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sesenic [268]
3 years ago
15

Do the ratios 10:9 and 17:15 form a proportion?

Mathematics
1 answer:
KIM [24]3 years ago
8 0

Answer:

Nope! these ratios do not form a proportion

Step-by-step explanation:

if you use a calculator to divide 10/9, you get 1.111 repeating.

if you use a calculator to divide 17/15, you get 1.133 repeating.

<em>since 1.111 does not equal 1.113, </em><em>these ratios are not proportional. </em>

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Answer:

the answer is \frac{1}{41} (23x-2ln(5sinx+4cosx))

Step-by-step explanation:

\int {\frac{3sinx+2cosx}{5sinx+4cosx} } \, dx

here,

a=3, b=2, c=5, d=4

M=\frac{ac+bd}{c^2+d^2 }=\frac{3*5+2*4}{5^2+4^2}=\frac{23}{41}

N=\frac{bc-ad}{c^2+d^2 }=\frac{2*5-3*4}{5^2+4^2}=\frac{-2}{41}

\int {\frac{3sinx+2cosx}{5sinx+4cosx} } \, dx=\int{\frac{\frac{23}{41}(5sinx+4cosx)-\frac{2}{41}(5cosx-4sinx)  }{5sinx+4cosx} }\,dx

=\frac{23}{41}\int\, dx -\frac{2}{41} \int{\frac{5cosx-4sinx}{5sinx+4cosx} }\, dx

=\frac{1}{41} (23x-2ln(5sinx+4cosx))

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