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3 years ago

Put the equation in standard form. y - 1 = -1/3 (x - 6)

Mathematics

1 answer:

Drupady [299]3 years ago

3 0

Answer:

x + 3y = 9

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y - 1 = - $\frac{1}{3}$ (x - 6)

Multiply through by 3 to clear the fraction

3y - 3 = - (x - 6) ← distribute parenthesis by - 1

3y - 3 = - x + 6 ( add x to both sides )

x + 3y - 3 = 6 ( add 3 to both sides )

x + 3y = 9 ← in standard form

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Super Dave Osborne stands at the bottom of a canyon elevation 256 feet below sea level, he throws a piano up at a velocity of 3

fgiga [73]

Answer:

The piano was in the air for 18.34 seconds.

Step-by-step explanation:

The height of the piano after t seconds is given by the following equation:

$f(t) = -16t^{2} + 320t - 256$

Initially, the piano is below the ground level. At the first root of the equation, it will go into the air, and then some time after that it will fall down again, which is at the second root of the equation.

Roots of a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$f(t) = -16t^{2} + 320t - 256$

$a = -16, b = 320, c = -256$

$\bigtriangleup = (320)^{2} - 4*(-16)*(-256) = 86016$

$t_{1} = \frac{-320 + \sqrt{86016}}{2*(-16)} = 0.8348$

$t_{2} = \frac{-320 - \sqrt{86016}}{2*(-16)} = 19.17$

Subtracting:

19.17 - 0.8348 = 18.34

The piano was in the air for 18.34 seconds.

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