Explain the difference between and exothermic VS. an endothermic reaction.
- An endothermic reaction is one that needs to ABSORB heat in order for it to proceed to the product side. An exothermic reaction is an opposite. It RELEASES heat on the product side after the reaction proceeds. - Examples of an endothermic reaction: Cooking food (you need heat for it to cook), photosynthesis (plants convert sunlight heat into energy) - Example of exothermic reaction: Combustion reactions release heat (fire releases heat)
Take the first derivative of the following: 5x^5 + 3x^3 + 5
STEP#1 - In order to take the derivative, we multiply the power of each term by its coefficient and subtract one unit from its power. The derivative of a number is simply zero. (5.5)x^4 + (3.3)x^2 25x^4 + 9x^2
Solve by completing the square in the following equation: x^2 + 4x - 9 = 0 * x^2 = The letter "x" is squared
STEP#1 - Add 12 to both sides of the equation: x^2 + 8x - 9 + 9 = 0 + 9 x^2 + 8x = 9 STEP#2 - Divide the coefficient of the second term by 2, square the result, and add it to both sides of the equation (We are "completing the square" by adding a squared number to both sides): 8/2 = 4 4^2 = 16 x^2 + 8x + 16 = 9 + 16 x^2 + 8x + 16 = 25 STEP#3 - The left side of our equation can now be consolidated because we can use this algebra identity, which is the square of two terms: a^2 + 2ab + b^2 = (a + b)^2 a^2 = x^2 therefore a = x b^2 = 16 therefore b = 4 a^2 + 2ab + b^2 = (a + b)^2 x^2 + 8x + 16 = (x + 4)^2 STEP#4 - And let us not forget that the left side of the equation was equal to 25 in STEP#2. So after we consolidate it in STEP#3, we set it equal to 25: (x + 4)^2 = 25 STEP#5 - We can solve for "x" by taking the square root of both sides. Keep in mind when we take the root of a positive number, the result is both positive and negative. So we will get two answers for x. Square root of (x + 4)^2 = x+4 Square root of 25 = +/- 5 *The +/- symbol means plus or minus x + 4 = +/- 5 when x + 4 = +5 the answer is x = 1 when x + 4 = -5 the answer is x = -9