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dem82 [27]
3 years ago
6

Peyton and Tanner were lifting a large boulder and relocating it within their property. Peyton ispushing the boulder with a forc

e of 110 newtons at an angle of 55° with respect to the positivex-axis. Tanner is pulling the boulder with a force of 165 newtons at an angle of 42° with respectto the positive x-axis. Find the magnitude and direction (with respect to the positive x-axis) of theresultant force.
Mathematics
1 answer:
Anvisha [2.4K]3 years ago
8 0

Wow, i wonder why they were lifting a large boulder? They should put it down they could get hurt!!

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Answer:

y = -3(x - 4)² - 2

Step-by-step explanation:

Given the vertex, (4, -2), and the point (2, -14):

We can use the vertex form of the quadratic equation:

y = a(x - h)² + k

Where:

(h, k) = vertex

a  =  determines whether the graph opens up or down, and it also makes the parent function <u>wider</u> or <u>narrower</u>.

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<em>h </em>=<em> </em>determines how far left or right the parent function is translated.

  • h = positive, the function is translated <em>h</em> units to the right.
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<em>k</em> determines how far up or down the parent function is translated.

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Now that I've set up the definitions for each variable of the vertex form, we can determine the quadratic equation using the given vertex and the point:

vertex (h, k): (4, -2)

point (x, y): (2, -14)

Substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

-14 = a(2 - 4)²  -2

-14 = a (-2)² -2

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Add to to both sides:

-14 + 2 = a4 + -2 + 2

-12 = 4a

Divide both sides by 4 to solve for a:

-12/4 = 4a/4

-3 = a

Therefore, the quadratic equation inI vertex form is:

y = -3(x - 4)² - 2

The parabola is downward-facing, and is vertically compressed by a factor of -3. The graph is also horizontally translated 4 units to the right, and vertically translated 2 units down.

Attached is a screenshot of the graph where it shows the vertex and the given point, using the vertex form that I came up with.

Please mark my answers as the Brainliest, if you find this helpful :)

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