All categories

2 years ago

Bonus problem. Find the ratio a :b if it is given that 3a=8b

Mathematics

1 answer:

steposvetlana [31]2 years ago

3 0

Answer:

$a:b = 8:3$

Step-by-step explanation:

To find the ration, we want to get in equation in the form $\frac{a}{b} =\frac{x}{y}$ .

We can start by dividing by b on both sides:

3a = 8b

÷b ÷b

$\frac{3a}{b} = 8$

Now, we can divide by 3 on both sides to get:

$\frac{a}{b} = \frac{8}{3}$

We can change the format into a ratio:

$a:b = 8:3$

You might be interested in

How to prove this???

swat32

$\cos^3 2A + 3 \cos 2A \\
\Rightarrow \cos 2A (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (1 - \sin^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - \sin^2 2A) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - (2\sin A \cos A)(2\sin A \cos A)) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - 4\sin^2 A \cos^2 A) \\ 
\Rightarrow 4(\cos^2 A - \sin^2 A) (1 - \sin^2 A \cos^2 A) 
$

go to right side now

$4( \cos^6 A - \sin^6 A)\\
\Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A)$

use $x^3 - y^3 = (x-y)(x^2 + xy + y^2)$ and $x^3 + y^3 = x^2 - xy + y^2$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A) \\
\Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\
~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A)$

so $\sin^2 A + \cos^2 A = 1$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\ ~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 + \cos A \sin A )(1- \cos A \sin A ) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \cos^2 A \sin^2 A )\\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \sin^2 A \cos^2 A ) \\
 \Rightarrow Left hand side$

4 0

2 years ago

If 2^x=1/32, find the value of x

Dovator [93]

Answer:

In this equation x is equal to -5.

Step-by-step explanation:

In order to find this, we first have to note for the base (2) to be larger than the answer (1/32), the exponent would have to be negative. We also can note that 2^5 is equal to 32, which allows us to know that the negated version would give us 1/32.

2^-5 = 1/32

3 0

2 years ago

Can somebody please help me !!

levacccp [35]

Answer:

I'm pretty sure it's both, but I can see this is a summative exam/test so I'm really sorry if it's wrong.

6 0

1 year ago

Which number shows 460,593 rounded to the nearest hundred thousand?

Mariulka [41]

Your answer is C. 500,000

4 0

2 years ago

a circle has a radius of 3. an arc in this circle has a central angle of 60° . what is the length of the arc

Mashcka [7]

Answer:

Step-by-step explanation:

120

8 0

2 years ago

Read 2 more answers

Bonus problem. Find the ratio a :b if it is given that 3a=8b​

Bonus problem. Find the ratio a :b if it is given that 3a=8b