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2 years ago

If A ⊂ B, then A ∩ B = ∅. true false

Mathematics

1 answer:

Aloiza [94]2 years ago

4 0

Answer: false

Step-by-step explanation:

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WILL MARK BRAINLIEST PLEASE HELP

Marrrta [24]

Answer:

$f(x)=-\frac{1}{8}(x-4)^2+3$

Step-by-step explanation:

The directrix given to us has equation,

$y=5$ and the focus is $(4,1)$ .

This means that the axis of symmetry of the parabola is parallel to the y-axis and has equation $x=4$ , because it must go through the focus.

This axis of symmetry of the parabola will meet the directrix at $(4,5)$ .

The vertex of this parabola is the midpoint of the point of intersection of the axis of symmetry and the focus.

Thus,

$V(h,k)=(\frac{4+4}{2},\frac{5+1}{2})$

$V(h,k)=(4,3)$ .

The equation is given by $(x-h)^2=4p(y-k)$ .

$(x-4)^2=4p(y-3)$ .

$|p|$ is the distance between the vertex and the focus, which is 2.

This implies that,

$p=-2$ or $p=2$

But the position of the directrix and the vertex implies that the parabola opens downwards.

$\therefore p=-2$ .

The equation of the parabola now becomes;

$(x-4)^2=4(-2)(y-3)$ .

$(x-4)^2=-8(y-3)$

We solve for y to obtain,

$y=-\frac{1}{8}(x-4)^2+3$

$f(x)=-\frac{1}{8}(x-4)^2+3$

7 0

3 years ago

What does the symbol zero or o with a diagonal line through it mean?

Anit [1.1K]

In mathematics, an empty set is a unique set having no elements inside it. Its size (which is based on the number of elements inside it) is also zero.

The empty set is sometimes called a null set as well.

Empty set is given the notation of o with a diagonal line through it as shown in the attached picture.