Tutor profile: Henry F.
How many moles are in 64 grams of O2.
So this is a very common stoichiometry question, converting from grams to moles, before solving this, one needs to know the molar mass of Oxygen, that information can be found on the periodic table, molar mass for oxygen is about 16, for O2 then you just have to double that amount, 16x2=32g then for every mole of O2 there are 32g of O2, so 64g/32g=2 moles of O2
Find the derivative of (sin(x))^2.
In order to solve the question, we have to understand what rule we need to apply to get to the answer, there are actually two rules you need know before solving this questions, there are the power rule and chain rule. power rule: when you take the derivative, bring down the power then subtract 1 from the power ex: derivative of x^3, in this case, 3 is the power, so we bring it down to the front, then subtract 1 from 3, 3-1=2, so the answer is 3x^2 Chain rule, derivative of outside function times derivative of the inside function so for (sin(x))^2, ()^2 is the outside function, and we can find the derivative by using the power rule 2sin(x) then we multiply this by the derivative of the inside function, derivative of sinx is cosx so the answer is 2sin(x)cos(x)
Solve for x in the following question 3x^2+15x+18=0
There are many different ways to solve a quadratic function, there are solving by factoring, by using the quadratic formula, or by graphing. The quickest way to obtain the solution is usually by factoring, but other methods might work better under different circumstances. So, by observing that 3 is a common factor in all three terms 3x^2, 15x and 18, we can factor out a 3. Then the equation becomes 3(x^2+5x+6)=0, then by factoring, we want to find two numbers that have a product of 6 and sum of 5. We can see that 2 and 3 satisfy the condition, then the equation 3(x^2+5x+6)=0 can be further reduced to 3(x+2)(x+3)=0. Then we solve for x from there, by setting each factor equal to 0 x+2=0 subtract 2 each side x=-2 x+3=0 subtract 3 each side x=-3 so x=-2 and x=-3 are the solutions.
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