Consider the following function. f(x) = x3/5, a = 1, n = 3, 0.7 ≤ x ≤ 1.3 (a) approximate f by a taylor polynomial with degree n at the number a. t3(x) = 3 5 (x−1)− 3 25 (x−1)2+ 7(x−1)3 125 +1 (b) use taylor's inequality to estimate the accuracy of the approximation f(x) ≈ tn(x) when x lies in the given interval. (round your answer to eight decimal places.) |r3(x)| ≤

Landon wallin is an auto mechanic who wishes to start his own business. he will need $4400 to purchase tools and equipment. landon decides to finance the purchase with a 48-month fixed installment loan with an apr of 5.5%. a) determine landon's finance charge. b) determine landon's monthly payment.

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Describe the symmetry of the figure. identify lines of symmetry, if any. find the angle and the order of any rotational symmetry.