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3 years ago

Equivalent Ratio 9:36=21:27=48:72=60:45=10:70=

Mathematics

1 answer:

Bezzdna [24]3 years ago

3 0

9514 1404 393

Answer:

Step-by-step explanation:

Reduced ratios are found by removing (dividing out) the greatest common factor (GCF). For several of these, that factor is the smallest number or the difference between the numbers. Knowledge of multiplication tables is helpful.

9 : 36 = 1 : 4 . . . . common factor of 9

21 : 27 = 7 : 9 . . . . common factor of 3

48 : 72 = 2 : 3 . . . . common factor of 24

60 : 45 = 4 : 3 . . . . common factor of 15

10 : 70 = 1 : 7 . . . . common factor of 10

_____

Comment on GCF

The greatest common factor can be found from your knowledge of multiplication tables and/or divisibility rules. It can also be found using Euclid's algorithm. For that, you ...

Divide the larger number by the smaller and keep the remainder.

If the remainder is 0, the smaller is the GCF.

If the remainder is not zero, replace the larger number with the remainder and repeat from the first step.

Example:

27/21 = 1 r 6

21/6 = 3 r 3

6/3 = 2 r 0 . . . . 3 is the GCF of 21 and 27

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$\bf f(x)=|3+9x|\implies f(x)=\sqrt{(3+9x)^2}\implies f(x)=[(3+9x)^2]^{\frac{1}{2}}
\\\\\\
\cfrac{dy}{dx}=\stackrel{chain~rule}{\cfrac{1}{2}[(3+9x)^2]^{-\frac{1}{2}}\cdot 2(3+9x)\cdot 9}\implies \cfrac{dy}{dx}=\cfrac{9(3+9x)}{[(3+9x)^2]^{\frac{1}{2}}}
\\\\\\
\cfrac{dy}{dx}=\cfrac{27+81x}{|3+9x|}\\\\
-------------------------------$

$\bf \textit{left-hand derivative at }x=-\frac{3}{9}\implies \cfrac{27+81x}{-(3+9x)}
\\\\\\
\cfrac{27+81\left( -\frac{3}{9} \right)}{-3-9\left( -\frac{3}{9} \right)}\implies \cfrac{27-27}{-3+3}\implies \stackrel{unde fined}{\cfrac{0}{0}}\\\\
-------------------------------\\\\
\textit{right-hand derivative at }x=-\frac{3}{9}\implies \cfrac{27+81x}{+(3+9x)}
\\\\\\
\cfrac{27+81\left( -\frac{3}{9} \right)}{3+9\left( -\frac{3}{9} \right)}\implies \cfrac{27-27}{3-3}\implies \stackrel{unde fined}{\cfrac{0}{0}}$

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3 years ago

Equivalent Ratio 9:36=21:27=48:72=60:45=10:70=​

Equivalent Ratio 9:36=21:27=48:72=60:45=10:70=