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Nata [24]
3 years ago
11

Please help me with the question 15 POINTS

Mathematics
1 answer:
amm18123 years ago
3 0
Each of these questions is substantially the same as the others. The answer is, "it depends" on what you want a random sample of. If you want random people in the country, you will not get that from these protocols.

If you want random people that meet certain criteria (have phones, shop in eyeglasses stores, use specific venues), then these protocols will deliver.
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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
V 1. (-6) -(-2) is equal to:<br>(-8<br>(+4<br>(-4)<br>None of these​
Marina CMI [18]

Answer:

I think the answer is -4

3 0
3 years ago
Read 2 more answers
Dan puts $11 of his allowance in his savings account every week. how much money will he have after 15 weeks.
EleoNora [17]
11 x 15 = $165
He will have $165 after 15 weeks.
4 0
3 years ago
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A farmer is dividing 128 eggs into 5 crates , how many eggs will go into each crate?
GaryK [48]
This is a division problem. You can use the standard algorithm of 128/ 5. Or you can create equal groups (draw five circles) and count out eggs until you distribute them all. I would start with 20 in each circle. That would be 20+ 20+ 20+ 20+ 20= 100 Then think 128-100= 28 Next count by 5's. 5+ 5+ 5+ 5+ 5= 25 Then think what is 28-25= 3 so 128/ 5= 25 with a reminder of 3 eggs left over.
8 0
3 years ago
A building has 9 windows each window is 5 feet tall About how tall is the building
anygoal [31]
9x5=45 the building would be 45 feet tall

4 0
3 years ago
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