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2 years ago

Help plsss whats the slope

Mathematics

1 answer:

Anettt [7]2 years ago

4 0

The slope is three because the x goes up 1 and y goes up 3 so it’s 3/1 which makes the slope 3

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-b+7c b=2 c=-4 What’s the answer

Neko [114]

Answer:

-30

Start with multiplication 7x(-4) will equal -28 then add that to the -2 and you will get -30

8 0

3 years ago

Read 2 more answers

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

Help please need an answer Fast

anygoal [31]

-7.5 times 1/3=-2.5

To take 1/3 of something, multiply the original by the fraction.

4 0

3 years ago

Calculaye the perimeter and area of these composite shapes

lora16 [44]

For this case we have that the perimeter of the figure is given by the sum of the lengths of the sides, that is:

$14 + 18 + 3 + 4 + 3 + 4 + 3 + 4 + (14-9) + (18-12) = 64$

Thus, the perimeter of the figure is 64 centimeters.

Now, we find the area of the figure:

We have that by definition, the area of a rectangle is given by:

$A = a * b$

Where:

a and b are the sides of the rectangle

We have 4 vertical rectangles from left to right:

$A_ {1} = 14 * (18-12) = 14 * 6 = 84 \ cm ^ 2\\A_ {2} = (3 + 3 + 3) * 4 = 9 * 4 = 36 \ cm ^ 2\\A_ {3} = (3 + 3) * 4 = 6 * 4 = 24 \ cm ^ 2\\A_ {4} = 3 * 4 = 12 \ cm ^ 2$