Consider functions f, g, and h.

Can you please answer my homework, its about sets.

Katyanochek1 [597]

The value of the set (A∪C)'∩B is {9 , 12} .

A subfield of mathematical logic called set theory examines sets, which are essentially collections of objects.

Set theory is a discipline of mathematics that largely addresses problems that are pertinent to mathematics as a whole, despite the fact that any kind of object can be constructed into a set.
Set theory is founded on a simple binary relationship between an object o and a set A.
It is written as o A if o is a part (or member) of A. Members of a set are enumerated with commas to denote separation when describing them, or a property of those parts is enclosed in braces.
Sets can be associated by the membership relation since they are objects.

The given sets are:

U ={1,2,3,4,5,6,7,8,9,10,11,12,13}

A = {3,7,11,13}

B = {3,6,9,12,13}

C = {2,3,5,6,7,8}

Now B' = {1,2,4,5,7,8,10,11}

b) B'∩C = {2,5,7,8,}

c) A∪C = {2,3,5,6,7,8,11,13}

(A∪C)' = {1,4,9,10,12}

(A∪C)'∩B = {9 , 12}

Hence the value of the set (A∪C)'∩B is {9 , 12} .

To learn more about set visit:

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#SPJ1

6 0

2 years ago

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

galina1969 [7]

<h2>Hello!</h2>

The answers are:

a) The height of the ball after 3 seconds is 49 feet.

b) The maximum height of the ball is 66 feet.

c) That the ball hit the ground after 4 seconds.

d) The domain would be only the positive real numbers, from 0 to 4, since we found that the ball hit the ground at t equal to 4 seconds. However, if we were talking about a quadratic function with no time involved, the domain would be all the real numbers.

Since we are working with a quadratic function which describes the ball's motion in function of the time, we need to remember the following:

- The general equation of the parabola is:

$y=ax^{2} +bx+c$

- We can calculate the coordinates of the vertex of the parabola using the following formula:

$x_{vertex}=\frac{-b}{2a}$

- Evaluating a function means replacing the variable with the given value to evaluate.

The given function is:

$h(t)=-16x^{2}+63t+4$

Where,

$a=-16\\b=63\\c=4$

Now, calculating we have:

a) What is the height of the ball after 3 seconds?

We need to evaluate the time of 3 seconds into the function, so:

$h(3)=-16(3)^{2} +63(3)+4=49feet$

So, the height of the ball after 3 seconds is 49 feet.

b) What is the maximum height of the ball?

Since the function is describing the motion of a ball thrown into the air, we can find the maximum height by finding the y-coordinate of the vertex. If the parabola opens downward or upward, the vertex will be always the highest or the lowest point of the parabola.

So, calculating the vertex we have:

$x_{vertex}=\frac{-b}{2a}=\frac{-63}{2*-16}\\\\x_{vertex}=\frac{-63}{2*-16}=\frac{-63}{-32}=1.97$

Then, replacing "x" into the equation of the parabola, we find the y-coordinate of the vertex:

$y=-16(1.97)^{2}+63(1.97)+4=-16*3.88+63*1.97+4\\y=-16*3.88+63*1.97+4=-62.08+124.11+4=66.03$

So, if the y-coordinate is 66.03, the maximum height of the ball is 66.03 feet, or 66 feet (rounded to the nearest foot).

c) When will the ball hit the ground?

We can find the time when the ball hit the ground by making equal to 0 the function and finding the roots (zeroes)

Since it's a quadratic function, we can find the zeroes using the quadratic equation:

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$

Substituting a, b and c, we have:

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}=\frac{-63+-\sqrt{63^{2}-4*(-16)*(4)} }{2*(-16)}\\\\\frac{-63+-\sqrt{63^{2}-4*(-16)*(4)} }{2*(-16)}=\frac{-63+-\sqrt{3969+256} }{-32}\\\\\frac{-63+-\sqrt{3969+256} }{-32}=\frac{-63+-\sqrt{4225} }{-32}=\frac{-63+-(65)}{-32}\\\\t1=\frac{-63-(65)}{-32}=4\\\\t1=\frac{-63+(65)}{-32}=-0.06$

Now, since negative time does not exists, we can conclude that the ball hit the ground after 4 seconds.

d) what domain makes sense for the function?

Since the function represents the motion of the thrown ball at "t" time, the domain would be only the positive real numbers, from 0 to 4, since we found that the ball hit the ground at t equal to 4 seconds. However, if we were talking about a quadratic function with no time involved, the domain would be all the real numbers,

Note: I've attached the graph of the function.

Have a nice day!

5 0

3 years ago

Mr.Jimerson earns $24 per hour working. He qualifies for a 25% raise in salary. What is his salary after his raise?

Ganezh [65]

(24)(.25)=6 dollars more per hour

24+6=30

3 0

3 years ago

11. The front and back walls of The front and back walls of an A-frame cabin are isosceles triangles, each with a base measuring

hichkok12 [17]

Answer:

Total area = 308'

Step-by-step explanation:

Given:

Base = 22'

Height = 28'

Find:

Total area

Computation:

Total area = 1/2[b][h]

Total area = 1/2[22][28]

Total area = 308'

8 0

3 years ago

Question#3<br> will give brainliest!

11111nata11111 [884]

Answer:

I think the answer is 2.56 = x

Step-by-step explanation:

pls like, vote, and give brainliest!

7 0

2 years ago