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3 years ago

Solve for Xexplain the process for this problem

Mathematics

1 answer:

aksik [14]3 years ago

5 0

Answer:

x = 40

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

126° is an exterior angle of the triangle, then

x + 2x + 6 = 126

3x + 6 = 126 ( subtract 6 from both sides )

3x = 120 ( divide both sides by 3 )

x = 40

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Bananas are being sold for $0.59 a pound at Store A and $0.55 a pound at Store B. A customer wants to buy 10 pounds of bananas.

andre [41]

Answer:

The customer saves 5.9 - 5.5 = $0.5

when he shops at store B

Step-by-step explanation:

Stores A and B sells bananas at different prices per pound.

Bananas are being sold for $0.59 a pound at Store A and $0.55 a pound at Store B.

If a customer wants to buy 10 pounds of bananas from store A and store B,

The customer would spend 0.59 × 10 pounds of bananas = $5.9

buying from store A and

The customer would spend 0.55 × 10 pounds of bananas = $5.5

buying from store B.

The customer spends more for 10 pounds of bananas if he buys from shop A.

The customer saves 5.9 - 5.5 = $0.5

when he shops at store B

8 0

3 years ago

Determine whether the series is convergent or divergent. 1 2 3 4 1 8 3 16 1 32 3 64 convergent divergent Correct:

Vanyuwa [196]

Answer:

This series diverges.

Step-by-step explanation:

In order for the series to converge, i.e. $\lim_{n \to \infty} a_n =A$ it must hold that for any small $\epsilon$ >0, there must exist $n_0\in \mathbb{N}$ so that starting from that term of the series all of the following terms satisfy that $|a_n-A|n_0$ .

It is obvious that this cannot hold in our case because we have three sub-series of this observed series. One of them is a constant series with $a_n=1$ , the other is constant with $a_n=3$ , and the third one has terms that are approaching infinity.

Really, we can write this series like this:

$a_n=\begin{cases} 1 \ , \ n=4k+1, k\in \mathbb{N}_0\\ 2^{k}\ , \ n=2k, k\in \mathbb{N}_0\\3\ , \ n=4k+3, k\in \mathbb{N}_0\end{cases}$

If we denote the first series as $b_n=1$ , we will have that $\lim_{k \to \infty} b_k=1$ .

The second series is denoted as $c_k=2^k$ and we have that $\lim_{k \to \infty} c_k=+\infty$ .

The third sub-series $d_k=3$ is a constant series and it holds that $\lim_{k \to \infty} d_k=3$ .

Since those limits of sub-series are different, we can never find such $n_0\\$ so that every next term of the entire series is close to one number.

To make an example, if we observe the first sub-series if follows that A must be equal to 1. But if we chose $\epsilon =1$ , all those terms associated with the third sub-series will be out of this interval $(A-1, A+1)=(0, 2)$ .