r
sin
θ
=
−
3
Explanation:
Imagine we have a point
P
with Rectangular (also called Cartesian) coordinates
(
x
,
y
)
and Polar coordinates
(
r
,
θ
)
.
The following diagram will help us visualise the situation better:
https://keisan.casio.com/exec/system/1223526375
https://keisan.casio.com/exec/system/1223526375
We can see that a right triangle is formed with sides
x
,
y
and
r
, as well as an angle
θ
.
We have to find the relation between the Cartesian and Polar coordinates, respectively.
By Pythagora's theorem, we get the result
r
2
=
x
2
+
y
2
The only properties we can say about
θ
are its trigonometric functions:
sin
θ
=
y
/
r
⇒
y
=
r
sin
θ
cos
θ
=
x
/
r
⇒
x
=
r
cos
θ
So we have the following relations:
⎧
⎪
⎨
⎪
⎩
r
2
=
x
2
+
y
2
y
=
r
sin
θ
x
=
r
cos
θ
Now, we can see that saying
y
=
−
3
in the Rectangular system is equivalent to say
r
sin
θ
=
−
3
Answer link
Jim G.
May 19, 2018
r
=
−
3
sin
θ
Explanation:
to convert from
cartesian to polar
∙
x
x
=
r
cos
θ
and
y
=
r
sin
θ
⇒
r
sin
θ
=
−
3
⇒
r
=
−
3
sin
θ
Answer:
22.5
Step-by-step explanation:
125
x 18
---------
1. first set up your problem
2 4
125
x 18
------
1000
2. next multiply the 8 by 5 getting 40, drop the 0 anf move the 4 to the top above 2.
3. multiply 8 by 2 getting 16, then add the 4 you have ontop of the 2 to the 16 getting 20. Drop the 0 and bring the 2 over and place it above the one.
4. multiply 8 by 1 getting 8 then add the 2 above the 1 to 8 getting 10. Then put the ten infront of the tw zeros. 1000
125
x 18
--------
1000
0
Next add a 0 as a place filler under the 0 at the end.
125
x 18
-------
1000
1250
Then multiply the 1 by 5, then 1 by 2, then finnaly 1 by 1, getting you 1250.
1000
+1250
add together
getting 2250
then move 2 decimal places over to get 22.5
Answer:
The average distance of each observation from the mean is 0.
Step-by-step explanation:
We are given the following in the question:
$7, $20, $9, $35, $12, $15, $7, $10, $20, $25
Formula:
Difference from the mean value of each term:
-9, 4, -7, 19, -4, -1, -9, -6, 4, 9
Average distances =
Thus, the average distance of each observation from the mean is 0.
Answer:
Step-by-step explanation:
Properties of a circumcenter;
1). Circumcenter of a triangle is a point which is equidistant from all vertices.
2). Point where perpendicular bisectors of the sides of a triangle meet is called circumcenter of the triangle.
From the picture attached,
9). AG = GB = GC = 21
10). BC = 2(DC)
= 2×16
= 32
11). By applying Pythagoras Theorem in ΔGFB,
GB² = GF² + FB²
(21)² = GF² + (19)²
441 = GF² + 361
GF² = 441 - 361
GF = 
GF = 8.9
12). By applying Pythagoras theorem in ΔGDB,
GB² = DG² + BD²
(21)² = (DG)² + (16)² [BD = DC = 16]
DG² = 441 - 256
DG = √185
DG = 13.6
