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Natasha_Volkova [10]
3 years ago
8

There are 50 campers at day camp and 10 counselors. Write the ratio of campers to counselor as a fraction . Explain how to use e

quivalent fractions to write a related rate and unit rate. what does the unit rate tell you
Mathematics
1 answer:
nadezda [96]3 years ago
4 0
Take the common denominator and divide by 3 then youll get 58
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This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, pl
Lostsunrise [7]

First,

tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)

and given that 90° < <em>θ </em>< 180°, meaning <em>θ</em> lies in the second quadrant, we know that cos(<em>θ</em>) < 0. (We also then know the sign of sin(<em>θ</em>), but that won't be important.)

Dividing each part of the inequality by 2 tells us that 45° < <em>θ</em>/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(<em>θ</em>/2) > 0 and sin(<em>θ</em>/2) > 0.

Now recall the half-angle identities,

cos²(<em>θ</em>/2) = (1 + cos(<em>θ</em>)) / 2

sin²(<em>θ</em>/2) = (1 - cos(<em>θ</em>)) / 2

and taking the positive square roots, we have

cos(<em>θ</em>/2) = √[(1 + cos(<em>θ</em>)) / 2]

sin(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / 2]

Then

tan(<em>θ</em>/2) = sin(<em>θ</em>/2) / cos(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / (1 + cos(<em>θ</em>))]

Notice how we don't need sin(<em>θ</em>) ?

Now, recall the Pythagorean identity:

cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1

Dividing both sides by cos²(<em>θ</em>) gives

1 + tan²(<em>θ</em>) = 1/cos²(<em>θ</em>)

We know cos(<em>θ</em>) is negative, so solve for cos²(<em>θ</em>) and take the negative square root.

cos²(<em>θ</em>) = 1/(1 + tan²(<em>θ</em>))

cos(<em>θ</em>) = - 1/√[1 + tan²(<em>θ</em>)]

Plug in tan(<em>θ</em>) = - 12/5 and solve for cos(<em>θ</em>) :

cos(<em>θ</em>) = - 1/√[1 + (-12/5)²] = - 5/13

Finally, solve for sin(<em>θ</em>/2) and tan(<em>θ</em>/2) :

sin(<em>θ</em>/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)

tan(<em>θ</em>/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

3 0
2 years ago
9100 dollard placed into an account with an annual intrest of 5% to the neareast year how long will it take for the account to v
shusha [124]

Answer:

81 years

Step-by-step explanation:

The answer is 81 because 5% of 9100 is 455 and 36900 divided by 455 is rounded to 81.

4 0
3 years ago
After the party, 3 1⁄4 pecan pies remained. The next day, Edward's family ate 1 1⁄4 of a pie. How many pecan pies were left?
vlabodo [156]

Answer:

2

Step-by-step explanation:

Because 3-1 is 2 and 1/4-1/4=0

So 2

4 0
2 years ago
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Draw hands on the clock to show 5 minutes after 6
PSYCHO15rus [73]
I can't draw a picture but the little hand would be on the 6 and the big hand would be on the 1.
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3 years ago
What multiplies to -32 and adds up to -14
just olya [345]
-16, +2 are two nhmbers that multiply to -32 and add to -14
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