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3 years ago

5

At Pizza Company, Lee made 50 pizzas one day. There were 110 pizzas sold that day. What fraction of the pizzas did Lee make? Sim

plify your answer, without using decimals.

1 answer:

sineoko [7]3 years ago

8 0

Answer:

50/110 or 5/11

Step-by-step explanation:

Use 5/11 as your final answer

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Answer: $g(x)=x^2+x-1$

Step-by-step explanation:

$(x+1)^2-2$

$x^2+2*1*x+1^2-2\\x^2+2x+1-2\\x^2+x-1$

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For what values of θ is sinθ < cosθ when 0 ≤ θ < π ?

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<h3>Answer: $0 \le \theta < \frac{\pi}{4}$ </h3>

=========================================================

How to get this answer:

Use the unit circle to note that $\sin\theta = \cos\theta = \frac{\sqrt{2}}{2}$ when $\theta = \frac{\pi}{4}$ (aka 45 degrees)

Beyond this point, cosine is smaller than sine. This means that anything from 0 to pi/4 will have sine be smaller than cosine. It might help to graph y = sin(x) and y = cos(x) on the interval from x = 0 to x = pi.

The two curves y = sin(x) and y = cos(x) intersect at the point $\left(\frac{\pi}{4}, \frac{\sqrt{2}}{2}\right)$

-------------------------------

Here's a more detailed picture of whats going on.

$\sin \theta < \cos \theta\\\\\sin \theta < \sqrt{1-\sin^2\theta}\\\\\sin^2 \theta < 1-\sin^2\theta \\\\2\sin^2 \theta < 1\\\\\sin^2 \theta < \frac{1}{2}\\\\\sin \theta < \sqrt{\frac{1}{2}}\\\\\sin \theta < \frac{1}{\sqrt{2}}\\\\\sin \theta < \frac{\sqrt{2}}{2}\\\\\theta < \arcsin\left(\frac{\sqrt{2}}{2}\right)\\\\\theta < \frac{\pi}{4}\\\\$

Intersect the intervals $0 \le \theta < \pi$ and $\theta < \frac{\pi}{4}$ and you'll end up with the final answer $0 \le \theta < \frac{\pi}{4}$

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Step-by-step explanation:

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