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3 years ago

What is the simplest form of i^16 plus i^6 minus 2i^5 plus i^13?

1 answer:

6 0

$\bf \textit{recall that}\qquad i^4=1\qquad i^3=-i\qquad i^2=-1\\\\
-------------------------------\\\\
i^{16}+i^6-2i^5+i^{13}\implies i^{4\cdot 4}~+~i^{4+2}~-~2i^{3+2}~+~i^{4+4+4+1}
\\\\\\
(i^4)^4~+~i^4\cdot i^2~-~2\cdot i^3\cdot i^2~+~i^4\cdot i^4\cdot i^4\cdot i^1
\\\\\\
(1)^4+[1\cdot -1]-[2(-i)(-1)]+[(1)(1)(1)(i)]
\\\\\\
1-1-2i+i\implies -i$

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Please help! 15 points to whoever graphs and solves it!

monitta

First you have to get the equation into slope/intercept format: y = mx + b

$3y > -3+6x\\\\\frac{3y}{3} >\frac{-3+6x}{3} \\y >\frac{3(-1+2x)}{3} \\y > -1+2x\\\\y>2x-1$

So the slope m = 2, and the y-intercept b = -1.

b tells you where the line intersects the y axis. The slope is rise (vertical distance) over run (horizontal distance). I have attached my best attempt at drawing this without graph paper. The dotted line represents the inequality, and the solution set includes the values above the line which is why it is shaded. Hope this helps!

4 0

3 years ago

Which graph best represents -5y = -6x + 15

frutty [35]

Answer: Option c.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the equation:

$-5y = -6x + 15$

Solve for "y" in order to write in Slope-Intercept form:

$y = \frac{-6}{-5}x + \frac{15}{-5}\\\\y = \frac{6}{5}x -3$

Now you can identify that that the slope and the y-intercept are:

$m=\frac{6}{5}\\\\b=-3$

A posive slope means that the the line moves upward from left to right.

With this information, you can conclude that the the graph that best represents the given equation is the graph shown in the Option c.

3 0

3 years ago

842 rounded to the nearest ten

g100num [7]

Answer:

842 rounded to the nearest ten is 840

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Find the integral, using techniques from this or the previous chapter.<br> ∫x(8-x)3/2 dx

Soloha48 [4]

Answer:

$\int x(8-x)^{3/2}dx= -\frac{16}{5} (8-x)^{\frac{5}{2}} +\frac{2}{7} (8-x)^{\frac{7}{2}} +C$

Step-by-step explanation:

For this case we need to find the following integral:

$\int x(8-x)^{3/2}dx$

And for this case we can use the substitution $u = 8-x$ from here we see that $du = -dx$ , and if we solve for x we got $x = 8-u$ , so then we can rewrite the integral like this: