3 cubed minus 2 squared times 5 equals ? ( 3 cubed - 2 squared x 5 =)
2 answers:
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Answer:
The equation is that of ellipse withe angle of rotation 30° ⇒ answer (d)
Step-by-step explanation:
* Lets talk about the general form of the conic equations
- Ax² + Bxy + Cy² +D = 0 (center is the origin)
- A is the coefficient of x² , B is the coefficient of xy
C is the coefficient of y² , D is the numerical term
* Now we will study how to know the type of the graph of this equation
- If A and C have different signs (different values)
∴ The equation is that of an ellipse
- If A and C have different signs (different values)
∴ The equation is on a hyperbola
* Now look at the equation:
13x² + 6√3 xy + 7y² - 16 = 0
∵ A = 13 , B = 6√3 , C = 7 , D = -16
∵ A and C have same sign
∴ The equation is that of an ellipse
* Now lets find the angle of rotation by using the Rule:
- tan(2Ф) = B/(A - C) ⇒ Ф is the angle of rotation
- By using the value of A , B and C
∴ tan(2Ф) = 6√3/(13 - 7) = 6√3/6 = √3
∴ 2Ф =
∴ 2Ф = 60° ⇒ divide both sides by 2
∴ Ф = 30°
∴ The angle of rotation is 30°
∴ The equation is that of ellipse withe angle of rotation 30°
* The graph represent the ellipse
- The purple line represents the angle of rotation
Answer:
<h2>D. The two functions have opposite output values of each other for any given input value.</h2>Step-by-step explanation:
The reflect function will have opposite output values than the original one, because reflection across the x-axis means that y-values will be with the opposite sign. All positive y-values in the original function will have negative values in the reflected one, and all negative y-values in the original will have positive values in the reflected.
The opposite values are just seen in the output, because those belong to y-axis, all x-axis values remain the same, which are input values. You can see this in the image attached, look for the horizontal reflection. That mirror effect across the x-axis is because the y-values are opposite.
