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3 years ago

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Mathematics

1 answer:

Snowcat [4.5K]3 years ago

7 0

Answer:

(1) e2x [ (2x -1 )cot x – x cosec2x]/x2

(2) e2x [ (2x +1 )cot x – cosec2x]/x2

(3) e2x [ (2x -1 )cot x + cosec2x]/x2

(4) none of these

Solution:

Given y = e2x cos x /x sin x

Differentiate w.r.t.x

Use quotient rule

dy/dx = [x sin x (d/dx)e2x cos x – e2x cos x (d/dx) x sin x]/ (x sin x)2

= [x sin x (e2x ×2× cos x – e2x sin x ) – e2x cos x ( sin x+ x cos x)]/ (x sin x)2

= [ x 2 sin x cos x e2x – e2x x sin2 x – e2x cos x sin x – e2x x cos2 x]/ (x sin x)2

= [ x sin 2x e2x – x e2x(sin2x+cos2x) – e2x sin x cos x]/(x sin x)2

= [ x e2x sin 2x – x e2x – e2x sin x cos x]/(x sin x)2

= [ 2x e2x cot x – x e2x cosec2 x – e2x cot x]/x2

= e2x [ 2x cot x – x cosec2 x – cot x]/x2

= e2x [ (2x -1 )cot x – x cosec2x]/x2

Hence option (1) is the answer

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4 years ago

Read 2 more answers

Goal

morpeh [17]

The development of the personal budget that convinces parents that one can maintain an independent living is detailed as follows using the 50: 30: 20 rule:

50% for necessities (housing, food, transportation, utilities) $740

30% for luxuries, savings, vacations, entertainment, etc. $461

20% for Emergency Funds and Retirement $335

<h3>What is a personal budget?</h3>

A personal budget is the household budget for a single person for a period.

The personal budget shows an estimate of the person's revenue and expenses over the period.

<h3>Data and Calculations:</h3>

Hourly rate of earnings = $12

Working hours per week = 40 hours

Working hours per month = 160 hours (40 x 4 weeks)

Total monthly earnings = $1,920 ($12 x 160)

Assumed tax rate = 20%

After-tax take-home pay = $1,536 ($1,920 x 1 - 20%)

<h3>Monthly Necessities:</h3>

Rent of apartment = $300

Heating = $40

Water cost = $20

Sewage bill = $10

Food = $300

Transportation = $50

Other costs = $20

Total cost for necessities = $740

Thus, the development of the personal budget shows that one can maintain an independent living from the parents as a single person.

Learn more about personal budgets at brainly.com/question/1943261

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2 years ago

The base of a right triangle is increasing at a rate of 2 meters per hour and the height is decreasing at a rate of 3 meters per

STatiana [176]

Answer:

dL/dt = - 2,019 m/h

Step-by-step explanation:

L² = x² + y² (1) Where x, and y are the legs of the right triangle and L the hypotenuse

If the base of the triangle, let´s call x is increasing at the rate of 2 m/h

then dx/dt = 2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h

If we take differentials on both sides of the equation (1)

2*L*dL/dt = 2*x*dx/dt + 2*y*dy/dt

L*dL/dt = x*dx/dt + y*dy/dt (2)

When the base is 9 and the height is 22 according to equation (1) the hypotenuse is:

L = √ (9)² + (22)² ⇒ L = √565 ⇒ L = 23,77

Therefore we got all the information to get dL/dt .

L*dL/dt = x*dx/dt + y*dy/dt

23,77 * dL/dt = 9*2 + 22* ( - 3)

dL/dt = ( 18 - 66 ) / 23,77

dL/dt = - 2,019 m/h

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