Please help, I will give thanks and 5 stars. I beg for an answer, since I have worked on this question for 2 hours, yet my effor
ts has not bear any fruit yet.
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The number of cookies and trays are illustrations of greatest common factors.
- The number of trays is 8
- 6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray
The given parameters are:
<u>(a) The number of trays</u>
To do this, we simply calculate the greatest common factor of 48, 64 and 120
Factorize the numbers, as follows:
So, the GCF is:
Hence, the number of tray is 8
<u>(b) The number of each type of cookie</u>
We have
Divide each cookie by the number of trays
So, we have:
Hence, 6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray
Read more about greatest common factors at:
Let . The tangent plane to the surface at (0, 0, 8) is
The gradient is
so the tangent plane's equation is
The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation
or ,
, and
.
(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
