Tutor profile: Nadim A.
What volume of 5.0 M H2SO4 is required to prepare 2.0 L of .25 M H2SO4?
With questions like this, we want to use a very important formula called the dilution equation M1V1 = M2V1. M stands for Molarity and V stands for Volume. In this case, we have 5.0 M (molar) H2SO4 and want to make 2.0 L (volume) of .25 M H2SO4 but do not know how much volume of the 5.0 solution we need. M1 = 5.0 M V1 = ? M2 = .25 M V2 = 2.0 L M1V1 = M2V2 (5.0M)V1 = (.25M)(2.0L) Divide both sides by 5.0M to get V1. V1 = (.25M)x(2.0L)/(5.0M) = .1 L However, keep in mind the answer ".1 L" is not technically correct because all of the terms in the problem are 2 significant digits therefore we must maintain 2 significant digits in the answer. So ".10 L" is the correct answer.
Find the derivative of 25e^(2x)
To do this, you want to implement the chain rule. This means that you want to take the derivative of 25 and multiply it by the derivative of e^(2x) and add it to e^(2x) times the derivative of 25. In other words: 25[e^(2x)]' + 25'e^(2x). " ' " means derivative. To take the derivative of e^(2x), we need to first understand that the derivative of e^u = e^u x u'. In this case u=2x and u'=2. So you'll get 25[e^(2x)] x 2 + 25'e^(2x) which can be simplified to 50e^(2x) + 25'e^(2x) Now we can proceed 25'e^(2x). The derivative of a number by itself will be 0 and therefore you will get 25x0=0. So, 50e^(2x) + 0 = 50e^(2x).
Given the equation 5(- 2x - 2) - (x - 5) = -4(4x + 3) + 10, solve for "x".
With a problem like this, you want to bring the variable of interest to one side of the equation. However, you first want to get rid of all of the parentheses and list everything as single terms. To do this, start by distributing the numbers outside of the parentheses to the numbers inside the parentheses. You get: -10x-10-x+5 = -16x-12+10 From here, group like terms on both sides. On the left side of the equation you can add "-10x" and "-x" to get "-11x" and you can also add "-10" and "5" to get "-5". On the right side of the equation you can add "-12" and "10" to get "-2". So we have: -11x-5 = -16x -2. Now you want to bring all the "x" terms to one side and all the terms without an "x" to the other side. Start by adding 16x to both sides to get 16x-11x-5 = -16x+16x-2. This simplifies to 5x-5 = -2. Now add 5 to both sides to get 5x-5+5 = -2+5. This simplifies to 5x = 3. Now to get "x" by itself, divide both sides by 5. This will get you 5x/5 = 3/5, which simplifies to x=3/5 or 0.6.
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