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3 years ago

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Write the point-slope form of the line that passes through (6,1) and is parallel to a line with a slope of -3 include all of you

r work in your final answer.

1 answer:

ycow [4]3 years ago

8 0

<u>Answer: </u>

The point-slope form of the line that passes through (6,1) and is parallel to a line with a slope of -3 is 3x + y – 19 = 0

<u>Solution: </u>

The point slope form of the line that passes through the points $\left(x_{1} y_{1}\right)$ and parallel to the line with slope “m” is given as

$y - y_{1} = m\left(x - x_{1}\right)$ --- eqn 1

Where “m” is the slope of the line. $x_{1} \text { and } y_{1}$ are the points that passes through the line.

From question, given that slope “m” = -3

Given that the line passes through the points (6,1).Hence we get $x_{1} = 6 ; y_{1} = 1$

By substituting the values in eqn 1, we get the point slope form of the line which is parallel to the line having slope -3 can be found out.

y – 1 = -3(x – 6)

y – 1 = -3x +18

On rearranging the terms, we get

3x + y -1 – 18 = 0

3x + y – 19 = 0

Hence the point slope form of given line is 3x + y – 19 = 0

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Answer:

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Step-by-step explanation:

The function that describes a parabola is a quadratic function

The standard form of a quadratic function is given as follows;

f(x) = a·(x - h)² + k, where "a" ≠ 0

When the value of part of the function a·x² after expansion is responsible for the curved shape of the function and the sign of the constant "a", determines weather the the curve opens up or is "u-shaped" or opens down or is "n-shaped"

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A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the flo

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The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

$y - k = C \cdot (x-h)^{2}$

Where:

$h$ - Horizontal component of the vertix, measured in inches.

$k$ - Vertical component of the vertix, measured in inches.

$C$ - Parabola constant, dimensionless. (Where vertix is an absolute maximum when $C < 0$ or an absolute minimum when $C > 0$ )

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

$V (x,y) = (0, 32)$ (Vertix)

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$0-32 = C \cdot (28 - 0)^{2}$

$-32 = 784\cdot C$

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The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

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$x^{2} = -\frac{49}{2}\cdot (y-32)$

$x = \sqrt{-\frac{49}{2}\cdot (y-32) }$

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$x = \sqrt{-\frac{49}{2}\cdot (22-32)}$

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