Using a calculator：練習問題

Which of the following calculations will give the largest result?

A student uses a calculator to determine the time taken for a long-distance cycling trip. The final result on the calculator screen is displayed as 4.45. Given that the calculation was performed in hours, identify the correct interpretation of this time in hours and minutes.

Evaluate the following expression using a calculator:

\( \frac{15.4^2 + \sqrt[3]{1250}}{\sin(35^\circ) \times 4.2} \)

Following standard mathematical conventions and rounding only your final answer, identify the result correct to 3 significant figures.

Evaluate the following expression using a calculator:

\( \frac{\sqrt{4.2^2 + 5.6^2}}{\cos(42^\circ) - \sin(12^\circ)} \)

Following the standard mathematical convention of not rounding intermediate values within a calculation, identify the result correct to 3 significant figures.

Using a calculator, evaluate the expression below and provide the result in standard form (\(A \times 10^n\)):

\( \frac{(3.2 \times 10^5) \times (1.5 \times 10^{-2})^2}{0.0004} \)

Calculate the value of \(V = \frac{k(1 + r)^t}{\sqrt{m}}\) given that \(k = 5250.75\), \(r = 0.042\), \(t = 4\) hours \(18\) minutes, and \(m = 0.5625\).
Note: Use your calculator efficiently without rounding any intermediate values. Write down the full calculator display for \(V\), and then interpret this result as a dollar amount correct to the nearest cent.

(a) Use your calculator to evaluate the following expression:
\(\frac{12.5^3 - \sqrt[3]{450.8}}{0.0052 \times 45.1}\)
(i) Write down the complete display shown on your calculator.
(ii) Round this value to 3 significant figures.

(b) A machine runs for \(5\) hours, \(35\) minutes, and \(12\) seconds.
(i) Use the appropriate function on your calculator to express this duration in decimal hours.
(ii) If the machine consumes \(2.85\) kWh of energy per hour, calculate the total energy used during this period. Round your answer to 2 decimal places.

(c) Calculate the value of \(P\) in the following formula:
\(P = \frac{1500}{(1 + \frac{0.042}{12})^{60}}\)
To earn full marks, you must use your calculator efficiently without rounding intermediate steps. Give your answer correct to 2 decimal places.