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3 years ago

You need dye for 500,000 t-shirts. Each shirt takes a deciliter of dye. How many liters of dye do you need?

Mathematics

1 answer:

Inessa [10]3 years ago

3 0

50,000 liters of dye there’s 10 deciliters in one liter so 500,000/10= 50,000

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Find the general solution of the nonhomogeneous differential equation x^2y''-2y=3(x^2) -1, (x>0).

Ira Lisetskai [31]

Answer:

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Step-by-step explanation:

We are given that non-homogeneous differential equation

$x^2y''-2y=3(x^2)-1$

It is Cauchy Euler equation

Substitute x=e^t x>0

Auxillary equation

$D'(D'-1)-2=0$

$D'^2-D'-2=0$

$(D'-2)(D'+1)=0$

$D'-2=0 \implies D'=2$

$D'+1=0\implies D'=-1$

Complementary solution

$y=C_1e^{-t}+C_2e^{2t}$

$y=C_1\frac{1}{x}+C_2x^2$

Particular solution

$y_p=\frac{3e^{2t}}{D'^2-D'-2}-\frac{e^{0t}}{D'^2-D'-2}$

$y_p=te^{2t}+\frac{1}{2}=x^2logx+\frac{1}{2}$

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Hence, general solution G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

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4 years ago

Integral of sin^4 (6x) dx

DENIUS [597]

Hello,

$\boxed{sin^4\ x= \frac{3}{8}- \frac{cos\ 2x}{2}+\frac{sin\ 4x}{8} }\\

Let's assume t=6x \ dt=6\ dx\\

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3 years ago

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dmitriy555 [2]

Cosθ = adjacent / hypotenuse

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3 years ago

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Rina8888 [55]

Answer:

x = -4 and x = -14

Step-by-step explanation:

Our equation is (x + 9)² = 25

Applying the square root property we would need to take the square root of both sides: $\sqrt{(x+9)^{2} } =\sqrt{25}$

This give us x + 9 = ±5

Here we have two equations since taking the square root gives us a positive and negative value

Our first equation is x + 9 = 5, and to isolate the variable we would need to subtract 9 from both sides, giving us x = -4

Our second equation is x + 9 = -5, and to isolate the variable we would need to subtract 9 from both sides, giving us x = -14

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