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Given that the original mathematical content appears to be a bit unclear and potentially nonsensical, it requires a meaningful reformulation. Here's an attempt to create a coherent task based on what might be intended:

Prove the following vector calculus identity:
[tex]\[ \nabla r^n = n r^{n-2} \mathbf{r} \][/tex]

where \(\mathbf{r}\) is the position vector \((x, y, z)\) and \(r = \sqrt{x^2 + y^2 + z^2}\).

(Note: The original text appears to mix unrelated mathematical concepts. This revision aims to propose a more standard and understandable vector calculus problem.)



Answer :

GinnyAnswer
Sure! Here’s your step-by-step solution for the problem related to a real-world context involving money, bagels, and their cost.

Let's start by setting up the problem:

1. Total Initial Money: The initial amount of money you have is $23.
2. Number of Bagels: You plan to buy 5 bagels.
3. Cost per Bagel: Each bagel costs $3.

Next, calculate the total amount of money spent on bagels:

1. Money Spent Calculation:
[tex]\[ \text{Money Spent} = \text{Number of Bagels} \times \text{Cost per Bagel} \][/tex]
Substituting in the numbers:
[tex]\[ \text{Money Spent} = 5 \times 3 = 15 \][/tex]

So, the amount of money spent on the bagels is $15.

2. Money Left Calculation:
[tex]\[ \text{Money Left} = \text{Total Initial Money} - \text{Money Spent} \][/tex]
Substituting in the values:
[tex]\[ \text{Money Left} = 23 - 15 = 8 \][/tex]

Thus, the amount of money you have left after buying the bagels is $8.

Summary:
- You spent $15 on bagels.
- You have $8 left after the purchase.

These computations match the results provided.