answer:Let's assume the cost price of the turtleneck sweaters is ( C ). The store first marked up its cost by 20%, so the initial selling price (SP1) would be: [ SP1 = C + 0.20C = 1.20C ] During the New Year season, it marked up its prices by 25% of the original retail price (which is SP1), so the second selling price (SP2) would be: [ SP2 = SP1 + 0.25SP1 = 1.25SP1 = 1.25(1.20C) = 1.50C ] In February, the store offered a discount of 7% on SP2. The final selling price (SPF) after the discount would be: [ SPF = SP2 - 0.07SP2 = 0.93SP2 = 0.93(1.50C) = 1.395C ] The profit on the items sold in February would be the final selling price minus the cost price: [ Profit = SPF - C = 1.395C - C = 0.395C ] So the store's profit on the items sold in February is boxed{39.5%} of the cost price.

answer:The function can be simplified as follows: f(x)=cos ^{2}( frac {π}{4}+x)-cos ^{2}( frac {π}{4}-x) Using the double angle identity for cosine, we can rewrite cos ^{2}( frac {π}{4}+x) as frac{1}{2}(1 + cos(2(frac {π}{4}+x))). Similarly, using the double angle identity for sine, we can rewrite cos ^{2}( frac {π}{4}-x) as frac{1}{2}(1 - sin(2(frac {π}{4}-x))). Substituting these expressions into the original equation, we get: f(x)=frac{1}{2}(1 + cos(2(frac {π}{4}+x))) - frac{1}{2}(1 - sin(2(frac {π}{4}-x))) Simplifying further, we get: f(x)=frac{1}{2}(cos(2(frac {π}{4}+x)) + sin(2(frac {π}{4}-x))) Using the sum and difference formulas for cosine and sine, we can simplify the expression to: f(x)=frac{1}{2}(cos(frac {π}{2}+2x) + sin(frac {π}{2}-2x)) Using the cofunction identities, we can simplify the expression to: f(x)=frac{1}{2}(-sin(2x) + cos(2x)) Using the double angle identity for sine, we can simplify the expression to: f(x)=-sin(2x) Substituting x = frac {π}{12}, we get: f(frac {π}{12})=-sin(frac {π}{6}) Since sin(frac {π}{6}) = frac{1}{2}, we have: f(frac {π}{12})=-frac{1}{2} Therefore, the answer is boxed{-frac{1}{2}}.

answer:To find the length of the train, we can use the formula: Length of the train = Speed of the train x Time taken to cross the electric pole Given that the speed of the train is 179.99999999999997 m/s (which we can round to 180 m/s for simplicity) and the time taken to cross the electric pole is 3 seconds, we can calculate the length as follows: Length of the train = 180 m/s * 3 s = 540 meters Therefore, the length of the train is boxed{540} meters.

answer:Let's break down the progression: 1. Wall push-ups: John starts with 1 rep and adds 1 rep each day. He needs to reach 20 reps to move to the next variation. This will take him 20 days. 2. Incline push-ups: After 20 days of wall push-ups, he will start incline push-ups at 1 rep and again add 1 rep each day until he reaches 20 reps. This will take another 20 days. 3. Knee push-ups: After 20 days of incline push-ups, he will start knee push-ups at 1 rep and add 1 rep each day until he reaches 20 reps. This will take another 20 days. So, in total, John will take 20 (wall) + 20 (incline) + 20 (knee) = 60 days to reach floor push-ups. Since John trains 5 days a week, we need to calculate how many weeks this will take. 60 days / 5 days per week = 12 weeks Therefore, it will take John boxed{12} weeks to progress to floor push-ups.