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3 years ago

Use a scientific calculator or unit circle to convert the polar form of the complex number to its equivalent rectangular form.

Mathematics

2 answers:

Vika [28.1K]3 years ago

6 0

16+16i squareroot 3 Im positive thats the answer. The other person idk what they did.

GuDViN [60]3 years ago

5 0

I assume 3.14 is meant to represent π. So x=32cos(π/3)=16 and y=32sin(π/3)=16√3=27.7128 approx.
If we take 3.14 directly (radians), then we get x=16.0147 and y=27.7043 approx.

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Eva reads 12 pages per hour. In all, how many hours reading will Eva have to do this week in order to have read a total of 48 pa

KiRa [710]

Since eva is a slow reader pacing at 12 pages an hour, she would have to read for 4 hours over the week in order to read 48 pages total.

12x4=48

8 0

3 years ago

Calculus piecewise function.

Kipish [7]

Part A

The notation $\lim_{x \to 2^{+}}f(x)$ means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows $\lim_{x \to 2^{+}}f(x) = 2$

Then for the left hand limit $\lim_{x \to 2^{-}}f(x)$ , we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, $\lim_{x \to 2^{-}}f(x) = 1$

===============================================================

Part B

Because $\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)$ this means that the limit $\lim_{x \to 2}f(x)$ does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since $\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3$ , this means the limit $\lim_{x \to 4}f(x)$ does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

4 0

1 year ago

pete got 7 items wrong out of 50 on a test. what fraction of the total number of problems did Pete get wrong?

Luba_88 [7]

7/50 would be the answer

4 0

3 years ago

2x to the power of 2 + x = ? When x=9

oee [108]

Answer:

Step-by-step explanation:

2x to the power of 2 + x = ? When x=9

(2x)^2 + x

= 4x^2 + x

When x = 9

= 4(9)^2 + 9

= 4(81) + 9

= 324 + 9

= 333

8 0

3 years ago

Read 2 more answers

The total cost of an item including sales tax is directly proportional to its price. If the total cost of a $32 item is $33.60 ,

pav-90 [236]

Let the total cost of the item be represented by C and the price be represented by P, then given that t<span>he total cost of an item including sales tax is directly proportional to its price, thus</span>

$C\propto P \\ \\ \Rightarrow C=kP$

where k is a constant.

Given that <span>the total cost of a $32 item is $33.60, thus

$33.60=32k \\ \\ \Rightarrow k= \frac{33.60}{32} =1.05$

Therefore, the total cost on a $55 item is given by

$C=1.05\times55=\$57.75$ </span>

3 0

3 years ago