Answer:
x = π/3, x = 5π/3, x = 4π/3
Step-by-step explanation:
Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.
Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.
Similarly:
The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.
So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.
Answer:
1. 13+18+13+14+13+16+14+21+13
= 145/9
=16.11
2. Range =145
3. Mode =13
4. Median =14
Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer: In the quadratic formula, if the discriminant is greater than or equal to 0, then the solutions to the quadratic equation will be real numbers. ... Looking at the graph of a quadratic equation, if the parabola does not cross or intersect the x-axis, then the equation has no real solution.
Answer:
x = 9 or x = 0 or x = -2
Step-by-step explanation:
Solve for x:
3 x^3 - 21 x^2 - 54 x = 0
The left hand side factors into a product with four terms:
3 x (x - 9) (x + 2) = 0
Divide both sides by 3:
x (x - 9) (x + 2) = 0
Split into three equations:
x - 9 = 0 or x = 0 or x + 2 = 0
Add 9 to both sides:
x = 9 or x = 0 or x + 2 = 0
Subtract 2 from both sides:
Answer: x = 9 or x = 0 or x = -2
