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3 years ago

Find the fifth term in the sequence An=2^n

Mathematics

1 answer:

klio [65]3 years ago

7 0

AN=2^n

for fifth term replace n with 5

a(5) = 2^5 = 32

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Consider the differential equation x^2 y''-xy'-3y=0. If y1=x3 is one solution use redution of order formula to find a second lin

Anastasy [175]

Suppose $y_2(x)=y_1(x)v(x)$ is another solution. Then

$\begin{cases}y_2=vx^3\\{y_2}'=v'x^3+3vx^2//{y_2}''=v''x^3+6v'x^2+6vx\end{cases}$

Substituting these derivatives into the ODE gives

$x^2(v''x^3+6v'x^2+6vx)-x(v'x^3+3vx^2)-3vx^3=0$

$x^5v''+5x^4v'=0$

Let $u(x)=v'(x)$ , so that

$\begin{cases}u=v'\\u'=v''\end{cases}$

Then the ODE becomes

$x^5u'+5x^4u=0$

and we can condense the left hand side as a derivative of a product,

$\dfrac{\mathrm d}{\mathrm dx}[x^5u]=0$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}[x^5u]\,\mathrm dx=C$

$x^5u=C\implies u=Cx^{-5}$

Solve for $v$ :

$v'=Cx^{-5}\implies v=-\dfrac{C_1}4x^{-4}+C_2$

Solve for $y_2$ :

$\dfrac{y_2}{x^3}=-\dfrac{C_1}4x^{-4}+C_2\implies y_2=C_2x^3-\dfrac{C_1}{4x}$

So another linearly independent solution is $y_2=\dfrac1x$ .

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3 years ago

Isabel Moreno<br> Simplify: (5p? +7 – 3p' – 5p)+(-7p* – 3p²-9-5p)

kkurt [141]

<h3>Answer: 21p^3+5p?-10p-3p'-2</h3><h3></h3>

Step-by-step explanation:

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3 years ago

The price of an item has risen to $ 299 today. Yesterday it was $130.

hoa [83]

Answer:

It has risen by $169

Step-by-step explanation:

299

130

----------

169

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3 years ago

Select the numbers that have a factor of 5. Mark all that apply.

faust18 [17]

Answer:

a number ending in 0 or 5 has a factor of 5

Step-by-step explanation:

5 is a factor of

5, 10, 15, 20, 25...

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5 0

3 years ago

Clifford is making a really big white cake for his sisters birthday. The recipe calls for 1.5 times as much flour as sugar. It a

pantera1 [17]

<u>Answer:</u>

The amount of butter, sugar and flour does Clifford need is 2.5 cups flour, 3.75 cups sugar and 1.25 butter

<u>Explanation</u>:

Consider the number of cup of flour used to be x

According to question,

Recipe calls for 1.5 times as much flour as sugar

Sugar = $1.5 \times Flour$

Sugar = 1.5x

Butter = ½ x = 0.5x

According to question,

Flour + Sugar + Butter = 7.5

x + 1.5x + 0.5x = 7.5

3x = 7.5

x = 2.5

Sugar = 1.5x = 1.5(2.5) = 3.75

Butter = 0.5(2.5) = 1.25

Clifford need is 2.5 cups flour, 3.75 cups sugar and 1.25 cups butter

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3 years ago