Question

Gary tried to solve an equation. e 4 = 2.5 e 4 ⋅ 4 = 2.5 ⋅ 4 setting up e = 8 calculating 4 e ​ 4 e ​ ⋅4 e ​ =2.5 =2.5⋅4 =8 ​ setting up calculating ​ where did gary make his first mistake? choose 1 answer: choose 1 answer: (choice a) setting up setting upstart color

Answer 1

Gary's initial mistake was improperly multiplying the exponent by 4 instead of applying the correct operation to solve for e. Relevant math concepts include taking roots, handling powers of 10, and maintaining significant figures in calculations.

Step-by-step explanation:

The question concerns Gary's attempt to solve an equation, but it appears there is a mistake in his method. Gary started with the equation e to the power of 4 equals 2.5, and to solve for e, he multiplied both sides by 4 which resulted in an incorrect solution. The mistake is in the application of the power rules. When solving exponent equations, one should not multiply the exponent directly, but rather apply the appropriate mathematical operations such as taking the fourth root or using logarithms.

For problems that involve powers of 10, moving the decimal point is an effective way to handle them. For example, 1.6 × 10² translates to 160 and 2.4 × 10-2 to 0.024. Furthermore, when dealing with significant figures, the answer should reflect the precision of the given numbers. If the numbers provided have two significant figures, the final answer should also be in two significant figures, such as calculating the area A to be 4.5 m².

Understanding how to handle scientific notation calculations, including multiplying powers of 10 and maintaining significant figures is crucial. For instance, in scientific notation calculations like multiplying (4.506 × 10&sup4;) by (1.003 × 10²), we add the exponents to get 106.

Answer 2

Gary made his first mistake when he initially set up the equation. He misunderstood 'e 4' as a multiplication rather than an exponent. The correct interpretation should be 'e' raised to the power of '4' equals 2.5.

In this problem, Gary was supposed to solve the equation e 4 = 2.5. It appears that Gary made his first mistake in the setting up phase. Rather than setting up the equation as e 4 = 2.5, he should've maintained the 'e' in the equation which is likely representing an exponential function.

That means the equation would be e^4 = 2.5, where '^' denotes to the power of. By wrongly setting up the equation, Gary misinterpreted the equation and came to an incorrect solution.

Correct Approach
The correct approach would be to read it as 'e to the power of 4 equals 2.5', and solve the equation from there.

This would generally require the use of logarithm operations.