We can compare g(x) with f(x) by looking at the b and c values of f(x+b)+c. Let's start with the b value. Remember that when horizontally shifting a function, if c is greater than 0, it shifts it to the left. So, in this case, g(x) is shifted 4 units left. Now, let's look at the c value. It is 2, meaning it shifts up in that direction. The correct answer is D, it was shifted 4 units left and 2 units up.
Answer: 7 units
Step-by-step explanation:
Just plot the numbers, then count the distance between them
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:
33% is 55% of 0.6
Step-by-step explanation:
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