Questions on Logic: Finite and infinite sets answered by real tutors!

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I'll do the first two to get you started


A)


To find A U B, simply combine the sets A and B to get

A U B = { 2, 3, 7, 9, 10}


Now to find the complement of A U B, just form a new set of elements that are in U, but NOT in A U B


So


(A U B)' = {1,4,5,6,8}

---

B)

To find A intersect C, just look for the elements that are in A AND in C


Since the element 10 is in both sets A and C, this means that


A intersect C = {10}

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Three hundred and three million nine hundred and twenty seven thousand in scientific notation.
303,927,000 = 3.03927*10^8
------------------
To be grammatically correct, it's "three hundred three million, nine hundred twenty-seven thousand", no 'ands'

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I can't make an arrow for "approaches" easy using 
the software here, so please interpret  
as though it were  → .


 =

We need to get that exponent 3 outside the limit.
First get it outside the parentheses:

 =

Then get it outside the limit:

 =

Now with that 3 exponent outside the limit, we can use 
l'Hopital's rule on the inside without it:

 =

Multiply numerator and denominator both by 

 =



Edwin

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To write a set in roster form, simply list EVERY element.


Set N is the set of natural numbers between ten and sixteen:

N = {10, 11, 12, 13, 14, 15, 16}

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Z = {2, 3, 4, 5, 6, 7, 8, 9, 10} = { x| x є N and 2 ≤ x ≤ 10}

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A = { x| x є N and 13 < x < 18} = {14, 15, 16, 17}

Since EVERY element in set A is also in set B, this means that A is a subset of B

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4,16,64,256,1024 totals 1,364*8=$10,912 is the total cost.

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Why is the set of natural numbers an infinite set but the set of blades of grass outside your yard a finite set?
--------------
You can count the number of blades of grass and there will not
be any that are uncounted.
--------------------
If you try to count the natural numbers you may arrive at
what you call the "last number"; but there is always a number
one greater than that "last number", and another number
one greater than than, and another number one greater than
that, forever.
==============
cheers,
Stan H.

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If an earthquake measured 5.9 on the richter scale, what was the intensity of the earthquake? Neeed to use the formula M=log(A/Ao).
------------------------
5.9 = log(A/Ao)
A/Ao = 10^5.9
A = 10^5.9 Ao
----------------
Intensity was 10^5.9 times the minimum measureable intensity of the sensing
equipment.
------------------
Cheers,
Stan H.

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Solve the auxiliaries for y first.
y<=24-3x
y<=33/2 -3x/2
Now, if y>=0,
24-3x >=0
33/2 - 3x/2 >=0
Moreover,
if x>=0,
-3x>=-24
-3x/2>=-33/2
Even further,
x<=8
x<=11
So the maximum of x will be 8.
Now,
y<=0 follows from the first condition with restriction x<=8. So the maximum of y will be 0.
Thus,
z=20x + 8y
z=20*11=220
Which is answer (a).

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correct option is c) (z=90)

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In this case, since they gave you a single point at (8,6), apply that point to each of the given equations:
a. 5x-3y=22
5(8)-3y=22
40-3y=22
-3y=-18
y = 6
.
b. 3/5x + 8/5
3/5(8) + 8/5
24/5 + 8/5
32/5 (Does NOT equal 6 -- toss it out)
.
c. 3x + 4y = 48
3(8) + 4y = 48
24 + 4y = 48
4y = 24
y = 6
.
d. -4x + 2y = -16
-4(8) + 2y = -16
-32 + 2y = -16
2y = 32
y = 16 (Does NOT equal 6 -- toss it out)
.
Right now, it could either be 'a' or 'c'
a. 5x-3y=22
c. 3x + 4y = 48
.
I would think, at this point, that you could possibly have a typo when you keyed it in. Can you verify that the problem is typed in correctly?
.
Or, if you proceeded, the other piece of information given was (2,)
we could try to plug it into both 'a' and 'c':
a. 5x-3y=22
5(2)-3y=22
10-3y=22
-3y=12
y = -4
.
c. 3x + 4y = 48
3(2) + 4y = 48
6 + 4y = 48
4y = 42
y = 10.5

