The dimensions of a closed rectangular box are measured

Mathematics

1 answer:

Damm [24]3 years ago

6 0

Answer:

The maximum error in calculating the surface area of the box is 152 square cm.

Step-by-step explanation:

We are given the following information in the question:

The dimensions of a closed rectangular box are measured as 80 cm, 60 cm, 50 cm, respectively.

Possible error = 0.2 cm

Surface area of rectangular box =

$S = 2(lb + bh + lh)$

where l, b and h are the length, breadth and height of the rectangular box respectively.

Change in area =

$\Delta S \approx dS = 2(l\Delta b + b\Delta l + b\Delta h + h\Delta b + l\Delta h + h\Delta l)\\$

Putting the values, we get,

Change in area =

$=2(\Delta l (b+h) + \Delta b (h+l) + \Deltah(l + b))\\=2(0.2(110) + 0.2(130) + 0.2(140))\\= 152\text{ square cm}$

The maximum error in calculating the surface area of the box is 152 square cm.

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salantis [7]

Answer:

h ≥ 0
C = 0; concentration eventually decays to nothing
(0, 0) is the only intercept in the domain. It means the concentration in the bloodstream is zero at the time the drug is injected.
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Step-by-step explanation:

1. a. The domain of the function in the context of this problem is h ≥ 0. The maximum value of h will correspond to the time at which the concentration is considered to be negligible. If that time is when the concentration decays to 1% of its peak value, then perhaps the suitable domain is 0 ≤ h ≤ 180.

b. The equation of the vertical asymptote of this function is where the denominator of C(h) is zero, that is ...

h^3 +8 = 0

h = ∛(-8)

h = -2 . . . . the equation of the vertical asymptote

This is not a concern for a medical professional because it is outside the domain of the function.

2. As h gets large the value of the function approaches 2/h, which is to say the horizontal asymptote is C = 0. It means the concentration of medication in the blood eventually decays to zero.

3. C(0) = 0 is the only intercept in the domain of the function. (h, C(h)) = (0, 0)

In the context of this problem, it means the blood concentration of medication is zero at the time of the injection.

4. About 1.95 hours after injection, a maximum concentration of the drug occur in the bloodstream. This value is easily found using a graphing calculator.

Taking the derivative of the function gives you ...

C'(h) = -2(h^4 +5h^3 -16h -20)/(h^3 +8)^2

This has two real zeros and two complex zeros. The positive real zero is near h = 1.94527, about 1.95.

That is, the concentration in the bloodstream reaches a maximum about 1.95 hours after injection into the muscle.