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3 years ago

Please help quickly

Mathematics

2 answers:

MatroZZZ [7]3 years ago

8 0

Answer:

See below

Step-by-step explanation:

<h2> $3^{-5}$ is equal to $\frac{1}{3^{5} }$ </h2><h2>so it is C</h2><h2>1/3x3x3x3x3 or $\frac{1}{3*3*3*3*3}$ </h2>

marin [14]3 years ago

3 0

Answer:

Step-by-step explanation:

the following that represents 3^(-5) is

1/(3x3x3x3x3)

the answer is C

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Evaluate the following integral using trigonometric substitution.

wariber [46]

Answer:

Step-by-step explanation:

1. Given the integral function $\int\limits {\sqrt{a^{2} -x^{2} } } \, dx$ , using trigonometric substitution, the substitution that will be most helpful in this case is substituting x as $asin \theta$ i.e $x = a sin\theta$ .

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From the given integral, $\int\limits {7\sqrt{49-x^{2} } } \, dx = \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx$ where a = 7 in this case.

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2.) Given $x = 7 sin\theta$

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$dx = 7cos\theta d\theta$

3.) Rewriting the given integral using the substiution will result into;

$\int\limits {7\sqrt{49-x^{2} } } \, dx \\= \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -(7sin\theta)^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -49sin^{2}\theta } } \, dx\\= \int\limits {7\sqrt{49(1-sin^{2}\theta)} } } \, dx\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, dx\\since\ dx = 7cos\theta d\theta\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, 7cos\theta d\theta\\= \int\limits {7\{7(cos\theta)} }}} \, 7cos\theta d\theta\\$