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yes it is strange, options could be a) and c) but without y coordinate of (2,) you can not do it

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The equation of the line through (8,6) and (2,) is
a. 5x-3y=22
b. 3/5x + 8/5
c. 3x + 4y = 48
d. -4x + 2y = -16
--------------
a. (8,6) is a point of the equation
b. that is not an equation
c. (8,6) is a point of the equation
d. (8,6) is not a point of the equation
---------------
Let x = 2 in "a" and in "c" you get the following:
In a: y = -4
In c: y = 21/2
==============================
Cheers,
Stan H.

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If n(A) = 22, n(B) = 13, and n(A and B) = 6 then n(A U B)=
a. 35
b. 28
c. 29
d. 27
----------------
n(AUB) = n(A)+n(B)-n(A and B)
n(AUB) = 22 + 13 - 6 = 29
======================
Cheers,
Stan H.

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(-1,2) satisfies the inequality; the other points do not.
Cheers,
Stan H.

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{x|x is a letter of the word SEEDED} ∩ {x|x is a letter of the word DRESSED}=
{S,E,D}∩{D,R,E,S}={S,E,D} (option a)

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P(E/F)=#(E∩F)/#(F)=6/25 (option b)

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The sample space of an experiment is:
{A, B, C, D} AND P(A) = 0.1, P(B) = 0.3, P(C) = 0.4, P({A,C})=
---------------
IF A and C are independent events the following is true:
P(A and C) = P(A)*P(C) = 0.1*0.4 = 0.04
----------------
If A and C are dependent events the following is true:
P(A and C) = P(A)*P(C|A) = 0.1*? = ?
----------------
Cheers,
Stan H.

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We want R=C.
So
22x=-9x+341
0=-31x+341
0=-31(x-11)
So x must=11.

R(11)=22*11=242.
So, (11,242).

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Please resubmit this question.

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whenever you see absolute signs you must consider the negative, that is:
consider |x|
if x is positive
|x| = x
if x is negative
|-x| = x
.
first case:
8x-17 <= 24
8x <= 41
x <= 41/8
.
second case:
-(8x-17) <= 24
17 - 8x <= 24
-8x <= 7
x >= 7/8
.
therefore
7/8 <= x <= 41/8

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Can anyone help me break this down so I understand it. Should it come with two answers? (1,0) for example?

Thanks you in advance

In an absolute value equation, you solve two equations:

1.  Write the equation substituting ""
    for "", and solve for x.

2.  Write the equation again substituting ""
    for "", and solve for x.
    

For your equation:



1. Write and solve the equation:


 





2. Write and solve the equation:


 



 

Edwin

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1.
2.

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1,4,9,1,6,2,5,3,6,4,9,6,4 _,_,_,_
observe the first number it's 1^2 =1
the second number is 2^2 =4
the third number is 3^2 = 9
the 4th and 5th number represents the square of 4 ie 4^2 = 1,6
the 6th and 7th number represents the sqaure of 5 ie 5^2 = 2,5
and so on ...
the first 2 blanks represent the square of 9 which is 8,1
the next 2 blanks should represent the square of 10 which is 1, 00

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Notice the first three terms

1,4,9

This looks like it might be the sequence of perfect squares. If you look at the next number you'll see 1. But if you look at the next two numbers as one number, you'll see 16. Once again if you look at the next pair as one number you get 25. If you keep doing this you get the sequence:

1,4,9,16,25,36,49,64,...


So that means the next two numbers are 81 and 100. These break down into

8,1,1,0,0


So the entire sequence then becomes

1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,1,0,0


But since the problem only asks for 4 numbers, we must drop the last zero. So the sequence is


1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,1,0

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1,4,9,1,6,2,5,3,6,4,9,6,4,8,1, _,_,_,_
-----------
You have 1^2=1, 2^2=4, 3^2=9, 4^2=16,...8^2=64,9^2=81
==================
Cheers,
Stan H.

 lim 
x->0+

 lim 
x->0+

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Find:
.
lim
x->0+
.
Since nobody else has taken a shot at this, maybe I can give you a way of looking at it.
.
Look at the exponent of e and recognize the limits on . The sine function
is limited to values between -1 and +1. So the exponent of e will range in value from
-1 to +1. That means that the term:
.

