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gogolik [260]
3 years ago
15

Simplify the complex fraction.

Mathematics
1 answer:
lilavasa [31]3 years ago
5 0

Given:

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}

To find:

The simplified fraction.

Solution:

Step 1: Simplify the numerator

$\frac{(4 r)^{3}}{15 t^{4}}=\frac{4^3 r^{3}}{15 t^{4}}=\frac{64 r^{3}}{15 t^{4}}

Step 2: Simplify the denominator

$\frac{16 r}{(3 t)^{2}}=\frac{16 r}{3^2 t^{2}}= \frac{16 r}{9 t^{2}}

Step 3: Using step 1 and step 2

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}} \right)}

Step 4: Using fraction rule:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}

$\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}}\right)}=\frac{64r^3 \cdot 9t^2}{16 r \cdot 15 t^4}

Cancel the common factor r and t², we get

           $=\frac{64 r^{2} \cdot 9 }{16  \cdot 15 t^2 }

Cancel the common factors 16 and 3 on both numerator and denominator.

           $=\frac{4 r^{2} \cdot 3 }{  5 t^2 }

           $=\frac{12 r^{2}  }{  5 t^2 }

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{12 r^{2}  }{  5 t^2 }

The simplified fraction is \frac{12 r^{2}  }{  5 t^2 }.

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3 0
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Prior to September, 2000, taxi fares from Washington DC to Maryland were described as follows: $2.00 up to and including 1⁄2 mil
GREYUIT [131]

The piecewise function is

f(x) = 2, 0 < x ≤ 1/2

f(x) = 2 + 0.7x, x > 1/2

<h3>How to determine the piecewise function?</h3>

From the question, we have:

Fares = $2.00 ⇒ up to (and including) 1/2 miles

Fares = $0.70 increment ⇒ greater than 1/2 miles

Let x represent the number of miles, and f(x) the fares.

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f(x) = 2, 0 < x ≤ 1/2

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Read more about piecewise function at:

brainly.com/question/18859540

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3 0
2 years ago
I need help please.
Rudiy27

Answer:

0.167, 0.164, 0.16

Step-by-step explanation:

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8 0
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Any help is appreciated, this is timed :)
tekilochka [14]

Answer:

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