Which problem can be solved using this equation?

Mathematics

2 answers:

Phantasy [73]3 years ago

7 0

The answer is B each friend received 2 pieces of candy

dezoksy [38]3 years ago

4 0

Answer:

Step-by-step explanation:

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Step 3: 2x > 10 Step 4: x > 5 What property justifies the work between step 3 and step 4? A. division property of inequali

BigorU [14]

Answer:

A. Division property of inequality.

Step-by-step explanation:

Let be $2\cdot x > 10$ , we proceed to show the appropriate procedure to step 4:

1) $2\cdot x >10$ Given

2) $x > 5$ Compatibility with multiplication/Existence of multiplicative inverse/Associative property/Modulative property/Result. (Division property of inequality)

In consequence, the division property of inequality which states that:

$\forall\, a, b, c \in \mathbb{R}$ . If $c > 0$ , then:

$a> b\,\longrightarrow a\cdot c > b\cdot c \,\lor\, a$

But if $c < 0$ , then:

$a> b\,\longrightarrow a\cdot c < b\cdot c \,\lor\, a b\cdot c$

Hence, correct answer is A.

5 0

3 years ago

Determine if the following infinite series converges or diverges

Mandarinka [93]

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

<h3>How do we verify if a sequence converges of diverges?</h3>

Suppose an infinity sequence defined by:

$\sum_{k = 0}^{\infty} f(k)$

Then we have to calculate the following limit:

$\lim_{k \rightarrow \infty} f(k)$

If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

$f(k) = \frac{k^3}{k^4 + 10}$

Hence the limit is:

$\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0$