Consider the following function. x6 1 + x2 dx (a) Determine an appropriate trigonometric substitution. Use x = sin(θ), where − π 2 ≤ θ ≤ π 2 , since the integrand contains the expression 1 + x2 . Use x = tan(θ), where − π 2 < θ < π 2 , since the integrand contains the expression 1 + x2 . Use x = sec(θ), where 0 ≤ θ < π 2 or π ≤ θ < 3π 2 , since the integrand contains the expression 1 + x2 . (b) Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate the integral. x6 1 + x2 dx = dθ

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).

Calculate the average rate of change over the interval [1, 3] for the following function. f(x)=4(5)^x a. -260 b. 260 c. 240 d. -240

Bonnie and bobby are saving money for a vacation. each friend starts with an amount and also saves a specific amount each week. bonnie created a table to show the total she has saved at the end of each week.. weeks 0 1 2 3 4 5 6 7 8 amount saved 12 16 20 24 28 32 36 40 44 bobby came up with the following equation to show the total, y, he has saved at the end of each week, x. y = 12x + 4 compare the rate at which each friend saves money. select the correct answer from the drop-down menu to complete the statement. the rate at which bobby is adding to his savings each week is $ more than the rate at which bonnie is adding to her savings each week.