All categories

3 years ago

Explain how to write the rational number 3.21 in the form a/b

Mathematics

2 answers:

igor_vitrenko [27]3 years ago

7 0

Answer:

$\frac{321}{100}$ .

Step-by-step explanation:

Given : 3.21

To find : Explain how to write the rational number.

Solution : We have given 3.21

We can remove the decimal.

We can see there are two numbers after decimal so, we write the 100 in denominator.

$\frac{321}{100}$ .

So, this is the $\frac{a}{b}$ .

a = 321 , b =100

Therefore, $\frac{321}{100}$ .

adoni [48]3 years ago

4 0

The answer is 3 21/100.

Hopes it Helps :]

You might be interested in

Sue is collecting eggs and she wants to sell them in egg cartons that hold a dozen eggs. If she collects 75 eggs, how many full

Setler [38]

Answer:

she would have 6 egg cartons to sell and 3 eggs left over (:

Step-by-step explanation:

75 divided by 12 equals 6.25

12 times 6 equals 72

75 minus 72 equals 3

egg cartons- 6

left over eggs-3

Hope this helps (:

4 0

3 years ago

Let alpha and beta be conjugate complex numbers such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}

miskamm [114]

Answer:

$-3+i\sqrt{3} , 1+\sqrt{3}$

Step-by-step explanation:

Given that alpha and beta be conjugate complex numbers

such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}.

Let

$\alpha = x+iy\\\beta = x-iy$

since they are conjugates

$\alpha-\beta = x+iy-(x-iy)\\= 2iy= 2i\sqrt{3} \\y =\sqrt{3}$

$\frac{\alpha}{\beta^2} }\\=\frac{x+i\sqrt{3} }{(x-i\sqrt{3})^2} \\=\frac{x+i\sqrt{3}}{x^2-3-2i\sqrt{3}} \\=\frac{x+i\sqrt{3}((x^2-3+2i\sqrt{3}) }{(x^2-3-2i\sqrt{3)}(x^2-3-2i\sqrt{3})}$

Imaginary part of the above =0

i.e. $\sqrt{3} (x^2-3)+2x\sqrt{3} =0\\x^2+2x-3=0\\(x+3)(x-1) =0\\x=-3,1$

So the value of alpha = $-3+i\sqrt{3} , 1+\sqrt{3}$

3 0

3 years ago

Please assist me with these problems

Vinil7 [7]

Part (a)

<h3>Answer: y1 and y3 are perpendicular</h3>

This is because the two slopes 2 and -1/2 multiply to -1. Perpendicular slopes multiply to -1 assuming neither line is vertical or horizontal.

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

Part (b)

Graph each line to see where they cross. The three points of intersection are

(0,4)

(2,-2)

(4,2)

The order of the points doesn't matter.

You could also form three systems of equations pairing up the equations, and solving each system. That way you can find the points of intersection. Graphing may be a better and faster route in my opinion. See the diagram below.