Find the value(s) of "k" that will cause the equation 4x^2 +kx + 4 to have one real solution.
1 answer:
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The rectangular equation for given parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π is which is an ellipse.
For given question,
We have been given a pair of parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π.
We need to convert given parametric equations to a rectangular equation and sketch the curve.
Given parametric equations can be written as,
x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.
We know that the trigonometric identity,
sin²t + cos²t = 1
⇒ (x/2)² + (- y/3)² = 1
⇒
This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.
The rectangular equation is
The graph of the rectangular equation is as shown below.
Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is which is an ellipse.
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3rd option: is the correct answer
Step-by-step explanation:
First of all, we have to observe the number line
Observing the number line we can see that the number -0.5 or -1/2 is not included in the solution as the circle on -1/2 is empty. An empty circle means that the number is not included in the solution.
While on the other side we can see that 3 has a filled circle which means 3 is included in the solution
This means that the solution might be:
By comparing the observation and the answer choices we can conclude that
3rd option: is the correct answer
Keywords: Inequalities, solution
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