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stealth61 [152]
3 years ago
6

Find the ratio a:b, if 2a−b/6 = b/3

Mathematics
1 answer:
evablogger [386]3 years ago
6 0

If 2a−b/6 = b/3, then ratio a:b = 3 : 2

<h3><u>Solution:</u></h3>

Given that 2a−b/6 = b/3

We have to find the ratio of a:b

In mathematics, a ratio indicates how many times one number contains another

A ratio between two or more quantities is a way of measuring their sizes compared to each other

let us first solve the given expression

\frac{2a -b}{6} = \frac{b}{3}

On cross multiplication we get,

6a - 3b = 6b

6a = 6b + 3b

6a = 9b

a = \frac{9b}{6}\\\\\frac{a}{b} = \frac{3}{2}

To convert a fraction to a ratio, first write down the numerator, or top number. Second, write a colon. Thirdly, write down the denominator, or bottom number

Therefore ratio a:b = 3 : 2

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Given sin A = 12/13 and that angle A is in Quadrant 1,
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We have been given that \text{sin}(A)=\frac{12}{13} and angle A is in quadrant 1. We are asked to find the exact value of \text{cot}(A) in simplest radical form.

We know that sine relates opposite side of right triangle with hypotenuse.

\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}

This means that opposite side is 12 units and hypotenuse is 13 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

\text{cot}=\frac{\text{Adjacent}}{\text{Opposite}}

Now we will find adjacent side using Pythagoras theorem as:

\text{Adjacent}^2=\text{Hypotenuse}^2-\text{Oppoiste}^2

\text{Adjacent}^2=13^2-12^2

\text{Adjacent}^2=169-144

\text{Adjacent}^2=25

Let us take positive square root on both sides:

\sqrt{\text{Adjacent}^2}=\sqrt{25}  

\text{Adjacent}=5

Therefore, adjacent side of angle A is 5 units.

\text{cot}(A)=\frac{5}{12}

Therefore, the exact value of cot A is \frac{5}{12}.

5 0
3 years ago
Length <br> Width <br><br> Pls help me
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3 years ago
BD and AC are directors of .0 identify each Arc as a minor Arc interior Arts Elementary art
Maru [420]

Given BD and AC is a diameter of the circle:

We need to find the following:

1. measure of the arc BA

So,

the measure of the minor arc BA = 44

The measure of the major arc BA = 360 - 44 = 316

2. the measure of the arc ACB = 360 - 44 = 316

3. The arc BCD is a semicircle of the circle

So, the measure of the arc BCD = 180

5 0
1 year ago
What is the solution of
loris [4]

Answer:

x = -1/2

Step-by-step explanation:

1-3x = x+3

Add 3x to each side

1-3x+3x = x+3x+3

1 = 4x+3

Subtract 3 from each side

1-3 = 4x+3-3

-2 = 4x

Divide each side by 4

-2/4 = 4x/4

-1/2 =x

5 0
3 years ago
Read 2 more answers
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