Where’s the mistake? Can someone explain in steps how do I solve this?

Mathematics

1 answer:

andreev551 [17]3 years ago

4 0

Answer: The unit rate is: " 1.5 patties / bun " ;
or, write as: "1.5 patties per bun" .
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The mistake is that the problem shown is incomplete.

The "unit rate" would be the "number of patterns per [single] bun."
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30 patties/ 20 buns = 3 pattern/ 2 buns;

= (3/2) patties/ bun = 1.5 patties / bun ;
or, write as: "1.5 patties per bun" .
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Evaluate the definite integral from pi/3 to pi/2 of (x+cosx) dx

Vadim26 [7]

Answer:

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General Formulas and Concepts:

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Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

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Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx$

Step 2: Integrate

[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {x} \, dx + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx$
[Left Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx$
[Right Integral] Trigonometric Integration: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \sin x \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}}$
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