Sxln (1+x) dx (Hint: use a u-substitution and then integration by parts)

Mike and his mom decided to go for a long walk from their house to grandma's house.  The total distance was 5 and 2/5 miles. They decided to stop 2/3 of the way to have a snack.  When they stoppedto have the snack, how far had they walked?  Show a model to illustrate the problem.

Megan is taking the bus fromNew York City to Montreal. Thedistance is 380 miles and the bustravels at a steady rate of 76 milesper hour. How long will the bus ride be?

Gwen is interested in the effect of bananas on the speed and endurance of high school cheerleaders.  She recruits 20 cheerleaders from high schools in California.  Each cheerleader was asked to run as many laps as they could in 20 minutes on a standard 100M track.  Two weeks later the same cheerleaders were asked to run as many laps as they could in 20 minutes, but were asked to eat a banana 10 minutes prior to starting.  The number of laps completed (to the nearest quarter lap) was recorded.  What is the sample of this study? 1. The 20 cheerleaders measured 2. All cheerleaders in California 3. Banana aficionados 4. All cheerleaders in California who regularly eat bananas

Drogon can melt the iron throne 50% faster then Viserion and 20% faster than Rhaegal, and together then can melt the iron throne in 4 mins. How long will it take Drogon to melt the iron throne alone?

John Starts work at 5pm at 5:30 he was 1/3 done how long does he take?

Each machine at a certain factory can produce 90 units per hour. The setup cost is 45 dollars for each machine and the operating cost is 19 dollars per hour (total, not 19 dollars per machine per hour). You would like to know how many machines should be used to produce 10000 units, with the goal of minimizing production costs. First, find a formula for the total cost in terms of the number of machines, n: TC = 45n+19(10000/(90n)) The minimum total cost is achieved when using machines for a total cost of dollars.

miles from their home. Being a little reluctant Travel: Recently Mr. and Mrs. Roberts s their vacation in San Francisco, which is 540 spent their vacation in San Francisco, which is 540 to return home, the Roberts took 2 hours longer on their return trip and their average speed was 9 mph slower than when they were going. What was their average rate of speed as they traveled from home to San Francisco?

You want to estimate how many fish there are in a small pond.  Let's suppose that you first capture n1=500 fish, tag them, and throw them back into the pond.  After a couple of days you go back to the pond and capture n2=120 fish, of which k=30 are tagged.  Estimate the number of fish in the pond. There are approximately Answer fish in the pond.

Superb Manufacturing is using a Kanban system for a component part. The demand for the component is 225 parts/hr. A container with 39 parts can be manufactured and delivered in 79 min. The safety factor is set to 8% of hourly demand. What is demand during lead time? (Round it to two decimal points)