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3 years ago

How do you know which fraction is greater 0 and 1/2 explain

1 answer:

6 0

0 is the middle number between negative numbers and positive numbers. Since 1/2 is positive, we know that 1/2 is greater than 0.

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Please help me find the value of x

-Dominant- [34]

Answer:

67°

Step-by-step explanation:

Corresponding angles are equal in parallel lines.

Here, ∠acb and ∠aed are corresponding angles for lines bc and de

hence ∠aed = ∠acb = 39

in triangle ade,

x + 74 + 39 = 180 (angle sum property of a triangle)

x = 67°

3 0

3 years ago

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

Ben can type 153 words in 3 minutes. At this rate, how many words can he type in 10 minutes.

GalinKa [24]

Answer:

In 10 minutes, he could type 510 words

Step-by-step explanation:

153/3=51 51 words a minute 51 times 10=510

8 0

3 years ago

Read 2 more answers

Can someone please help me with this????<br> Thanks

natta225 [31]

Answer:

A (I believe)

Step-by-step explanation:

since the part with the triangle is 6 yards, and it looks about half of that whole side, I'm going to assume that that side is 12 yards, and since it's a square each side will be the same length. so multiply 12 and 12 to get 144.

Now divide that by four so you can get the area of a fourth of the square and find the area of the triangle. 144 ÷ 4 = 36

Now divide 36 by 2 to get the area of the little triangle. 36 ÷ 2 = 18

Now divide 18 by 6 to get x. 18 ÷ 6 = 3

In conclusion, the answer should be A.

Hope this helped!!! :3

8 0

2 years ago

HELP ASAP I WILL GIVE YOU THE POINTS !!! <br><br> What is the value of x?

Crazy boy [7]

Answer:

Step-by-step explanation:

70 + 30 = 100

180 - 100 = 80

7 0

3 years ago

Read 2 more answers