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Lelu [443]
3 years ago
8

rita and neha can do certain work indivisually in 20 hours and 25 hours. how much time will it take to complete the work togethe

r
Mathematics
1 answer:
vladimir2022 [97]3 years ago
7 0

Answer:

11.11 hours

Step-by-step explanation:

Rita = 20 hours

Neha = 25 hours

Let the time that they can complete the work together be written as x

1/20 + 1/25 = 1/x

Lowest Common Denominator is 500

25 + 20/500 = 1/x

45/500 = 1/x

Cross Multiply

45x = 500

x = 500/45

x = 11.111111111 hours

Approximately = 11.11 hours

Therefore, it would take Rita and Neha 11.11 hours to complete the work together.

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Answer:Increasing in x∈(0,π/4)∪(5π/4,2π) decreasing in(π/4,5π/4)

Step-by-step explanation:

given f(x) = sin(x) + cos(x)

f(x) can be rewritten as \sqrt{2} [\frac{sin(x)}{\sqrt{2} }+\frac{cos(x)}{\sqrt{2} }  ]..................(a)\\\\\ \frac{1}{\sqrt{2} } = cos(45) = sin(45)\\\\

Using these result in equation a we get

f(x) = \sqrt{2} [ cos(45)sin(x)+sin(45)cos(x)]\\\\= \sqrt{2} [sin(45+x)]..........(b)

Now we know that for derivative with respect to dependent variable is positive for an increasing function

Differentiating b on both sides with respect to x we get

f '(x) = f '(x)=\sqrt{2}  \frac{dsin(45+x)}{dx}\\ \\f'(x)=\sqrt{2} cos(45+x)\\\\f'(x)>0=>\sqrt{2} cos(45+x)>0

where x∈(0,2π)

we know that cox(x) > 0 for x∈[0,π/2]∪[3π/2,2π]

Thus for cos(π/4+x)>0 we should have

1) π/4 + x < π/2  => x<π/4  => x∈[0,π/4]

2) π/4 + x > 3π/2  => x > 5π/4  => x∈[5π/4,2π]

from conditions 1 and 2 we have  x∈(0,π/4)∪(5π/4,2π)

Thus the function is decreasing in x∈(π/4,5π/4)

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