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forsale [732]
3 years ago
10

Homemade applesauce is one of Jared's favorite foods, so he stocked up on 10 pounds of

Mathematics
1 answer:
Vanyuwa [196]3 years ago
8 0

Answer:

<h2>5 quarts</h2>

Step-by-step explanation:

Let's think through this bit by bit.

<em>10 lbs * 16 oz/lb = 160 oz. of apples.</em>

In the proportion below, we can see we simply divide by 8, in terms of magnitude.

8 oz -> 1 cup

160 oz -> 160/8 -> 20 cup

20 cups! Is it the answer? NO! They're asking for it in units of <em>quarts, not cups.</em>

We must remember that 1 quart = 4 cups.

20 cups * 1/4 qt/cups = 5 quarts

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3 years ago
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Alla [95]

Answer:  Choice A

\tan(\alpha)*\cot^2(\alpha)\\\\

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

Explanation:

Recall that \tan(x) = \frac{\sin(x)}{\cos(x)} and \cot(x) = \frac{\cos(x)}{\sin(x)}. The connection between tangent and cotangent is simply involving the reciprocal

From this, we can say,

\tan(\alpha)*\cot^2(\alpha)\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\left(\frac{\cos(\alpha)}{\sin(\alpha)}\right)^2\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos^2(\alpha)}{\sin^2(\alpha)}\\\\\\\frac{\sin(\alpha)*\cos^2(\alpha)}{\cos(\alpha)*\sin^2(\alpha)}\\\\\\\frac{\cos^2(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\\\\frac{\cos(\alpha)}{\sin(\alpha)}\\\\

In the second to last step, a pair of sine terms cancel. In the last step, a pair of cosine terms cancel.

All of this shows why \tan(\alpha)*\cot^2(\alpha)\\\\ is identical to \frac{\cos(\alpha)}{\sin(\alpha)}\\\\

Therefore, \tan(\alpha)*\cot^2(\alpha)=\frac{\cos(\alpha)}{\sin(\alpha)}\\\\ is an identity. In mathematics, an identity is when both sides are the same thing for any allowed input in the domain.

You can visually confirm that \tan(\alpha)*\cot^2(\alpha)\\\\ is the same as \frac{\cos(\alpha)}{\sin(\alpha)}\\\\ by graphing each function (use x instead of alpha). You should note that both curves use the exact same set of points to form them. In other words, one curve is perfectly on top of the other. I recommend making the curves different colors so you can distinguish them a bit better.

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3 years ago
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GarryVolchara [31]
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Answer:

-2

Step-by-step explanation:

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John is using two right triangles to build a rabbit cage. Can his right triangles also be isosceles? Explain
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Sure, there's such a thing as an isosceles right triangle.   It's what you get when you draw the diagonal of a square.  It has one right angle (of course) and two 45 degree angles.   It's the shape that vexed the Pythagoreans.

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