Solve the following equation |-3i + 5i|
To solve this equation first solve without the absolute value. -3i +5i can also be written as (-3 + 5)i. Therefore you can simplify the equation to be 2i. Next plug this into the absolute value signs, |2i|. The solution to this is 2i as a positive value.
Given the formula for caffeine, C8H10N4O2, determine mass of two moles of caffeine.
To find the mass of one mole of caffiene begin by finding the mass of each element in the compound, Carbon, Hydrogen, Nitrogen and Oxygen. Then, multiply each of these masses by the number of times they appear in the compound. For example there are 8 carbons so you would multiply, the molar mass of carbon, 12.011 g by 8 to get 96.088. Next, add all of the masses of each element together to get 194.194 g. To find the mass of two moles, multiply the mass of one mole by 2 to get 388.388 g.
Two two blocks of equal mass, M, are stacked on a frictionless table. There is friction between the two blocks. A horizontal force, F, is applied to the lower block, moving it a distance of length D. What is the work done by the horizontal force on the two blocks? What is the work done by gravity?
To find the work done by the horizontal force we must use the equation where work is the dot product of the force times the distance. Therefore, the work done by the horizontal force on the two blocks is simply the horizontal force applied times the distance traveled. W = FxD. To find the work done by gravity we use the same formula. The force of gravity is equal to the mass times the universal constant g. Therefore the F of gravity is 2Mg, because we have two blocks of equal mass, M. The Work is found by taking the dot product of the weight force and the distance traveled. Gravity is perpendicular to the distance traveled, so the dot product result is zero. Therefore the work done by gravity is 0.