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  • Question #8a446 - Socratic
    First, we'll do a u-substitution with #u=1 x# and # (du) dx=-1 x^2# We divide by the derivative to integrate with respect to #u#: #int\ e^u (x+1)^2*-x^2\ du# We can solve for #x# to get #x=1 u#, and plug in: #-int\ e^u ( (1 u+1)^2u^2)\ du=-int\ e^u (u (1 u+1))^2=#
  • Question #9e77c - Socratic
    This integral may seem tricky at first, but it comes apart quite quickly once you realize a certain u-substitution If we let #u=ln (ln (x))#, we get by the chain rule that the derivative is:
  • Question #df3e8 - Socratic
    H (n) = sum_ (i=1)^n 1 i = int_1^ (n+1) 1 floor (x) dx Compare this with the integral: int_1^ (n+1) 1 x dx = ln (n+1) The smooth graph of 1 x touches each of the steps of 1 floor (x)
  • Question #f14a1 - Socratic
    It is 1 sinx+c where c is the integration constant It is the following integral int cosx (sin^2x)dx=int (1 sinx)'dx=1 sinx+c
  • Question #167c1 - Socratic
    To answer the first question, we have to find two solutions to a quadratic equation that equates v(t) to 0: 2t-t^2 4=0 We don't even have to apply a general formula to solve this equation since it easily transformed into a product of two linear polynomial: t(2t-t 4)=0 Solutions are: t_1=0 (when an insect started moving) and t_2=8 (it landed on some surface) The second question about the
  • Question #35325 - Socratic
    yes it can Two main chemical reactions occur in photosynthesis One takes place only in the presence of light and is called the light reaction and the other can occur with or without light and is called the dark reaction -Dark reaction- The chemical energy possessed by ATP and NADPH2 is used in making carbohydrates from hydrogen and carbon dioxide (The carbon dioxide is obtained from the
  • Question #3ee15 - Socratic
    I will try to solve this problem without using any variable Notice that an engineering classroom has 32-24=8 more seats than a typical one If all 16 classrooms were typical ones, then we would have only 24 times 16=384 seats total, which is 424-384=40 seats short So, we have to turn 40 divide 8=5 classrooms into engineering ones Hence, the wing has 11 typical and 5 engineering classrooms
  • Question #1e2e8 - Socratic
    Explanation: #cos 2t = - sqrt2 2# Trig table and unit circle give 2 solutions: #2t = +- (3pi) 4 + 2kpi# #t = +- (3pi) 8 + kpi# The arc # (-3pi) 8# is co-terminal to
  • Question #2a59b - Socratic
    51 708 N resolving the weight in components, force acting along the plane (driving force)=Mgsin (theta)=51 708N M=8 6Kg; theta=37 8 degrees and g= 9 81 normal force= Mgcos (theta)=66 66 max static friction (since the body is at rest initially we use static friction)= coeff of static friction normal force=1 43*66 66=95 037: which is more than driving force hence the body remains at rest and





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