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3 years ago

7(4 + 3x) = 45(x - 3) - 3(2x -12)

Mathematics

1 answer:

Bezzdna [24]3 years ago

4 0

7(4 + 3x) = 45(x - 3) - 3(2x - 12)

Distribute:

28 + 21x = 45x - 135 - 6x + 36

Collect like terms:

28 + 21x = 39x - 99

Rearrange terms to get them all on one side (add 99 to both sides):

28 + 99 + 21x = 39x - 99 + 99

Simplify:

127 + 21x = 39x

Subtract 21x from both sides:

127 + 21x - 21x = 39x - 21x

Simplify:

127 = 18x

Divide by 18 on both sides to isolate the x variable and solve the expression:

127/18 = 18x/18

Simplify:

x = 127/18

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A structure which has a square base and four triangular sides meeting at a point is called pyramid.

At distance of 3.97 feet from its vertex , pyramid is cut by plane so that the two solids of equal weight will be formed.

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Substituting value of a in equation $k*(\frac{1}{3}* a* h)=400$

So, $k*(\frac{1}{3}* \frac{h^{2} }{25}A * h)=400$

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60 = a * (-30)^2
a = 1/15
So y = (1/15)x^2

abc)
The derivative of this function is 2x/15. This is the slope of a tangent at that point.
If Linda lets go at some point along the parabola with coordinates (t, t^2 / 15), then she will travel along a line that was TANGENT to the parabola at that point.
Since that line has slope 2t/15, we can determine equation of line using point-slope formula:
y = m(x-x0) + y0
y = 2t/15 * (x - t) + (1/15)t^2
Plug in the x-coordinate "t" that was given for any point.

d)
We are looking for some x-coordinate "t" of a point on the parabola that holds the tangent line that passes through the dock at point (30, 30).
So, use our equation for a general tangent picked at point (t, t^2 / 15):
y = 2t/15 * (x - t) + (1/15)t^2
And plug in the condition that it must satisfy x=30, y=30.
30 = 2t/15 * (30 - t) + (1/15)t^2
t = 30 ± 2√15 = 8.79 or 51.21
The larger solution does in fact work for a tangent that passes through the dock, but it's not important for us because she would have to travel in reverse to get to the dock from that point.
So the only solution is she needs to let go x = 8.79 m east and y = 5.15 m north of the vertex.

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