The steepness, or grade, of a highway or railroad is expressed as a percent. in the photo of the cog railway at pike’s peak, in colorado, the grade is 18%. thus, for every 100 ft of horizontal run, the train rises 18 ft. find the angle of the inclination of the railway.

Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

Afamily has five members. a mom, a dad, two sisters, & a brother. the family lines up single file. what is the probabillity that the mom is at the front of the line

Liz is shipping a package to her friend. the maximum weight of a medium flat-rate box is 20 pounds, including the box which weighs 6 ounces. write and solve an inequality to describe the possible weight in pounds, w, of the contents that liz will ship to her friend if she must use a medium flat-rate box. use the drop-down menus to explain your answer.