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3 years ago

why do whole numbers raised to an exponent get greater while fractions raised to an exponent get smaller?

1 answer:

6 0

Because 3^2 = 9
When you do (⅓)^2 what you are really doing is
(1^2)/(3^2) = 1/9

If you have (⅔)^2 you do
(2^2)/(3^2) = 4/9

Fractions get smaller because the denominator is also being squared which makes the denominator get bigger and when the denominator is bigger, you are dividing by a larger number which gives you a smaller answer. Whereas when you raise a whole number to an exponent, only the numerator get bigger because the denominator is 1 and 1 raised to any exponent is still 1

3^2 = (3^2)/(1^2) = 9/1 = 9

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dexar [7]

Answer:

Step-by-step explanation:

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3 years ago

Mr. Mole's burrow lies 5 meters below the ground. He started digging his way deeper into the ground, descending 3 meters each mi

Sedbober [7]

Answer:

The slope of the equation is -3.

Step-by-step explanation:

Given : Mr. Mole's burrow lies 5 meters below the ground. He started digging his way deeper into the ground, descending 3 meters each minute.

To find : What is the slope ?

Solution :

Let x be the number of minutes taken to dig the ground.

He started digging his way deeper into the ground, descending 3 meters each minute i.e. '-3x'

Let y is the total distance travel to dig the ground.

Mr. Mole's burrow lies 5 meters below the ground.

The equation form is $y=-3x-5$

Comparing with general slope form i.e. $y=mx+c$ where m is the slope.

The slope of the equation is -3.

5 0

3 years ago

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Mr. Jones took a survey of college students and found that 60 out of 65 students are liberal arts majors. If a college has 8,943

Anit [1.1K]

Should be 5812.95 Students

8 0

3 years ago

Let A, B, C and D be sets. Prove that A \ B and C \ D are disjoint if and only if A ∩ C ⊆ B ∪ D

ANEK [815]

Step-by-step explanation:

We have to prove both implications of the affirmation.

1) Let's assume that A \ B and C \ D are disjoint, we have to prove that A ∩ C ⊆ B ∪ D.

We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

Therefore, x ∈ (A \ B) ∩ (C \ D), absurd!

It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

The absurd came from assuming that A ∩ C ⊄ B ∪ D.

That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e. A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that A \ B ∩ C \ D is not empty. That means there is an element x that belongs to A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

As x ∈ A \ B, x belongs to A but x doesn't belong to B.

As x ∈ C \ D, x belongs to C but x doesn't belong to D.

With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

It's absurd because we were assuming that A ∩ C ⊆ B ∪ D, therefore every element of A ∩ C must belong to B ∪ D.

The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

7 0

3 years ago

So teacher asked her to find 42.6÷10 to the second power how many places in what direction should sue move the decimal point to

ki77a [65]

move the decimal point 2 places to the left

42.6 / $10^{2}$ = 0.426

4 0

2 years ago