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larisa [96]
3 years ago
14

The total number of toothpicks also forms a sequence: 4, 12, 24, 40, ... What rule describes this sequence?

Mathematics
1 answer:
astraxan [27]3 years ago
4 0
<span> rule describes this sequence is 
</span><span> an = 2 ( n^2 + n )

n = 1

</span> an = 2 ( 1^2 + 1 )
 an = 2 ( 1 + 1 )
 an = 2 ( 2 )
 an =  4

n = 2

 an = 2 ( 2^2 + 2 )
 an = 2 ( 4 + 2 )
 an = 2 ( 6 )
 an =  12

n = 3

 an = 2 ( 3^2 + 3 )
 an = 2 ( 9 + 3 )
 an = 2 ( 12 )
 an =  24

n = 4

 an = 2 ( 4^2 + 4 )
 an = 2 ( 16 + 4 )
 an = 2 ( 20 )
 an =  40
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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
3 years ago
I NEED HELP PLEASE!
jeyben [28]

9514 1404 393

Answer:

  y = 1/4x + 5

Step-by-step explanation:

The given line has a "rise" of -8 for a "run" of 2, so a slope of ...

  m = rise/run = -8/2 = -4

The perpendicular line will have a slope that is the opposite of the reciprocal of this slope. Its slope will be ...

  -1/m = -1/(-4) = 1/4

The equation you're looking for will have an x-coefficient of 1/4. The suitable choice is ...

  y = 1/4x + 5 . . . . the third choice

5 0
3 years ago
What is 37% of 293? Plz help me people this is for tomorrow
stira [4]
108.41 i pretty sure
5 0
3 years ago
Read 2 more answers
Let make sum friendss..
sukhopar [10]

Answer:

hi!

Step-by-step explanation:

u look beautiful

Thanks for the pts

✌️❤️✌️

3 0
2 years ago
Read 2 more answers
What numbers multiply up to -72 and add up to -1?
Verdich [7]
8 and -9 hope this helps 
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