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PolarNik [594]
3 years ago
6

Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.)

Mathematics
1 answer:
Alinara [238K]3 years ago
8 0
The standard conversion toolbox:
x=rcos(θ)
y=rsin(θ)

Here r=7csc(θ)
so 
x=7csc(θ)*cos(θ)=7cos(θ)/sin(θ)=7cot(<span>θ)
y=7csc(</span>θ)*sin(θ)=7sin(θ)/sin(<span>θ) = 7
therefore the rectangular coordinates are (7cot(</span><span>θ), 7)</span>
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Ann wants to choose from two telephone plans. Plan A involves a fixed charge of $10 per month and call charges at $0.10 per minu
Kay [80]
Ann wants to choose from two telephone plans. Plan A involves a fixed charge of $10 per month and call charges at $0.10 per minute. Plan B involves a fixed charge of $15 per month and call charges at $0.08 per minute.

Plan A $10 + .10/minute

Plan B $15 + .08/minute

If 250 minutes are used:

Plan A: $10+$25=$35
Plan B: $15+$20=$35

If 400 minutes are used:

Plan A: $10+$40=$50
Plan B: $15+$32=$47

B is the correct answer. How to test it:

Plan A: $10+(.10*249 minutes)
$10+$24.9=$34.9

Plan B: $15+(.08*249 minutes)
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4 0
3 years ago
The first two terms in an arithmetic progression are -2 and 5. The last term in the progression is the only number in the progre
Rudik [331]

Given:

The first two terms in an arithmetic progression are -2 and 5.

The last term in the progression is the only number in the progression that is greater than 200.

To find:

The sum of all the terms in the progression.

Solution:

We have,

First term : a=-2

Common difference : d = 5 - (-2)

                                      = 5 + 2

                                      = 7

nth term of an A.P. is

a_n=a+(n-1)d

where, a is first term and d is common difference.

a_n=-2+(n-1)(7)

According to the equation, a_n>200.

-2+(n-1)(7)>200

(n-1)(7)>200+2

(n-1)(7)>202

Divide both sides by 7.

(n-1)>28.857

Add 1 on both sides.

n>29.857

So, least possible integer value is 30. It means, A.P. has 30 term.

Sum of n terms of an A.P. is

S_n=\dfrac{n}{2}[2a+(n-1)d]

Substituting n=30, a=-2 and d=7, we get

S_{30}=\dfrac{30}{2}[2(-2)+(30-1)7]

S_{30}=15[-4+(29)7]

S_{30}=15[-4+203]

S_{30}=15(199)

S_{30}=2985

Therefore, the sum of all the terms in the progression is 2985.

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