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mrs_skeptik [129]
2 years ago
15

In physics, it is important to use mathematical approximations. for instance, in a small angle approximation, tanα ∼ sin α . fin

d the largest angle α for which the difference between the sine and the tangent of an angle is less than 10.4% of the sinα value. answer in units of rad.
Mathematics
1 answer:
siniylev [52]2 years ago
5 0
Note that x is measured in radians.
The percent difference or error between sin(x) and tan(x) is calculated as 
d = 100( \frac{|sin(x)-tan(x)|}{sin(x)} )

We want this percent difference to be less than 10.4%.
Because tan(x) > sin(x) for small values of x, define
f(x) =  \frac{tan(x)-sin(x)}{sin(x)}= 0.104 \\ or \\ sec(x) - 1  = 0.104 \\ sec(x) = 1.104

From the calculator, obtain
sec⁻¹ 1.104 = 0.4375

Answer:  x = 0.4375 radians

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Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

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Normal probability distribution

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In this problem, we have that:

n = 250, p = 0.58

So

\mu = E(X) = 250*0.58 = 145

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.58*0.42} = 7.80

If the population proportion of adults who watch news videos is 0.58​, what is the probability that fewer than half in your sample will watch news​ videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

Z = \frac{X - \mu}{\sigma}

Z = \frac{124 - 145}{7.8}

Z = -2.69

Z = -2.69 has a pvalue of 0.0036

0.36% probability that fewer than half in your sample will watch news​ videos

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