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3 years ago

What is the greatest common factor of 48, 112, and 80

Mathematics

1 answer:

pickupchik [31]3 years ago

4 0

9514 1404 393

Answer:

Step-by-step explanation:

48 = 16·3

112 = 16·7

80 = 16·5

3, 5, 7 have no common factors. The GCF of {48, 112, 80} is 16.

_____

It can be helpful to recognize 48 = 16·3 and 80 = 16·5. A simple check shows 112 = 16·7, so 16 is the GCF.

You can find GCF(48,112) using Euclid's algorithm:

112 mod 48 = 16

48 mod 16 = 0 ⇒ GCF(48, 112) = 16

and the GCF(16, 80) is ...

80 mod 16 = 0 ⇒ GCF(16, 80) = 16

So, GCF(48, 80, 112) is 16.

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3 years ago

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garik1379 [7]

Answer:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

$\displaystyle y=\sin^{-1}\big(\frac{x}{5}\big)\text{ at } x=\frac{5}{2}$

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

$\displaystyle y^\prime=\frac{1}{\sqrt{1-(\frac{x}{5})^2}}\cdot\frac{1}{5}$

Simplify:

$\displaystyle y^\prime=\frac{1}{5\sqrt{1-\frac{x^2}{25}}}$

We can factor out the denominator within the square root:

$\displaystyle y^\prime =\frac{1}{5\sqrt{\frac{1}{25}\big(25-x^2)}}$

Simplify:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}$

So, we can find the slope of the tangent line at x = 5/2. By substitution:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}$

Evaluate:

$\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\frac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}$

We will also need the point at x = 5/2. Using our original equation, we acquire that:

$\displaystyle y=\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}$

So, a point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}(x-\frac{5}{2})$

Distribute:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}$

Isolate. Hence, our equation is:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

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Answer:

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Step-by-step explanation:

thats what i got

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