Use the Order of Operations to evaluate this expression

Mathematics

1 answer:

Veronika [31]2 years ago

6 0

(-2+1^2)+5(12/3)-9
(1)+5(4)-9
1+20-9
21-9
12

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How do I simplify the following to "a+bi" form: (1+2i)^3

damaskus [11]

Answer:

Expand it.

(1+2i)^3 is equal to (1+2i)(1+2i)(1+2i).

Multiply everything out (being sure to multiply <em>every</em> term. (1+2i) * (1+2i) = 1+2i+2i+4i^2.

i is the square root of negative one, so i^2 is just -1. 1+2i+2i-4 is what you get from the first two, so now simplify that:

1-4 + 2i+2i = (-3+4i) and now multiply that by (1+2i):

(-3+4i) * (1+2i) = -3 - 6i +4i +8i^2.

Simplify again, and the answer is: -11-2i

Step-by-step explanation:

I hope this helps - really my only tip is don't spend time thinking about what i is, that just hurts your brain. Just remember that i^2 is equal to negative one, and treat it like regular multiplication and you will be fine.

7 0

1 year ago

Write the equation of a line in slope-intercept form with a slope of −13 and a y-intercept of 4 .

frosja888 [35]

Answer:

y = -13x + 4

Step-by-step explanation:

You want to put it in the form y = mx + b where m is the slope and b is the y-intercept (For example, in the equation y = 2x + 3 the slope is 2 and the y-intercept is 3)

Since the slope is -13, m = -13.

Since the y-intercept is 4, b = 4.

This means the equation is y = -13x + 4

6 0

3 years ago

Read 2 more answers

Find the maximum rate of change of f(x,y,z=x y/z at the point (2, -3, 5 and the direction in which it occurs. maximum rate of ch

kherson [118]

$f(x,y,z)=x+\dfrac yz$
$\implies \nabla f(x,y,z)=\left(1,\dfrac1z,-\dfrac y{z^2}\right)$
$\implies \nabla f(2,-3,5)=\left(1,\dfrac15,\dfrac3{25}\right)$

The maximum rate of change is then

$\|\nabla f(2,-3,5)\|=\dfrac{\sqrt{659}}{25}$

which occurs in the direction of $\nabla f(2,-3,5)$ above.