Answer:
2 y x
Step-by-step explanation:
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
Answer:
yes, 2
Step-by-step explanation:
10 over 5 is 2
2 is a whole number
Answer:
Option A is the correct one.
Step-by-step explanation:
If f(x) = x² then g(x) = f(4x) = (4x)² = 16x² ........ (1)
Now, for any real value of x, the g(x) is positive.
Therefore, option B and option C is not correct.
Now, from the graph given in option A, it is clear that for y = 5, x value is near ±
.
So, putting x = in the equation (1), we get g(x) = 16(0.5)² = 4 which is close to 5.
Therefore, option A is the correct one. (Answer)
The probability of drawing a goldfish on the first draw is 16 / ( 16 + 24 ), or 16/40, or 2/5. Supposing that the first fish drawn is actually a goldfish, then there are 15 goldfish left among 39 fish, and the probability of drawing a goldfish on the 2nd draw is 15/39, or 5/13. The (joint) probability of drawing 2 goldfish on the 1st 2 draws, without replacement, is (5/13)(2/5) = 2/13.
