Answer:
1771 possible ways
Step-by-step explanation:
In this case, we need to know first how many candidates are in total:
10 + 3 + 10 = 23 candidates in total.
Now, we need to choose 3 of them to receive an award. In this case, we have several scenarios, but as it's an award we can also assume that the order in which the candidates are chosen do not matter, so, the formula to use is the following:
C = m! / n! (m - n)!
Where m is the total candidates and n, is the number of candidates to be chosen. Replacing this data we have:
C = 23! / 3! (23 - 3)!
C = 2.59x10^22 / 6(2.43x10^18)
C = 1771
So we have 1771 ways of choose the candidates.
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:
x>-2
Step-by-step explanation:
-3x+2<8
Subtract 2 from each side
-3x+2-2<8 -2
-3x < 6
Divide each side by -3. remembering to flip the inequality
-3x/-3 >6/-3
x>-2
Answer:
4√2i , -4√2i.
Step-by-step explanation:
3x^2 + 64 = 2x^2/2
3x^2 + 64 = x^2
2x^2 + 64 = 0
2x^2 = -64
x^2 = -32
x = +/- √-32
x = +/- √16* -2
x = +/- 4√2 i.
