Questions: Divide: (6 x^7 - 12 x^3 + 12 x^2) / (3 x^2)

Divide: (6 x^7 - 12 x^3 + 12 x^2) / (3 x^2)

Transcript text: Divide: $\frac{6 x^{7}-12 x^{3}+12 x^{2}}{3 x^{2}}$

Solution

Solution Steps

Step 1: Rewrite the division as separate fractions

\[ \frac{6x^7 - 12x^3 + 12x^2}{3x^2} = \frac{6x^7}{3x^2} - \frac{12x^3}{3x^2} + \frac{12x^2}{3x^2} \]

Step 2: Simplify each fraction

\[ \frac{6x^7}{3x^2} = 2x^{7-2} = 2x^5 \] \[ \frac{12x^3}{3x^2} = 4x^{3-2} = 4x \] \[ \frac{12x^2}{3x^2} = 4x^{2-2} = 4x^0 = 4 \]

Step 3: Combine the simplified terms

\[ 2x^5 - 4x + 4 \]

Final Answer

\(\boxed{2x^5 - 4x + 4}\)

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Does the work below meet the criteria of the instructions? this is the instruction: explain how learningactivity 4.5 reflects the big ideas of the learning activity and section of the course. This is the work: The Learningactivity4.5plan reflects on a physical training plan for Aaron, which is a big idea in the learning activity, and this is done when the Learning activity4.5plan has a four-week plan for Aaron, who sits a lot during his workdays and occasionally runs, and the plan started off with easier exercises to match the level that he is at while still being effective. The week one plan focuses on establishing a foundation, and the plan consists of a mixture of strength training, jogging, cross-training, and a rest day for Aaron to recover. The variation in exercises like core stability, stretching, and long runs is meant to improve Aaron's fitness journey while reducing the risk of injury. In the week, two plans, the running duration is extended, and strength training has heavier weights, focusing on the core and the lower part of his body because they are essential for running efficiency. Additionally, tempo runs help with enhancing Aaron's cardiovascular fitness and speed, while the long run gradually increases in distance in order to test his endurance further. In week three, the focus was on endurance and speed. The exercises started to include explosive strength training exercises, which are necessary for enhancing muscle power and agility. The running sessions were good for maintaining proper form and breathing techniques, which are essential when running long distances. Week four is the most advanced week with the exercises. The sessions are made to push Aaron further by having longer runs and different levels of strength training exercises, which focus on the core's stability. The tempo run has a variety of paces so that it can simulate racing conditions, which can improve Aaron's ability to manage fatigue. Aaron's week four plan is more intense than weeks one, two, and three because the intensity level for each week got increased gradually so that Aaron is well prepared to reach his goal, which is running a half marathon successfully. The Learningactivity4.5plan reflects on a nutritional plan for Aaron, which is a big idea in section 4.5, and this is done when the Learningactivity4.5plan goes through a carefully crafted nutrition plan that entails a balanced intake of complex carbohydrates such as fruits and vegetables, healthy fats such as avocado and olive oil, and lean proteins such as chicken and beans. This balanced diet will ensure that Aaron has sufficient energy for his workouts and adequate nutrients to help with recovery. Hydration is essential for Aaron, especially when he lengthens his running distances. The nutritional plan for Aaron meets his nutritional needs, which will ensure that he has enough fuel to support his training. The Learningactivity4.5plan reflects on the relationship between nutrition and human performance, which is a big concept in section 4.5 , and the Learningactivity4.5plan does this reflection when it goes through the benefits that a runner can get from different kinds of foods; for example, the Learningactivity4.5plan mentions that if the runner consumes complex carbohydrates, it will give them the energy that is needed for a long distance run or intense training. The Learningactivity4.5plan mentions that when lean protein is consumed, it will help with the runner's recovery by repairing the muscles after intense training. The Learningactivity4.5plan highlights the importance of a runner's hydration, especially before, during, and after a run, by explaining the downside of being dehydrated, which would be the runner having a decline in their performance because the lack of water lowered their cardiac output. The Learningactivity4.5plan mentioned that hydration is important to replenish minerals that were lost from being active, and a good way to get these minerals is by drinking coconut water, which is rich in electrolytes. Nutrition does have a big impact on performance because if a runner has poor nutrition, it can result in lower energy levels and slowed muscle repair, which will have a negative effect on the runner's performance, and they will not see their full potential. The information that is in the Learningactivity4.5plan is related to section 4.5 because the section mentions how Kenyan runners are able to perform better than the best runner in the world with the help of their nutritious diet that is high in carbohydrates, all natural and sourced from farmers markets, no junk food, and eating meat occasionally. Additionally, the Learningactivity4.5plan highlights how the Kenyan runners stay away from vitamin supplements, sports drinks, and special protein shakes and how they do not have much access to highly junk food, so it basically leaves them with one choice, which is to eat healthy, nutritious foods that will give them the best result in their performance. Another big idea in section 4.5 that the Learningactivity4.5plan reflects on is macronutrients and micronutrients, and the Learningactivity4.5plan does this by emphasizing the importance of macronutrients: Carbohydrates provide the energy for intense physical activities, proteins are essential for muscle repair after intense training, healthy fats contribute to overall energy needs, and water is essential to maintain performance along with reducing the risk of overheating. The Learningactivity4.5plan highlights that coconut water can be added to Aaron's diet to supply him with electrolytes and replenish minerals and vitamins that were lost after long trainings. This relates to section 4.5 when it highlights that macronutrients are substances that are needed in large amounts for a person to be healthy, with carbohydrates, proteins, and fats serving as examples of macronutrients. Even though micronutrients, such as minerals and vitamins, are needed in small amounts, they are just as essential for one's overall health.

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