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frozen [14]
3 years ago
5

I turn my dial on my stove 45degrees from the start position if i continue to turn the dial, how many degrees further will i nww

d to rotate it to return to the start position
Mathematics
1 answer:
AveGali [126]3 years ago
6 0

Answer:

315 degrees

Step-by-step explanation:

Assume that the dial is a perfect circle and therefore makes a full 360 degree rotation. If the dial is already turned 45 degrees, the rotation angle required to return all the way to the initial position is:

A = 360 - 45\\A=315\ degrees

You will need to rotate 315 degrees.

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Answer:

2+i

Step-by-step explanation:

Given the expression:

\dfrac{4+\sqrt{16-(4)(5)}}{2}

To find:

The expression of above complex number in standard form a+bi.

Solution:

First of all, learn the concept of i (pronounced as <em>iota</em>) which is used to represent the complex numbers. Especially the imaginary part of the complex number is represented by i.

Value of i =\sqrt{-1}.

Now, let us consider the given expression:

\dfrac{4+\sqrt{16-(4)(5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-(4\times 5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-20}}{2}\\\Rightarrow \dfrac{4+\sqrt{-4}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)(4)}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)}\sqrt4}{2}\\\Rightarrow \dfrac{4+\sqrt4i}{2} \ \ \ \ \ (\because \sqrt{-1} =i) \\\Rightarrow \dfrac{4+2i}{2}\\\Rightarrow 2+i

So, the given expression in standard form is 2+i.

Let us compare with standard form a+bi so we get a =2, b =1.

\therefore The standard form of

\dfrac{4+\sqrt{16-(4)(5)}}{2}

is: \bold{2+i}

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