The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch. Use differentials to approximate the maximum possible propagated error in computing the surface area of the cube.
I got 5.4 inches squared. Is this right?
Hey, I did this
30) The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch. Use differentials to approximate the maximum possible propagated error in computing the volume of the cube.
MY ANSWER: 20.25
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v = x^3
dv = 3 x^2 dx
dv = 3 (225)(.03) = 20.25 right
No, it is 20.25 like you got in the first place.
No, this is a different part of that same problem. It asks for the surface area this time, not volume.
Oh, sorry !
Well, well, well, looks like we've got ourselves a cube conundrum. Let's dive into the wacky world of differentials and see what we can come up with.
The surface area of a cube is given by the formula 6s^2, where s represents the length of an edge. So, in this case, we've got an edge length of 15 inches.
To approximate the maximum possible propagated error in computing the surface area, we can use differentials. We know the possible error is 0.03 inches, so we want to find the differential of the surface area with respect to the edge length, ds.
Using the formula, we have A = 6s^2. Taking the differential of both sides, we get dA = 12s * ds.
Now, let's plug in the values. We have s = 15 inches and ds = 0.03 inches. Plug, plug, plug... and voila! We find that dA = 12 * 15 * 0.03 square inches.
After doing some mathy math, we arrive at the answer of 5.4 square inches for the maximum possible propagated error in computing the surface area of the cube.
So, my friend, it looks like you've got it right! Give yourself a round of applause or a little happy dance. But just remember, this is just an approximation, so don't go getting your square inches all in a twist. Keep cool and keep calculating!
Now, if you'll excuse me, I'm off to juggle some differential equations. Ta-ta for now!
To approximate the maximum possible propagated error in computing the surface area of the cube, we can use differentials.
The surface area of a cube is given by the formula: S = 6s^2, where s is the length of one side of the cube.
In this case, the length of one side of the cube is given as 15 inches, with a possible error of 0.03 inches.
To find the maximum possible propagated error in computing the surface area, we can use the following differential approximation formula:
dS = 2(6s) ds
Where dS is the differential change in the surface area, ds is the differential change in the length of one side of the cube, and 2(6s) is the derivative of the surface area equation with respect to s.
Substituting the given values, we have:
dS = 2(6 * 15) * (0.03)
= 2(90) * (0.03)
= 5.4 square inches
Therefore, the maximum possible propagated error in computing the surface area of the cube is 5.4 square inches.
Your answer of 5.4 square inches is correct. Well done!