/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 \(\frac{(\sqrt{2}) \times 23}{50... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 3

\(\frac{(\sqrt{2}) \times 23}{50}\) A. \(0.12\) B. \(0.49\) C. \(0.65\) D. \(1.1\)

Short Answer

Expert verified
C. 0.65

Step by step solution

01

- Simplify the numerator

First, calculate the value of \(\text{\(\sqrt{2}\)}\). The square root of 2 is approximately 1.414. Next, multiply this value by 23.
02

- Perform the multiplication

Multiply 1.414 by 23:\(1.414 \times 23 = 32.522\).
03

- Divide by the denominator

Next, divide the result by 50:\(32.522 \div 50 = 0.65044\).
04

- Compare with the given options

Compare the obtained result, 0.65044, with the given options. It is closest to option C, which is 0.65.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Square Root Calculation
The square root calculates a number that, when multiplied by itself, equals the original number. For example, the square root of 2 is a number which, when squared, gives 2. Mathematically, this means if \(\text{\text{sqrt(2) = x}}\), then \( x \times x = 2 \). The value of the square root of 2 is approximately 1.414. It's important to remember this approximation as it often comes up in various problems. Approximating the square root helps simplify more complex calculations.
Performing Multiplication in MCAT Problems
Multiplication is a fundamental math operation where you combine multiple groups of a number into one total amount. In this problem, after approximating \( \sqrt{2} \) as 1.414, we need to multiply it by 23. Multiplying large numbers can be done easily with a calculator. For instance, 1.414 multiplied by 23 gives 32.522. Knowing multiplication tables or strategies for multiplying can speed up your problem-solving skills significantly.
Mastering Division for Simplification
Division is the process of splitting a number into equal parts. After multiplying \( \sqrt{2} \) by 23 to get 32.522, the next step is dividing this result by 50. Division can help us understand how many times one number fits into another. Using a calculator, we find \(32.522 \div 50 = 0.65044\). This is our simplified answer, which can then be compared with the options provided.
Using Approximation for Quick Answers
Approximation involves finding a value close to, but not exactly, the actual value. This is especially useful for quick calculations in exams like the MCAT. Knowing that the square root of 2 is approximately 1.414 allows for faster problem-solving. After computing \( \frac{32.522}{50} = 0.65044 \), we can see it's close to 0.65, the provided answer option. Remember, approximation helps in checking the accuracy of your answers swiftly.

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Most popular questions from this chapter

The coefficient of surface tension is given by the equation \(\gamma=(F-m g) /(2 L)\), where \(F\) is the net force necessary to pull a submerged wire of weight \(\mathrm{mg}\) and length \(L\) through the surface of the fluid in question. The force required to remove a submerged wire from water was measured and recorded. If an equal force is required to remove a separate submerged wire with the same mass but twice the length from fluid \(x\), what is the coefficient of surface tension for fluid \(x .\left(\gamma_{\text {water }}=0.073 \mathrm{mN} / \mathrm{m}\right)\) A. \(0.018 \mathrm{mN} / \mathrm{m}\) B. \(0.037 \mathrm{mN} / \mathrm{m}\) C. \(0.073 \mathrm{mN} / \mathrm{m}\) D. \(0.146 \mathrm{mN} / \mathrm{m}\)

\(\frac{1.6 \times 10^{-19} \times 15}{36^2}\) A. \(1.9 \times 10^{-21}\) B. \(2.3 \times 10^{-17}\) C. \(1.2 \times 10^{-9}\) D. \(3.2 \times 10^{-9}\)

\(1 / 2\left(3.4 \times 10^2\right)\left(2.9 \times 10^8\right)^2\) A. \(1.5 \times 10^{18}\) B. \(3.1 \times 10^{18}\) C. \(1.4 \times 10^{19}\) D. \(3.1 \times 10^{19}\)

\(\left(2.5 \times 10^{-7} \times 3.7 \times 10^{-6}\right)+4.2 \times 10^2\) A. \(1.3 \times 10^{-11}\) B. \(5.1 \times 10^{-10}\) C. \(4.2 \times 10^2\) D. \(1.3 \times 10^{13}\)

\(\frac{2.3 \times 10^7 \times 5.2 \times 10^{-5}}{4.3 \times 10^2}\) A. \(1.2 \times 10^{-1}\) B. \(2.8\) C. \(3.1 \times 10\) D. \(5.6 \times 10^2\)
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