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3 years ago

What is the integral of 1/(y²-1)

Mathematics

1 answer:

ANTONII [103]3 years ago

3 0

Hello here is a solution :

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The value of a car depreciates by 15% each year. The value of the car when new is $14000. WHat will be the value of the car afte

deff fn [24]

Answer:

$11,900

Step-by-step explanation:

6 0

3 years ago

Evaluate this exponential expression.

Afina-wow [57]

It's -32 since 10-42=-32

8 0

3 years ago

Find the following when a = -3, b = 6, c = −4/5 9b−72a+1

Vadim26 [7]

271.

Hope this helped!

8 0

2 years ago

Consider the differential equation x2y′′ − 9xy′ + 24y = 0; x4, x6, (0, [infinity]). Verify that the given functions form a funda

pantera1 [17]

Answer:

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

$y= c_1x^4+c_2x^6$

Step-by-step explanation:

Given equation is

$x^2y'' - 9xy+24y=0$

This Euler Cauchy type differential equation.

So, we can let

$y=x^m$

Differentiate with respect to x

$y'= mx^{m-1}$

Again differentiate with respect to x

$y''= m(m-1)x^{m-2}$

Putting the value of y, y' and y'' in the differential equation

$x^2m(m-1) x^{m-2} - 9 x m x^{m-1}+24x^m=0$

$\Rightarrow m(m-1)x^m-9mx^m+24x^m=0$

$\Rightarrow m^2-m-9m+24=0$

⇒m²-10m +24=0

⇒m²-6m -4m+24=0

⇒m(m-6)-4(m-6)=0

⇒(m-6)(m-4)=0

⇒m = 6,4

Therefore the auxiliary equation has two distinct and unequal root.

The general solution of this equation is

$y_1(x)=x^4$

and

$y_2(x)=x^6$

First we compute the Wronskian

$W(x)= \left|\begin{array}{cc}y_1(x)&y_2(x)\\y'_1(x)&y'_2(x)\end{array}\right|$

$= \left|\begin{array}{cc}x^4&x^6\\4x^3&6x^5\end{array}\right|$

=x⁴×6x⁵- x⁶×4x³

=6x⁹-4x⁹

=2x⁹

≠0

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

$y= c_1x^4+c_2x^6$

5 0

3 years ago

Frank purchased an air conditioner for $3000. Its value depreciates at a rate of 8% each year. How much will the air conditioner

Lina20 [59]

Answer:

$2280

Step-by-step explanation:

Given: Cost of Air conditioner= $3000.

Rate of depreciation= 8%

Number of year= 3 years.

Now, finding the depreciation for 3 years.

Depreciation= $\frac{Cost\ of\ air\ conditioner\times rate\ of\ depreciation\times years}{100}$

Amount of depreciation= $\frac{\$ 3000\times 8\times 3}{100} = \$ 30\times 24$

∴ Amount of depreciation in 3 years is $720.

Cost of Air conditioner after 3 years= $Original\ cost - Amount\ of\ depreciation$

⇒ Cost of Air conditioner after 3 years= $\$ 3000-\$ 720= \$ 2280.$

∴ Cost of Air conditioner in 3 years is $2280.

5 0

3 years ago

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