.
has a finite value ranging from to . Since this range of values
is finite (and positive) the limiting factor in this problem is and since
x is approaching 0+, the expression gets closer and closer to zero times the finite value
of the term involving e. Therefore, the limit is zero, just as the problem proposes that
you prove.
.
Hope this gets you on the right track and at least gives you a feel for a way of proving the
premise.

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Assuming the digits of the decimal don't repeat, the number 17.2353617 is a real number and an irrational number (since it cannot be represented by a fraction)

Natural number
Whole number
Integer
Rational number
Irrational number √
Real number √

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Assume the following statements:
P= the termperature is 70 degrees
Q= It is raining
R= There is no wind
Find the following statement in symbolic form:
If there is no wind, then i is raining or the temperature is 70 degrees.
A. R --> (Q v ~P)
. R --> (Q v P)
C. (Qv ~P) <-->
D. None of the above.
Happy Calculating!!!

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Assume the following statements:
P= The temperature is 70 degrees
Q= It is raining
R= There is no wind
Find the following statement in word form: Q --> (~R conjunction ~P)
If it is raining then there is wind and the temperature is not 70 degrees.
This matches none of the possible answers. D
:
Happy Calculating!!!

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what is the length of the diagonal of a square with area 40.5 square inches?
--------------
Draw the picture.
Let each side of the square be "x".
Then x^2=40.5
Then, diagonal^2 = side^2 + side^2
diagonal^2 = 40.5 + 40.5 = 81
diagonal = 9 inches
=============
Cheers,
Stan H.

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The intersection of a set and its inverse will be the empty set.
The union of a set and its inverse is the universal set.
So the original statement is False as it involves the intersection of the two sets..

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use the following sets: U = (2,4,6,8,10,12,14)
A = (4,6,8), B = (2,6,10,12), C = (2,8,14)
Find A U B
A. (4,6,8,2,6,10,12)
B. (6)
C. Null Set
. (2,4,6,8,10,12) It has everything in A and everything in B
Find A U C '
. (4,6,8,10,12) It has everything in A and everything not in C
B. (4,6)
C. (2,4,6,8,14)
D. (8)

Find A' U (B n C)
A. (2)
. (2,10,12,14)It has everything not in A and what's everything that's in common between B and C.
C. (2,4,6,8)
D. U = Universal Set
Find n(B' n C)
A. (8,14)
B. (2)
. 2 The number of elements that aren't in B and also in C are 2.
D. 4
Happy Calculating!!!

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.
The problem asks for you to take the derivative of the above expression. I presume that
the derivative is with respect to r and that v is a constant.
.
One term at a time. The product is a constant so it is a multiplier of the derivative
of r. The rule that applies is that the derivative of is
In this first term the exponent of r is 1. So you are taking the derivative of which
the rule tells you in and this simplifies to .
Putting this all together for the first term, the derivative is .
.
On to the second term. The most critical point here is to recognize that a positive
exponent in the denominator is equivalent to a negative exponent in the numerator.
Using this we can convert to an equivalent form .
.
Now we can apply the same technique as we did for the first term. The factor (2v) is
presumed to be a constant and therefore will be a multiplier of the derivative of .
Again we use the rule that the derivative of is .
So the
derivative of is which simplifies to .
Don't forget that this gets multiplied by the constant (2v) so that the derivative
for this second term is . Multiplying this out results in:
.
and since a negative exponent in the numerator becomes a positive
exponent in the denominator, we could also write the derivative as:
.
.
.
Finally we combine the derivatives for the first and second terms to get:
.

.
and taking care of the signs for the second term concludes the effort by producing
the result:
.

