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saul85 [17]
3 years ago
7

Find a polar equation of the form r2=f(θ) for the curve represented by the cartesian equation x2−y2=1. (note the power of r in t

he equation!)
Mathematics
1 answer:
iragen [17]3 years ago
4 0
The equations to transform from Cartesian to polar :
x = r cos θ   , y = r sin θ
Or
x² = r² cos² θ   , y² = r² sin² θ

To <span>represent the Cartesian equation x²−y²=1
substitute with the values of </span><span>x² and y²
</span>
∴ r² cos² θ - r² sin² θ = 1
   r² (cos² θ - sin² θ) = 1
but cos² θ - sin² θ = cos 2θ
∴ r² cos 2θ = 1
   r² = 1/cos 2θ

∴ r² = sec 2θ  ⇒⇒⇒⇒ The required equation







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Answer:

P43=4!(4–3)!=241=24

Step-by-step explanation:

There are four choices you can make for the lead reindeer. For each possible choice, there are then three remaining you can choose to fly second, making 4×3=12 choices for the lead pair. For each possible choice there are two remaining reindeer to take up the back position, making 12×2=24 choices for the team of three.

This type of problem is called a permutation problem, and we write Pnr for the number of ways of choosing r items from n possibilities when the order of the items matters. In this case we are choosing 3 reindeer from 4 possibilities, and the order they appear in the flying line does matter, so the answer we want is P43. The general formula is Pnr=n!(n−r)!. For the answer we are looking for we therefore have:

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Answer:

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Step-by-step explanation:

The common difference is 4, so the general term can be written:

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... 18 = n -1 . . . . . . . . . . . divide by 4

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