anonymous
  • anonymous
grr
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
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Michele_Laino
  • Michele_Laino
we know that your function has to be a polynomial of degree 2 from your drawing we see that x=6 and x=-6 are two zeroes of the requested polynomial
anonymous
  • anonymous
Oh! So would it be -1(x+6)(x-6) ??
Michele_Laino
  • Michele_Laino
the simpler polynomial which satisfies those requisites is: \[y = \left( {x - 6} \right)\left( {x + 6} \right)\] even if, we have to check if my function contains the point (0,36) does my function pass at point (0,36)?

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Michele_Laino
  • Michele_Laino
yes! that's right!
anonymous
  • anonymous
Ok so then I got -x^2+36?
Michele_Laino
  • Michele_Laino
correct!
anonymous
  • anonymous
There is a 2nd part to this question, I'm not getting
anonymous
  • anonymous
I know, I'm lost too:)
Michele_Laino
  • Michele_Laino
you have to create a table for a straight line like this one: |dw:1438706644480:dw|
Michele_Laino
  • Michele_Laino
step#1 please chose two point on your rainbow
Michele_Laino
  • Michele_Laino
oops.. choose*
anonymous
  • anonymous
um 3?
Michele_Laino
  • Michele_Laino
you have to choose 2 values for x-coordinate
Michele_Laino
  • Michele_Laino
between -6 and 6
anonymous
  • anonymous
oh okay then 5
Michele_Laino
  • Michele_Laino
x1=5 and x2=?
anonymous
  • anonymous
11?
Michele_Laino
  • Michele_Laino
no, your value has to be less than 6 and grater than -6
Michele_Laino
  • Michele_Laino
x=5 is right! the other value can be x=2
Michele_Laino
  • Michele_Laino
what do you think?
anonymous
  • anonymous
yes, i agree
Michele_Laino
  • Michele_Laino
ok!
Michele_Laino
  • Michele_Laino
now we have to compute the corresponding y-value, so, if x=5 then: y=-5^2+36=-25+36=11
Michele_Laino
  • Michele_Laino
whereas if x=1, then: y=-1^2+25=...?
anonymous
  • anonymous
I see, I see:)
anonymous
  • anonymous
24
Michele_Laino
  • Michele_Laino
sorry if x=1, then: y=-1^2+36=35 we have these points: (1,35) and (5,11)
anonymous
  • anonymous
I agree:)
anonymous
  • anonymous
so then we would have to make a chart, and another function right?
Michele_Laino
  • Michele_Laino
now: step#2 we have to write the equation of the straight line which passes at points (1,35) and (5,11)
Michele_Laino
  • Michele_Laino
for example we can use this equation: \[\Large y - 35 = m\left( {x - 1} \right)\] where: \[\Large m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{11 - 35}}{{5 - 1}} = ...?\]
anonymous
  • anonymous
-24/4
anonymous
  • anonymous
-6
Michele_Laino
  • Michele_Laino
yes!
Michele_Laino
  • Michele_Laino
so, what is the equation of your straight line?
anonymous
  • anonymous
um y=6x+1?
anonymous
  • anonymous
i mean y=-6x
Michele_Laino
  • Michele_Laino
we have to substitute our value of m, into my equation above: \[\Large y - 35 = - 6 \cdot \left( {x - 1} \right)\]
Michele_Laino
  • Michele_Laino
please, simplify
anonymous
  • anonymous
y-35=-6x+6
Michele_Laino
  • Michele_Laino
so: y=...?
anonymous
  • anonymous
y=-6x-29
Michele_Laino
  • Michele_Laino
I got: Y=-6x+41 am I right?
anonymous
  • anonymous
yes. whoops:)
Michele_Laino
  • Michele_Laino
ok! Now the exercise asks you at least four points
Michele_Laino
  • Michele_Laino
you have already two points: (1,35) and (5,11)
Michele_Laino
  • Michele_Laino
so you have to choose another 2 values for x, and compute the corresponding value for y. Please keep in mind that x has to be greater than -6 and less than 6
anonymous
  • anonymous
what about 2?
Michele_Laino
  • Michele_Laino
whit those four points you have to create a table like this: |dw:1438708104245:dw|
Michele_Laino
  • Michele_Laino
ok! x=2 is good, so: y= -2^2+36=-4+36=...?
anonymous
  • anonymous
32
Michele_Laino
  • Michele_Laino
so the third point is: (2,32)
Michele_Laino
  • Michele_Laino
now, we can choose x=-3
Michele_Laino
  • Michele_Laino
what is y?
anonymous
  • anonymous
45
Michele_Laino
  • Michele_Laino
I got this: y=-(-3^2)+36=-9+36=27
anonymous
  • anonymous
yes<3
anonymous
  • anonymous
Yayyy! We did it! So just to make sure, the 2nd equation is y=-6x?
Michele_Laino
  • Michele_Laino
so, the requested table is: |dw:1438708531419:dw|
Michele_Laino
  • Michele_Laino
the second equation is: \[\Large y = - 6x + 41\]
anonymous
  • anonymous
oh, so is it possible that we could have plug the points into that equation to get the points too?
Michele_Laino
  • Michele_Laino
please wait
Michele_Laino
  • Michele_Laino
I have made an error, at x=2 we have to compute the value of the y-coordinate of the line, namely: \[\Large y = - 6 \cdot 2 + 41 = ...\]
Michele_Laino
  • Michele_Laino
similarly at x=-3: \[\Large y = - 6 \cdot 3 + 41 = ...\]
anonymous
  • anonymous
29
anonymous
  • anonymous
so can we draw the chart again and see?
Michele_Laino
  • Michele_Laino
ok! so we got these points: (2,29) and (-3,23)
anonymous
  • anonymous
|dw:1438708966376:dw|
anonymous
  • anonymous
what would the domain/range be?
Michele_Laino
  • Michele_Laino
that's right!
Michele_Laino
  • Michele_Laino
the domain of the direction of the drone, it is all the real line
anonymous
  • anonymous
so would the domain be -6 and 6 then?
Michele_Laino
  • Michele_Laino
it is the domain of the rainbow, I think
anonymous
  • anonymous
ohhh
anonymous
  • anonymous
Thanks for all your help!!!!! :D
Michele_Laino
  • Michele_Laino
please wait, I have made another error, the fourth point is: (-3,59)
anonymous
  • anonymous
Good thing you caught that!
Michele_Laino
  • Michele_Laino
since we have: \[\Large y = \left( { - 6} \right) \cdot \left( { - 3} \right) + 41 = 18 + 41 = 59\]
Michele_Laino
  • Michele_Laino
the domain of the rainbow is the subsequent interval: (-6,6) whereas its range is (0,36)
anonymous
  • anonymous
what would that represent?
Michele_Laino
  • Michele_Laino
the range is the set af possible values of the function -x^2+36 when x is inside the domain
anonymous
  • anonymous
Is the linear function you created positive or negative? Explain.
Michele_Laino
  • Michele_Laino
I think that it represents the possible Rainbow heights with respect to the Earth's surface
Michele_Laino
  • Michele_Laino
the linear function which we have created has a negative slope, so I think it is negative
anonymous
  • anonymous
What are the solutions or solution to the system of equations created? Explain what it or they represent.
anonymous
  • anonymous
thanks so much:)
Michele_Laino
  • Michele_Laino
the requested solution is given by the coordinates of the intersection points, namely: (1,35) and (5,11)
Michele_Laino
  • Michele_Laino
:)

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