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3 years ago

**At noon the minute and the hour hands overlap. When will it happen next?

Mathematics

1 answer:

Svetllana [295]3 years ago

7 0

Answer: At 01:05 p.m. it will overlap again.

Explanation:

Since there are 22 times in a day the minute and the hour hands overlap.

During the first half of the day , it overlaps 11 times and during the rest of the day it overlap 11 more times.

At noon, the minute and the hour hands overlap and after that it will happen at 01:05 p.m.

Since the minute hand completes a full circle in one hour, so it forms 6 degrees per minute .

So, at 01:05 p.m. it will overlap again.

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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

valentina_108 [34]

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 $10.4 \:cm^2$

4 0

3 years ago