Evaluate the line integral ∫cf⋅dr, where f(x, y,z)=3sinxi−4cosyj−xzk and c is given by the vector function r(t)=t5i−t4j+t3k , 0≤t≤1.

Abus travels 36 miles in 45 minutes. enter the number of miles the bus travels in 60 minutes at this rate.

Astore ordered 750 candles a total wholesale cost of $7910.20. the soy candles cosy $12.17 each and thespecialty candles cost $9.58each. how many of each were bought?

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.