -\frac{3}{2} x + b

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   of the mid-point

∵ -1 = -\frac{3}{2} × 3 + b

∴ -1 = -\frac{9}{2} + b

- Add  \frac{9}{2}  to both sides

∴ \frac{7}{2} = b

∴ y = -\frac{3}{2} x + \frac{7}{2}

∴ The equation of the perpendicular bisector is y = -\frac{3}{2} x + \frac{7}{2}

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