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3 years ago

Prove that the value of the expression: 731^2−631^2 is divisible by 100

Mathematics

1 answer:

Ivanshal [37]3 years ago

7 0

Answer:

Step-by-step explanation:

731² - 631² is the difference of squares.

731² - 631² = (731+631)(731-631) = 1362×100

therefore, 731² - 631² is divisible by 100

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Show that B = {[a, b) ⊂ ℝ | a < b} is a basis for a topology on ℝ

loris [4]

Answer:

Remember that a set $\mathcal{B}$ is a base for some topology on $\mathbb{R}$ if satisfy the following properties:

1. $\mathbb{R}=\cup\{B: B\in\mathcal{B}\}$

2. For $B, B^* \in \mathcal{B}$ , If $p\in B\cap B^*$ then exist $B_p\in\mathcal{B}$ such that $p\in B_p\subset B\cap B^*$ .

Now, for $B=\{[a,b)\subset\mathbb{R}| a < b\}$ we verify the above properties:

1. It's clear that $\mathbb{R}=\cup_{a,b \text{ with }a$

2. Let $B=[a,b), B^*=[c,d) \in \mathcal{B}, p\in B\cap B^*$ . Without loss of generality suppose that $a$ . Then $c\leq p < b$ , this implies that $p\in[c,b)$ and $B_p=[c,d) \in \mathcal{B}$ and $B_p\subset B\cap B^*$ .

Then, B satisfy the two properties. This show that B is a basis for a topology in $\mathbb{R}$

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3 years ago

Find the degree of the monomial −6x^2y^5.

MatroZZZ [7]

Pick highest exponent of placeholder
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3 years ago

F(x)=x^2+10<br><br> Over which interval does fff have a positive average rate of change?

ohaa [14]

Answer:

(0, inf)

Step-by-step explanation:

The average rate of change of a function is related to it's first derivative. When the first derivative is positive, the average rate of change is positive, which means that the function is crescent.

Now, when the first derivative is negative, the average rate of change will be negative too, and the function is going to be decrescent.

In your function.

We have: f'(x) = 2x

2x > 0 when x > 0. So when x > 0 the average rate of change of your function is positive, and it's values increases as the time increases. When x < 0, the average rate of change is negative, so, as the time increases, the values of f decrease.

You can use a graphic tool to plot f and visualize this better.

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3 years ago

Read 2 more answers

Cristina financed a $799 laptop with a 7.2% interest rate on a 2-year loan. If she can afford to make a $75 payment, how quickly

KatRina [158]

Your question is missing some elements but to answer the question I have to make an assumption.

Assuming that she make a monthly payment of $75.

The value of an loan at the end of the two year is given by

$FV=PV(1+r)^n$

where PV = $799, r = 7.2% = 0.072 and n = 2 years.

Thus,

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If she makes a monthly payment of $75, the number of months it will take her to pay off for her laptop is given by

$\frac{\$918.20}{\$75} =12.24\, months$

Therefore, it will take her 13 months to pay off for the laptop.

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3 years ago

Can you guys help me? I need to study this for a test 1/2=2/3x

Aleksandr [31]

1/2=2/3x
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3 years ago