Tutor profile: Emma B.

Find the derivative: f(x) = 4x^5 + 2x^3 - cos(x) - 8ln(x)

We need to find the derivative of the equation: f(x) = 4x^5 + 2x^3 - cos(x) - 8ln(x) First, we will find the derivative of 4x^5: 4x^5 d(4x^5) = (5*4)x^(5-1) = 20x^4 Second, we will find the derivative of 2x^3: 2x^3 d(2x^3) = (3*2)x^(3-1) = 6x^2 The derivative of cos(x) is -sin(x). Lastly, we know the derivative of aln(x), where a is a constant is a/x. So, the derivative of 8ln(x)= 8/x. Now we can put it all together. f'(x) = d(4x^5 + 2x^3 - cos(x) - 8ln(x)) f'(x) = 20x^4 + 6x^2 - (-sin(x)) - 8/x f'(x) = 20x^4 + 6x^2 + sin(x) - 8/x Therefore, the answer is: f'(x) = 20x^4 + 6x^2 + sin(x) - 8/x. ***Make sure you are paying attention to signs!***

Write 150 words describing your perfect day. You may write about when you wake up, activities you may do during the day, food you eat, or people you spend time with. Make sure to use transition words to outline the order of your day.

The start of my perfect day would be waking up at 9:00 in the morning. Once I wake up, I would get ready for the day by showering, brushing my teeth, getting dressed, and putting make-up on. Next, I would take my grandma and cousins out for breakfast at a local diner called the Olive Tree. Then, I would meet my best friend Alexis at Niagara Falls to go for a hike around it. We may even try the zip line! After a few hours around there, I would meet my family for dinner for wings at Duffs, home of the famous buffalo chicken wings. For dessert, we'd go to a local soft serve ice cream place. Finally, I would meet some of my friends for a bonfire in the back of my friend Alison's house. Sounds like the perfect day to me.

Joe had 8 tigers at his home in Oklahoma. It costs approximately $15 to feed one tiger per day because he uses a meat truck. Carole has x amount of tigers at her home in Florida. It costs her $23 to feed one tiger per day because she uses gourmet food. How many tigers does Carole have if she pays $5656 more than Joe for tiger food alone in the month of February?

First, lets look at the information given to us: Joe Carole Number of tigers: 8 x Price of food (per tiger per day): $15 $23 Number of days in February: 28 28 Cost of food for February: y y + $5656 Since we know that Carole pays $5656 more than Joe in food for the month of February, we can say that Joe pays y in food, and Carole pays y + $5656 in food. Because we have more information in Joe's column, we will solve for y first. Then we will use that answer to solve for x. We want to find Joe's cost of food for February. This means that we will need to multiply the number of days in February by the price of food per tiger per day and the number of tigers Joe has. The calculations are: y = Number of days in February * Price of food (per tiger per day) * Number of tigers y = 28 * 15 * 8 y = $3360 Therefore Joe pays $3360 for food in the month of February. Now that we know y, we can find out how much Carole pays for food in the month of February by: Cost of food for February = y + $5656 Cost of food for February = $3360 + $5656 Cost of food for February = $9016 Now that we know all the information in the table except for x, we may solve for x. We can use the same equation we used for y to find x. Look at the calculations below: y = Number of days in February * Price of food (per tiger per day) * Number of tigers $9016 = 28 * $23 * x $9016 = $644x 14 = x Therefore, Carole has 14 tigers.