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NikAS [45]
3 years ago
7

Please help me I got three more I need help with

Mathematics
1 answer:
Softa [21]3 years ago
8 0
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Find the distance between P1(4,16degrees) and P2(-2,177degrees) on the polar plane.
bazaltina [42]
Polar coordinates give the distance from the origin and the angle from the positive x axis. Cartesian coordinates give the distance from the x and y axes.

You can draw a right triangle with these values. (see attached)
If you know the r value and theta of that triangle below, you can use trig to find x and y.

Let's convert (4, 16°) to Cartesian coordinates.

Note that since our angle is acute, (in Quadrant I) our sine and cosine will both be positive, as you should be able to derive from the unit circle, where cosine is represented as an x value and sine is represented as a y value.

cosine = adjacent / hypotenuse
cosθ = x/r
cos(16°) = x/4
4cos(16°) = x ≈ 3.84504678375

sine = oppsite / hypotenuse
sinθ = y/r
sin(16°) = y/4
4sin(16°) = y ≈ 1.10254942327<span>

So (4, 16°) </span>⇒ (3.84504678375, 1.10254942327).

Let's convert (-2, 177°)  to Cartesian coordinates.
Whenever you have a negative radius, that means to put the point opposite where it would have been if it had a positive radius. (see attached)

In that case, we can essentially add 180° to our current 177° to the same effect. That means that (-2, 177°) = (2, 357°).

Note that since our angle is in Quadrant IV, our cosine will be positive, but our sine will be negative. (as derived from the unit circle) We don't have to worry about this since our calculator figures this for us, but you should pay attention to it if you are converting from Cartesian to polar.

cosine = adjacent / hypotenuse
cosθ = x/r
cos(357°) = x/2
2cos(357°) = x ≈ 1.99725906951

sine = opposite / hypotenuse
sinθ = y/r
sin(357°) = y/2
2sin(357°) = y ≈ -0.10467191248

So (-2, 177°) ⇒ (1.99725906951, -0.10467191248).

Now we must use the distance formula with our two points.
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
d\approx\sqrt{(1.99725906951-3.84504678375)^2+(-0.10467191248-1.10254942327)^2}
d\approx\sqrt{-1.84778771^2+-1.20722134^2}
d\approx\sqrt{3.41431942+1.45738336}
d\approx\sqrt{4.87170278}
\boxed{d\approx2.20719342}

7 0
2 years ago
14 is 4 less than three times k
UkoKoshka [18]
14= 3k-4
_ less than _ = -
3* k simplified= 3k
6 0
2 years ago
At an airport , it costs $7 to park for up to one hour and $5 per hour for each additional hour. Let x represent the number of h
avanturin [10]
C(x) = 5x + 2

This is because at 1 hour it only cost 7 dollars, so it should only have 2 added to the end. 
5 0
3 years ago
What's 6/7 written as a fraction with a denominator of 42? A. 36/42 b. 7/42 c. 42/42 d. 6/42
7nadin3 [17]

Pls mark Brainliest.

Answer:

A. 36/42

Step-by-step explanation:

What do you multiply 7 by to get 42?

6. That is what the denominator was multiplied by, and so, the equivalent fraction must have a numerator that is 6 times larger than the original.

6 is the numerator so the numerator of the equivalent fraction with denominator 42 must be 36 since 6 * 6 = 36/

A. 36/42

4 0
3 years ago
A personal computer is bought for $2860. A down payment of $520 is made. The remainder of the cost is paid in 20 equal payments.
Zanzabum

Answer:

C.None of these

Step-by-step explanation:

atleast I think

3 0
3 years ago
Read 2 more answers
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