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3 years ago

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

Mathematics

1 answer:

never [62]3 years ago

8 0

Answer:

Triangles ABC and MNO are similar by SSS

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional

In this problem

If this problem the corresponding sides are

AB and MN

BC and NO

AC and MO

Verify if the corresponding sides are proportional

$\frac{AB}{MN}=\frac{BC}{NO}=\frac{AC}{MO}$

substitute the given values

$\frac{5}{7.5}=\frac{5}{7.5}=\frac{8}{12}$

$0.67=0.67=0.67$ ----- is true

When two triangles have corresponding sides with identical ratios , the triangles are similar by SSS Similarity

therefore

Triangles ABC and MNO are similar by SSS

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4 years ago

1. Use separation of variables to find the solution to the differential equation subject to the given initial condition.

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Answer:

Step-by-step explanation:

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Substituting the value of C back into the expression;

$lny = 5 lnx+5(ln4/5)\\lny = 5lnx+ln4\\lny = lnx^5+ln4\\lny = ln(4x^5)\\y = 4x^5$

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integrate both sides of the equation

$\int\limit {u^{-2}} \, du = \int\limits\frac{1}{4} \, dt\\\\\frac{u^{-1}}{-1} = \frac{t}{4} + C\\\\\frac{-1}{u} = \frac{t}{4} + C$

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Hence the solution to the DE is $\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}$

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