What is the value of 4.2(46-65). A.798 b.-79.8 C.79.8 D.798. I just need the answer you don’t have to work it out
1 answer:
You might be interested in
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
The correct answer is actually the last one.
The second derivative gives us information about the concavity of a function: if
then the function is concave downwards in that point, whereas if
then the function is concave upwards in that point.
This already shows why the first option is wrong - if the function was concave downwards for all x, then the second derivate would have been negative for all x, which isn't the case, because we have, for example,
Also, the second derivative gives no information about specific points of the function. Suppose, in fact, that passes through the origin, so
. Now translate the function upwards, for example. we have that
doesn't pass through the origin, but the second derivative is always
. So, the second option is wrong as well.
Now, about the last two. The answer you chose would be correct if the exercise was about the first derivative . In fact, the first derivative gives information about the increasing or decreasing behaviour of the function - positive and negative derivative, respectively. So, if the first derivative is negative before a certain point and positive after that point. It means that the function is decreasing before that point, and increasing after. So, that point is a relative minimum.
But in this exercise we're dealing with second derivative, so we don't have information about the increasing/decreasing behaviour. Instead, we know that the second derivative is negative before zero - which means that the function is concave downwards before zero - and positive after zero - which means that the function is concave upwards after zero.
A point where the function changes its concavity is called a point of inflection, which is the correct answer.