.
Hope this helps you to see your way through the problem.

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s = speed in still air
(s+25)*4 = (s-25)*5
4s + 100 = 5s - 125
s = 225 mph

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cos[/2-x]/sin[/2-x]
1/tan[/2-x]
1/tan^-1(x)
tan(x)

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I have a parabolic shape that is shown as: y = 2x^2
I also need to graph an ellipse: (y - 2)^2/1 + x^2/4 = 1
Then, I need to decide if the parabola fits in the hole.
----------------
You need to carefully sketch the parabolic shape and the
information about the ellipse on a graph. Then make a
determination regarding the answer to your question.
-----------------
Your parabolic shape has a vertex at (0,0) but you haven't
said what it's domain is---that would determine how far up
or down or to he right or to the left it goes.
--------
The ellipse has its center at (0,2).
------------
When x=0, (y-2)^2=1 ; y-2=+-1; y=3 or y=1
So the ellipse intersects the y-axis at (0,1) and (0,3)
---------
When y=2, x^2=4; x=+-2
So the ellipse passes through (2,2) and (-2,2)
When y=0, 4+x^2/4=1; x^2=-12;
So the ellipse does not touch the x-axis.
----------
Hopefully from all this you can figure out the
answer to your question.
Cheers,
Stan H.

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I guess it does fit if you mean 3D. But it is just plain in 2D.

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first one is dividing by -3 over and over again
and the second is subtracting 7 over and over again.

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1 + 1/2 + 1/3 + 1/4 + 1/9 + 1/8 + 1/27 + 1/16 + ...
excuse me as you'll have to post

"Find the sum of the following series: 

1 + 1/2 + 1/3 + 1/4 + 1/9 + 1/8 + 1/27 + 1/16 + ...


I tried to use the sume of an infinite series formula, but there is no common
 ratio. I also tried seeing if some of the terms will cancel or add
 up to the same thing, but I am still not getting anywhere."

again, but do the numbers have a pattern at all?
1+1/2+1/3+1/4+1/9+1/8+1/27+1/16...?
Do you mean 1+1/2+1/3...?

---

Hey I found it!
it's 1/1+1/2+1/3+1/4+1/9+1/8
you see, 4 is 2*2, 8 is 4*2, 9 is 3*3, get it?
it's the sum of two infinite series:
1/3+1/9+1/27 etc..
AND 1/1+1/2+1/4+1/8...
1/1+1/2+1/3+1/4+1/9+1/8+1/27+1/16...
COOL! so now just use the formula (which I can't recall) to get each's infinite sum, and add them up!

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A very bored grocer was stacking oranges one day. She decided to stack them in a triangular pyramid. There was one orange in the top layer, three oranges in the second layer, six oranges in the third layer, and so on. Each layer except the top formed an equilateral triangle. How many oranges woluld it take her to build a pyramid 50 layers high?
LAYER NUMBER........ORANGES
I ....................1
II....=3+2+1=.........6
III...=6+5+4=.........15
IV....=9+8+7=.........24
.......
SO TOTAL ORANGES ARE 1+(6+15+24+.......49 TERMS)
SEQUENCE IN BRACKETS IS A.P WITH A=6,D=9 AND N=49
HENCE SUM =SN=(N/2)(2A+(N-1)D)=(49/2)(2*6+(49-1)*9)=10878
SO NUMBER OF ORANGES REQD =1+10878=10879

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The area of a prism is equal to the product of the area of the base and the height.
hope this helps!! :)

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Yes a quadrillion:1,000,000,000,000,000.
Then a quintillion:1,000,000,000,000,000,000.
A Googol has a 1 with 100 zeroes.Not even Bill Gates has that much!
Pete

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If the number of grains of sand in the world were a finite number,and did not change ever in response to anything,then this set would be a finite set.
However,old rocks are weathered to form sand all the time,forming new grains of sand.
Now,I won't pretend to be an expert on this subject.If you say that all grains of sand can be counted and assumed to be finite,then this is a finite set.Otherwise,by the argument above,this would be an infinite set.