Rewrite the expression as a complex number in standard form a+bi

Answers

Answer 1

Answer:

Answer:

$\textbf{$a + bi = 2 + i$}\n$

Step-by-step explanation:

$\textup{Given:}\n$$(4 + √(16 - (4)(5)))/(2)$$\n\textup{This can simplified as:}\n\vspace{6mm}\n$

$(4 + \sqrt(-4))/(2)$\vspace{6mm}\n$\implies (4 + 2i)/(2)$\vspace{5mm}\n$\implies 2 \left( (2 + i)/(2) \right)$\vspace{5mm}\n$$\therefore a + bi = 2 + i$$

Answer 2

Answer:

The expression

$4 + (√(16 - (4)(5)))/(2)$

can be rewritten as a complex number in standard form as 4 + i.

How did we get the value?

To rewrite the expression

$4 + (√(16 - (4)(5)))/(2)$

as a complex number in standard form a + bi, we need to simplify the expression inside the square root and then perform the necessary calculations.

The expression inside the square root is 16 - (4)(5) = 16 - 20 = -4. Since we have a negative value inside the square root, we can rewrite it as 2i√{1} to simplify it.

Now, let's rewrite the expression:

$4 + (√(16 - (4)(5)))/(2) = 4 + (√(-4))/(2) = 4 + (2i√(1))/(2) = 4 + i√(1)$

Since √{1} = 1, the expression becomes:

4 + i√{1} = 4 + i

Therefore, the expression

$4 + (√(16 - (4)(5)))/(2)$

can be rewritten as a complex number in standard form as 4 + i.

learn more about complex number in standardform: brainly.com/question/12241782

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Answers

Each paper cup is a cone.
The volume if a cone is (1/3) (pi) (radius)² (height)

Notice, in the picture they labeled the diameter of the cup = 8 cm.
But we need the radius. that's 1/2 of the diameter = 4 cm.

So, the volume of these paper cups is

   (1/3) (pi) (4cm)² (11 cm) = about 184 cm³
=====================

It says that tons of lemons have been sacrificed, and you have
about 37,850 cm³ of lemonade.

How many cups will that fill ?

   37,850 cm³ / 184 cm³ = about 205 cups.
========================

How many packs of cups do you need to buy ?
Unfortunately, they only come in packs of 50.

1 pack = 50 cups . . . . . not enough
2 packs = 100 cups . . . not enough
3 packs = 150 cups . . . not enough
4 packs = 200 cups . . . oh so close but still not enough

You need to buy 5 packs = 250 cups.
=================================

It started raining, so you only sold 80% of the lemonade that you had.

80% means 0.80
"of" means "times"

You started out with 37,850 cm³ .

You sold (0.8) x (37,850 cm³) = about 30,280 cm³ of it.

How many cups did you fill with that much lemonade ?
(Remember, each cup holds about 184 cm³.)

   30,280 cm³ / 184 cm³ = about 164 cups sold.

You bought 250 cups to start out.
You sold 164 cups of lemonade.

You had (250 bought - 164 used) =

   86 clean, unused paper cups, still in the wrappers, left over.

Which pair of ratios form a proportion? A.
3 : 4 and 4 : 5

B.
10 : 12 and 16 : 18

C.
7 : 10 and 10 : 14

D.
5 : 8 and 20 : 32