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Diano4ka-milaya [45]
3 years ago
10

Sports City is having a blowout sale on sports equipment. You have a total of $450 to spend. What discount would have to be offe

red in order for you to afford a set of golf clubs regularly priced at $600 plus 15% sales tax? Make sure you show all of your work and explain your process.
Mathematics
1 answer:
Lunna [17]3 years ago
7 0

Answer:

34.8%

Step-by-step explanation:

$600+15%

=600+15/100*600

=600+90

=$690

You have $450 and you want to purchase a product of $690(regular price+sales tax)

$690-$450

=$240

Percentage of $240 discount

=240/690*100

=34.78%

Approximately 34.8%

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Setting x=5\sin\theta, you have \mathrm dx=5\cos\theta\,\mathrm d\theta. Then the integral becomes

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Now, \sqrt{x^2}=|x| in general. But since we want our substitution x=5\sin\theta to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means \theta=\sin^{-1}\dfrac x5, which implies that \left|\dfrac x5\right|\le1, or equivalently that |\theta|\le\dfrac\pi2. Over this domain, \cos\theta\ge0, so \sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta.

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and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to

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