Answer:
1)6
2)36
Step-by-step explanation:
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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)
1/3
Y2-y1/x2-x1
9-3/25-7 substitute
6/18. Subtract
1/3. Simplify

Step-by-step explanation:

<em>We change the argument and the value:</em>

<em>Divide both parts of the equation by 2:</em>

<em>The restrictions are imposed on the inverse function by on x:</em>

<em>The restrictions are imposed on the inverse function by on y:</em>

<em>Then the original function is defined on the sets:</em>

<em>The initial function, a parabola, is constrained because of the inverse function; only in this case the functions are reciprocal.</em>
Answer: The area of the grass is 3360 units.
Step-by-step explanation: Find 60% of the area of the whole garden.