What is the slope of the line tangent to the graph of the function f(x)=ln(x+100) at the point x=0?
GIVEN- Function, f(x)=ln(x=100) TO FIND- Slope of the tangent line to the given function. SOLUTION- To find the slope of tangent line to given function, we basically need to find its derivative i.e df(x)/dx so, f(x)=ln(x+100) finding its derivative at x=0. df(x)/dx=d[ln(x+100)]/dx or, =1/(x+100) (SINCE, d(ln(x+a))/dx = 1/x+a , WHERE 'a' IS A CONSTANT) so, slope at x=1, =1/x+100 or, =1/0+100 or, =0.01 ANSWER- Slope of the tangent line to the given function f(x)=ln(x+100) is 0.01.
Kevin is twice as old as his youngest sister. If the difference between their ages is 15 years. How old is his youngest sister?
GIVEN- Kevin is twice as old as his sister. Difference between their ages is 15. TO FIND- Age of Kevin's youngest sister. SOLUTION- Let the age of Kevin be x And let the age of his sister be y Therefore from the question, x=2y ---------(1) and also, x-y=15 ---------(2) Therefore putting value of x from equation (1) in equation(2), we get- x-y=15 or, 2y-y=15 or, y=15 ANSWER- So, Kevin's youngest sister is 15 years old.
Suppose we had 684.6 grams of sucrose and proceeded to mix it into some water. It would dissolve and make sugar water. We keep adding water, dissolving and stirring until all the solid was gone. We then made sure that when everything was well-mixed, there was exactly 5 liter of solution. What would be the molarity of this solution? (Given molecular mass of sucrose is 342.3g/mol)
GIVEN- Molecular mass of sucrose=M=342.3g/mol Weight of sucrose sample=W=684.6g Volume of the solution=V=5L TO FIND- Molarity of the solution. SOLUTION- The formula which is used in this problem is, Molarity=(Number of moles of solute)/(Volume of solution in liter) And, Number of moles=Weight of compound/Molecular weight of compound = W/M Now, the number of moles=W/M =684.6/342.3 =2mol Therefore, the molarity of the solution is=Number of moles/Volume =2/5 =0.4M ANSWER- The molarity of the given solution is 0.4M.