Tutor profile: Alec C.

What is an acronym we can use to remember some of the general components of exercise? What does each word within the acronym mean?

The acronym we can remember is FITT. This stands for frequency (F), intensity (I), time (T), and type (T). Frequency represents how often you will exercise, typically within the measurable span of a week. Intensity refers to how hard you work within a given exercise. Time refers to how long you work for each specific session. Type refers to the variable method in which you exercise, such as cardio workouts versus strength or power training.

[(5^2)(3) + 25] / 20

To solve this problem, we remember the order in which we solve expressions through PEMDAS (parentheses, exponents, multiply from left to right, divide from left to right, add from left to right, subtract from left to right). We first see that [(5^2)(3) + 25] is within two parentheses: an initial one and a secondary one. We therefore work from the initial, smaller parentheses up to the largest one. Because there is an exponent of 5^2 within the parenthesis, we start with that. 5^2, otherwise known as 5 times 5, is 25. We therefore see the full expression as [(25)(3) + 25] / 20. Within the big parentheses, we now see that we have to multiply and add. Given PEMDAS, we multiply first. 25 times 3 is 75. Thus, the new full expression is [75 + 25] / 20. Lastly within the parentheses is the need to add 75 and 25, which is 100. We now have a simplified expression of 100 / 20. Our last step is to simply divide the final form of the expression. 100 / 20 is 5. Thus, the answer is 5.

X + X + X = 30 (X)(X) - Y = 73 X^z + Y = 1027 ^z√Y = ?

To find the answer, we start by determining the value of each of the three variables: X, Y, and Z. Finding the value of X can be done using the first given equation. If X + X + X = 30, that means 3X = 30. We can therefore divide 3X and 30 each by 3 to isolate the variable. Thus, we find that X = 10. We then use this known value of X to solve for Y in the second equation. We first determine the value of (X)(X), otherwise known as 10 multiplied by 10. The value is therefore 100. We now know that 100 - Y = 73. To solve for Y, we can subtract 73 from both sides of the equation to tell us that 100 - 73 - Y = 0, otherwise seen as 27 - Y = 0. We then know that a single integer must be subtracted from a number of the exact same numerical value in order to get 0. Thus, 27 - 27 = 0, and we find that Y = 27. We then use the known values of X and Y to solve for Z in the third equation. By inputting the known values of X and Y, we can simplify the third equation to 10^z + 27 = 1027. Our first step is to simply the equation further by subtracting 27 from each side of the equation. This therefore leaves us with 10^z = 1000. For the next step, we have to use a logarithm to find the value of z. We would therefore input log10(1,000) into our calculators. We put in this specific logarithm because the given base is 10, and integer on the right side of the initial equation is 1000. The answer we come up with is 3. Thus, z = 3. Now that we know the values of X, Y, and Z, it is simple to find the answer to ^z√Y, which is otherwise known as ^3√27. By inputting this function into our calculator, we find that the answer to the fourth and final problem is 3.