All categories

3 years ago

Determine whether each of these sets is the power set of a set, where a and b are distinct elements.

1 answer:

4 0

A. $\varnothing$ cannot be the power set of any set. Consult Cantor's theorem, which says that the cardinality of the power set of any set (even the empty set) is strictly greater than the cardinality of the set.

(No part b?)

c. Also not the power set of any set, because any power set must have $2^n$ elements, where $n$ is the cardinality of the original set. The cardinality of this set is 3, but there is no integer $n$ such that $2^n=3$ . This set would be a power set if $\{\varnothing\}$ (that is, the set containing the empty set) were a member of it.

You might be interested in

What is the growth factor associated with the following growth rate: 30% decrease

fenix001 [56]

Given:

Growth rate = 30% decrease

To find:

The growth factor associated with the given growth rate.

Solution:

The general exponential function is:

$y=a(1+r)^x$

$y=a(b)^x$

Where, a is the initial value, r is the growth rate in decimal and $b=1+r$ is the growth factor.

It is given that the growth rate is 30% decrease. So,

$r=-30\%$

$r=-\dfrac{30}{100}$

$r=-0.3$

Now,

$b=1+r$

$b=1+(-0.3)$

$b=1-0.3$

$b=0.7$

Therefore, the growth factor is 0.7.

5 0

3 years ago

The width and length of a rectangle are (x+2) and (2x+5). Find the expression that can be used to represent the perimeter and ar

Aliun [14]

To find the area of this rectangle you multiply the length by the width, like so (x+2) x (2x+5) .

To find the perimeter of this rectangle you add all the sides using this equation,
(x+2)+(x+2)+(2x+5)+(2x+5) .

3 0

3 years ago

A 1 inch thick stack of printer paper is found to contain 175 sheets to the nearest thousandth of an inch how thick is each shee

MariettaO [177]

the answer you're looking for, rounded to the nearest thousandth, is 0.006 and we get that answer because we must round 0.0057 to the nearest thousandth, meaning that we must look at the seven, and realize that the seven tells us that the 5 is supposed to be a 6 because we are rounding to the nearest thousandth. So the answer is 0.006 I hope that this helps!

3 0

3 years ago

A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of

Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0

3 years ago

What is the factored form of y = x² - 12x + 36

djverab [1.8K]

Answer: y = (x - 6)^2

work:

y = x^2 - 12x + 36

y = (x - 6) (x - 6)

y = (x - 6)^2

7 0

3 years ago