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Virty [35]
3 years ago
11

Use logarithmic differentiation to find dy/dx

Mathematics
1 answer:
liq [111]3 years ago
7 0

Answer:

dy/dx  =  (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

Step-by-step explanation:

y = (x^2 - 3)^sinx

ln y = ln  (x^2 - 3)^sinx

ln y = sin x * ln (x^2 - 3)

1/y * dy/dx  =   sin x * {1 / (x^2 - 3)} * 2x + ln(x^2 - 3) * cos x

1/y dy/dx =  2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)

dy/dx  =   [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)] * y

dy/dx  =  (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

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In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen to study the re
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Answer:

REQUIRED TEST STATICS IS 35.19

Step-by-step explanation:

total size of sample = 10,000

                                     men                            women

voted                           2777                            3466

did not vote                  1444                             2313

By chi square test we can find the relationship between gender and participation in the election

<em>X^2 = \frac{ N(ad-bc)^2}{(a+c)(b+d)+(a+b)(c+d)}</em>

where

a represent  = 2777, b = 3466, c= 1444, d = 2313, N = 10000

Putting values to get chis square statics

<em>X^2 = \frac{ 10000(2777*2313-3466*1444)^2}{(2777+1444)(3466+2313)+(2777+3466)(1444+2313)}</em>

<em>X^2 = = 35.159</em>

HENCE REQUIRED TEST STATICS IS 35.19

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A man is four times as old as his son. 10 years later, the man will be three times as old as his son. What is the man’s current
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A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters
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Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

\Rightarrow y=\sqrt{x^2+100}

Differentiating with respect to t

\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}

\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}

Since the car driving towards the intersection at 13 m/s.

so,\frac{dx}{dt}=-13

\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)

Now

\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)

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               =\frac{24\times (-13)}{26}

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Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0
3 years ago
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