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1 year ago

Weiming, Farhan and Sam had some comic books.

Mathematics

1 answer:

mixas84 [53]1 year ago

5 0

Answer:

Farhan had 9 comic books

Sam had 51 comic books and lived in his Mother's basement

Step-by-step explanation:

W + F = 36

W = 3F

3F + F = 36

F = 9

W = 27

S + F = 60

S + 9 = 60

S = 51

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2 years ago

Read 2 more answers

If 10a+10b=35, what is the average (arithmetic mean) of a and b?

worty [1.4K]

Answer:

1.75

Step-by-step explanation:

If a and b are two numbers, then their arithmetic mean is

$\dfrac{a+b}{2}$

Given:

$10a+10b=35$

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Now, divide it by 2:

$\dfrac{a+b}{2}=\dfrac{3.5}{2}\\ \\\dfrac{a+b}{2}=1.75$

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2 years ago

The rate of transmission in a telegraph cable is observed to be proportional to x2ln(1/x) where x is the ratio of the radius of

sergij07 [2.7K]

Answer:

The value of x that gives the maximum transmission is 1/√e ≅0.607

Step-by-step explanation:

Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.

$f'(x) = k*((x^2)'*ln(1/x) + x^2*(ln(1/x)')) = k*(2x\,ln(1/x)+x^2*(\frac{1}{1/x}*(-\frac{1}{x^2})))\\= k * (2x \, ln(1/x)-x)$

We need to equalize f' to 0

k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
1/x = e^(1/2)
x = 1/e^(1/2) = 1/√e ≅ 0.607

Thus, the value of x that gives the maximum transmission is 1/√e.

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2 years ago