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OleMash [197]
3 years ago
15

The length and width of a rectangle are measured as 55 cm and 49 cm, respectively, with an error in measurement of at most 0.1 c

m in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Mathematics
1 answer:
valentina_108 [34]3 years ago
4 0

Answer:

The maximum error in the calculated area of the rectangle is 10.4 \:cm^2

Step-by-step explanation:

The area of a rectangle with length L and width W is A= L\cdot W so the differential of <em>A</em> is

dA=\frac{\partial A}{\partial L} \Delta L+\frac{\partial A}{\partial W} \Delta W

\frac{\partial A}{\partial L} = W\\\frac{\partial A}{\partial W}=L so

dA=W\Delta L+L \Delta W

We know that each error is at most 0.1 cm, we have |\Delta L|\leq 0.1, |\Delta W|\leq 0.1. To find the maximum error in the calculated area of the rectangle we take \Delta L = 0.1, \Delta W = 0.1 and L=55, W=49. This gives

dA=49\cdot 0.1+55 \cdot 0.1

dA=10.4

Thus the maximum error in the calculated area of the rectangle is 10.4 \:cm^2

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Answer:

3.14

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The answer is going to be 3.14

Hope it helps!

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2 years ago
I buy a MP3 player for £40 in a sale where it was 20% off. What was the original price
natta225 [31]
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Question 101 3.1 What is the constant difference between the consecutive terms? &lt; 612,18.24 e 7.14.21.28​
rewona [7]

Answer:

The constant between two consecutive terms is called the common difference. The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.

6 0
3 years ago
A person borrows $50000 loan from bank at a rate of 10% for 5 years compounded yearly.
Hatshy [7]
<h3>Given:</h3>
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  • R= 10%
  • T= 5 years
<h3>Note that:</h3>
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  • R= Rate of interest
  • T= Time period
<h3>Solution:</h3>

\large\boxed{Formula: A= P(1+ \frac{R}{100}{)}^{T}}

Let's substitute according to the formula.

A= 50000(1+ \frac{10}{100}{)}^{5}

<em>A=</em><em> </em><em>$80525.5</em>

Now, we can find the interest paid

\large\boxed{I= A-P}

We'll have to deduct the total amount from the principal amount.

Let's substitute according to the formula.

I= 80525.5-50000

<em>I=</em><em> </em><em>$30525.5</em>

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7 0
2 years ago
Jennifer used 0.42 gallons of paint to completely cover a square wall with an area of 168 square feet. Which measurement is clos
Marina86 [1]

Answer:

The answer to this question is: 12.96 ft ≈ 13 ft

Step-by-step explanation:

Data

Area 168 ft²

Length = ?

Volumen = 0.42 gallons

But we do not need the volume of paint because we know that the wall is squared-shape.

Only we need to know the formula to obtain the area of an square.

Formula   area = length²

So            168 = length²

Finally      √168 = length

             length = 12.96 ≈ 13 ft

6 0
3 years ago
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