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miv72 [106K]
3 years ago
12

Jacob struggled to solve 0.96 divided by 0.2 so he solved 96 divided by 2 instead. After finding the quotient of 96 divided by 2

, what must jacob do to find the value of the original expression
Mathematics
1 answer:
LekaFEV [45]3 years ago
5 0
Take away the decimal?
You might be interested in
Power Series Differential equation
KatRina [158]
The next step is to solve the recurrence, but let's back up a bit. You should have found that the ODE in terms of the power series expansion for y

\displaystyle\sum_{n\ge2}\bigg((n-3)(n-2)a_n+(n+3)(n+2)a_{n+3}\bigg)x^{n+1}+2a_2+(6a_0-6a_3)x+(6a_1-12a_4)x^2=0

which indeed gives the recurrence you found,

a_{n+3}=-\dfrac{n-3}{n+3}a_n

but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that a_2=0, and substituting this into the recurrence, you find that a_2=a_5=a_8=\cdots=a_{3k-1}=0 for all k\ge1.

Next, the linear term tells you that 6a_0+6a_3=0, or a_3=a_0.

Now, if a_0 is the first term in the sequence, then by the recurrence you have

a_3=a_0
a_6=-\dfrac{3-3}{3+3}a_3=0
a_9=-\dfrac{6-3}{6+3}a_6=0

and so on, such that a_{3k}=0 for all k\ge2.

Finally, the quadratic term gives 6a_1-12a_4=0, or a_4=\dfrac12a_1. Then by the recurrence,

a_4=\dfrac12a_1
a_7=-\dfrac{4-3}{4+3}a_4=\dfrac{(-1)^1}2\dfrac17a_1
a_{10}=-\dfrac{7-3}{7+3}a_7=\dfrac{(-1)^2}2\dfrac4{10\times7}a_1
a_{13}=-\dfrac{10-3}{10+3}a_{10}=\dfrac{(-1)^3}2\dfrac{7\times4}{13\times10\times7}a_1

and so on, such that

a_{3k-2}=\dfrac{a_1}2\displaystyle\prod_{i=1}^{k-2}(-1)^{2i-1}\frac{3i-2}{3i+4}

for all k\ge2.

Now, the solution was proposed to be

y=\displaystyle\sum_{n\ge0}a_nx^n

so the general solution would be

y=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots
y=a_0(1+x^3)+a_1\left(x+\dfrac12x^4-\dfrac1{14}x^7+\cdots\right)
y=a_0(1+x^3)+a_1\displaystyle\left(x+\sum_{n=2}^\infty\left(\prod_{i=1}^{n-2}(-1)^{2i-1}\frac{3i-2}{3i+4}\right)x^{3n-2}\right)
4 0
3 years ago
1,679 rounded to the nearest thousand
polet [3.4K]
The answer is 1700 because 1679 rounded to the nearest hundred is 1700
8 0
3 years ago
45 is 3% of what number?<br><br> quick I need an answer!<br> hurry pls!
Airida [17]

Answer:

stop rushing brat

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please help me I really need it in the next 2 mins first and correct answer gets brainly.est
WITCHER [35]
13 units because 7 + 6 = 13

3 0
3 years ago
Read 2 more answers
Please help me and no crazy answers!!!!!!
lisov135 [29]

<em>1</em><em> </em><em>I </em><em>do </em><em>not </em><em>know</em>

<em>2</em><em> </em><em>t</em><em>h</em><em>i</em><em>s</em><em> </em><em>is </em><em>so </em><em>hard</em>

<em>3</em><em> </em><em>i</em><em> </em><em>don't </em><em>know</em><em> </em><em>what</em><em> </em><em>is </em><em>the </em><em>answer</em><em />

6 0
3 years ago
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