Answer:
The answers are 0, 1 and −2.
Step-by-step explanation:
Let α=arctan(2tan2x) and β=arcsin(3sin2x5+4cos2x).
sinβ2tanβ21+tan2β2tanβ21+tan2β23tanxtan2β2−(9+tan2x)tanβ2+3tanx(3tanβ2−tanx)(tanβ2tanx−3)tanβ2=3sin2x5+4cos2x=3(2tanx1+tan2x)5+4(1−tan2x1+tan2x)=3tanx9+tan2x=0=0=13tanxor3tanx
Note that x=α−12β.
tanx=tan(α−12β)=tanα−tanβ21+tanαtanβ2=2tan2x−13tanx1+2tan2x(13tanx)or2tan2x−3tanx1+2tan2x(3tanx)=tanx(6tanx−1)3+2tan3xor2tan3x−3tanx(1+6tanx)
So we have tanx=0, tan3x−3tanx+2=0 or 4tan3x+tan2x+3=0.
Solving, we have tanx=0, 1, −1 or −2.
Note that −1 should be rejected.
tanx=−1 is corresponding to tanβ2=3tanx. So tanβ2=−3, which is impossible as β∈[−π2,π2].
The answers are 0, 1 and −2.
Your answer is not correct.
The correct answer is the third one:
-No, because the distance from the origin to point (7,-7) is greater than the radius of the circle.
The complete question in the attached figure
we know that
[arcs rc +arc cs arc sm]---------------> they take up half a circle-------->180°
<span> they are all congruent
so
divide 180 by 3 ----------------> 180/3=60</span>°
Find the length of arc rc=60°<span>
if 360</span>°----------------> (2*pi*7) length of circumference
60° -------------------> X
<span>X=60*2*pi*7/360------------> 7.327 units
the answer is
</span>
the length of arc rc= <span>
7.33 units</span>
An even number is a number that is divisible by 2.
This means that dividing this number by 2 yields no remainder (the remainder is zero).
The even numbers between 7 and 16 are:
8 as 8/2 = 4 and remainder is zero
10 as 10/2 = 5 and remainder is zero
12 as 12/2 = 6 and remainder is zero
14 as 14/2 = 7 and remainder is zero