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Alja [10]
3 years ago
10

The dimensions of a closed rectangular box are measured as 90 centimeters, 50centimeters, and 90 centimeters, respectively, with

the error in each measurement at most .2.2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.
Mathematics
1 answer:
gogolik [260]3 years ago
5 0

Answer:

184 cm²

Step-by-step explanation:

Surface area of the rectangular box is expressed as S = 2(LW+LH+WH)

L is the length of the box = 90 cm

W is the width of the box = 50 cm

H is the height of the box= 90 cm

If there are error of at most 0.2 cm in each measurement, then the total surface area using differential estimate will be expressed as shown;

S = 2{(LdW+WdL) + (LdH+HdL) + (WdH+HdW)

Note that dL = dW = dH = 0.2 cm

Substituting the given values into the formula to estimate the maximum error in calculating the surface area of the box

S = 2{(90(0.2)+50(0.2)) + (90(0.2)+90(0.2)) + (50(0.2)+90(0.2))

S = 2{18+10+18+18+10+18}

S = 2(92)

S = 184 cm²

Hence, the maximum error in calculating the surface area of the box is 184cm²

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The Demand function for a product is given by:
VikaD [51]

Answer:

The average rate of change of Demand between 40 and 175 units sold is of -0.1045.

Step-by-step explanation:

Average rate of change:

The average rate of a function f(x) in an interval [a,b] is given by:

A = \frac{f(b) - f(a)}{b - a}

In this question:

D(q) = -0.0003q^2 - 0.04q + 23.56

What is the average rate of change of Demand between 40 and 175 units sold?

a = 40, b = 175. So

D(40) = -0.0003*40^2 - 0.04*40 + 23.56 = 21.48

D(175) = -0.0003*175^2 - 0.04*175 + 23.56 = 7.3725

So

A = \frac{f(b) - f(a)}{b - a} = \frac{7.3725 - 21.48}{175 - 40} = -0.1045

The average rate of change of Demand between 40 and 175 units sold is of -0.1045.

3 0
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Ne4ueva [31]

Answer:

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I = 19.5 Hours

Step-by-step explanation:

Start by creating a system.

I = time which the inlet pipe takes alone to fill the pond

H = time which the hose takes alone to fill the pond

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aivan3 [116]

Answer:

why do we tell actors to "break a leg"?

Step-by-step explanation:

6 0
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4. A yellow cab Taxi charges $5.00 flat rate in addition of $0.65 per mile. Jan has no more than $20 to spend on a ride.
gogolik [260]

Answer:

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Step-by-step explanation:

Let x be the number of miles Jan can drive in a taxi.

The cost of this ride consists of

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So, per x miles Jan will pay $0.65x and the total cost of the ride will be

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Jan has no more than $20 to spend on a ride, then the total cost of his ride must be less or equal to $20. Mathematically, you can write this as

5+0.65x\le 20

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