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2 years ago

6

Jared and Casey splurged on a special dinner for their anniversary. Their dinner cost $262.57, and the local sales tax is 4%. If

they left a 20% tip on the $262.57, how much in total did they pay?

1 answer:

Maru [420]2 years ago

3 0

Answer:

325.58

Step-by-step explanation:

so im not good at explaining but JUST their DINNER costed $262.57. so you also have to ADD TAX because everything has tax so to find the 4% sale tax you need to set up the equation 262.57 x .04 (which is 4%). you will get 10.50 if you round. now you need to ADD TIP which is 20%. so to find that you need to do 262.57 x .20 (which is 20%). you will get 52.51. so now take BOTH 52.51 and 10.50 and ADD them. when you get this you also add it to the 262.57 and it gets you to 325.58

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I'm having trouble with #2. I've got it down to the part where it would be the integral of 5cos^3(pheta)/sin(pheta). I'm not sur

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$\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx$

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 $\sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta$ .

Long story short, this allows us to go from

$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

to

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Now undo the substitution to get the antiderivative back in terms of $x$ .

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Step-by-step explanation:

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The width of this interval is: 49-45=4

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Step-by-step explanation:

A complementary angle equals 90°.

Let the measure of the angle be a

Therefore, its complement will be:

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90-a = 3a - 25

90 + 25 = 3a + a

115 = 4a

a = 115/4

a= 28.75

Since the angle is 28.75°, the complement will be:

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The angles are 28.75° and 61.25°

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Answer:

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Step-by-step explanation:

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