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forsale [732]
2 years ago
15

A scientist is studying red maple tree growth in a state park. She measured the trunk diameters of a sample of trees in the same

month every other year. The tables show the data for two of the trees.
This is the final year in which she will collect data. When her data collection is complete, she will predict future red maple tree growth. The scientist plots the data for tree 2 on a coordinate grid.

Which point is correct for year 3?

1. Point a
2.Point b
3.Point c
4.Point d
Mathematics
1 answer:
Natali5045456 [20]2 years ago
4 0
Point b is the correct answer love!
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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
Answer quick and show work
shutvik [7]

Answer:

$15.19

Step-by-step explanation:

Write an equation

8.5% of 14 =

Convert percent into decimal:

8.5% = 0.085

"Of" means to multiply so multiply 0.085 to 14

0.085 x 14 = $1.19

14 + 1.19 = $15.19

8 0
3 years ago
Read 2 more answers
Can someone please help me
borishaifa [10]
Add up all the sides and you get 10
4 0
3 years ago
Read 2 more answers
Let x1 = 12, y1 = 15, and y2 = 3. Let y vary inversely with x. Find x2.
vladimir1956 [14]

Answer:

x2 = 60

Step-by-step explanation:

If the variables x and y are inversely proportional, the product x * y is a constant.

So using x1 and y1 we can find the value of this constant:

x1 * y1 = k

12 * 15 = k

k = 180

Now, we can use the same constant to find x2:

x2 * y2 = k

x2 * 3 = 180

x2 = 180 / 3 = 60

So the value of x2 is 60.

3 0
2 years ago
Can you please help me with this, I have no idea
sergejj [24]
I have no clue sorry
6 0
3 years ago
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