If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?
1 answer:
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Answer:
Step-by-step explanation:
We are given the trigonometric equation of:
Let u = 4x then:
Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).
Convert u-term back to 4x:
Divide both sides by 4:
The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.
Therefore:
Answer:
100 in²
Step-by-step explanation:
The area of the banner is equal to the area of the initial rectangle minus the area of the cutout triangle.
The rectangle has a height of 8 inches and width of 14 inches, so its area is:
A = (8 in) (14 in) = 112 in²
The triangle has a base of 8 inches and a height of 3 inches, so its area is:
A = ½ (8 in) (3 in) = 12 in²
So the area of the banner is 112 in² − 12 in² = 100 in².
