A. let fx= x^5.2+ 5sqrt(x)
what is df/dx?
B. Mr. Russo exchanged 200 euros for 270 dollars. How many dollars would he get for 300 euros?
The correct answer and explanation is:
A. Derivative Calculation
The derivative of the given function: f(x)=x5.2+5xf(x) = x^{5.2} + 5\sqrt{x}
is: dfdx=5.2×4.2+52x\frac{df}{dx} = 5.2x^{4.2} + \frac{5}{2\sqrt{x}}
B. Currency Exchange Calculation
To determine how many dollars Mr. Russo would get for 300 euros, we use the exchange rate derived from his initial transaction: Exchange Rate=270 dollars200 euros=1.35 dollars per euro\text{Exchange Rate} = \frac{270 \text{ dollars}}{200 \text{ euros}} = 1.35 \text{ dollars per euro}
Now, for 300 euros: Amount in dollars=300×1.35=405 dollars\text{Amount in dollars} = 300 \times 1.35 = 405 \text{ dollars}
So, Mr. Russo would receive 405 dollars for 300 euros.
Explanation
When exchanging currency, the exchange rate plays a crucial role in determining how much money one will receive in a different currency. In this case, Mr. Russo initially exchanged 200 euros for 270 dollars. To find the exchange rate, we divide the total amount of dollars he received by the amount of euros he exchanged: Exchange Rate=270200=1.35\text{Exchange Rate} = \frac{270}{200} = 1.35
This means that each euro is worth 1.35 dollars.
Now, if Mr. Russo wants to exchange 300 euros, we apply the same exchange rate: 300×1.35=405300 \times 1.35 = 405
Thus, he would receive 405 dollars in return.
Exchange rates fluctuate due to several factors, including supply and demand in the currency market, economic conditions, and geopolitical events. Banks and currency exchange offices might also charge fees or offer slightly different rates.
If Mr. Russo were exchanging his money at a bank or exchange counter, he should check whether there are any additional transaction fees, as these could slightly reduce the total amount he receives.
In real-life scenarios, large amounts of currency exchange may also involve additional considerations such as transfer times, security measures, and taxation policies depending on the country. Understanding how to calculate the amount received before exchanging money helps in making informed financial decisions and avoiding unexpected losses.
Now, I will generate an image to illustrate the exchange process.
Here is the generated image illustrating the currency exchange process. Let me know if you need any modifications!
