Answers edited by Trevor Ryan.

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• How do you use the second fundamental theorem of Calculus to find the derivative of given #int cos 2t dt# from x to pi/4?
  
• Does #a_n=x^n/(n!) # converge for any x?
  
• A projectile is shot from the ground at an angle of #(5 pi)/12 # and a speed of #4/9 m/s#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?
  
• Question #f45fa
  
• How do you determine if #f(x) = x^3 + x# is an even or odd function?
  
• How do you find the determinant of #((1, 0, 0, 0), (sqrt3, 2, 0, 0), (-0.003, 0, -3, 0), (1.432, sqrt37, pi, 1))#?
  
• Question #6dc14
  
• Question #eefeb
  
• If a cup of coffee has temperature 95∘C in a room where the temperature is 20∘C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(x)=20+75e^(-t/50). ?
  
• The cost function for a product is C(x)=0.8x^2 +120x+110. How to find average cost over [0,600] ?
  
• What is the derivative of #2^sin(pi*x)#?
  
• It takes 23.5 kJ of heat energy to raise the temperature of 100 g of a substance by 50°C. What is the substance?
  
• If a current of 40 mA flows through a series circuit consisting of a 0.4 µF capacitor and a resistor in series with a 4 kHz, 40 Vac source, what is the total circuit impedance?
  
• What is the trigonometric form of #12 e^( ( pi)/2 i ) #?
  
• A ball with a mass of #14 kg# moving at #15 m/s# hits a still ball with a mass of #17 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?
  
• Question #490a9
  
• How do you find the determinant of #((2, -3, 5), (0, 1, -3), (0, 0, 2))#?
  
• An atom contains 70 protons, 70 electrons, and 99 neutrons. What is the mass number?
  
• How do you evaluate #sec(18pi)#?
  
• Why can't a triangle have a right angle and an obtuse angle?
  
• How do you find the derivative of #sin(x)/[1-cos(x)]#?
  
• Given #f(x) = |2x + 1|#, #g(x) = 3x³ -1# how do you find f(g(x))?
  
• A balanced lever has two weights on it, the first with mass #3 kg # and the second with mass #37 kg#. If the first weight is # 9 m# from the fulcrum, how far is the second weight from the fulcrum?
  
• What is the greatest common factor of 21 and 63?
  
• Question #55e72
  
• Question #d9e88
  
• How do you find the asymptotes for #f(x) = (3x + 5) / (2x - 3)#?
  
• What is the limit of #sinx / x# as x goes to infinity?
  
• How would you balance: C3H8 + O2 --> CO2 + H2O?
  
• A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of an arc covering #pi # radians on the circle?
  
• ∥v∥=3 ∥w∥=4 The angle between v and w is 1.2 radians. How to calculate ? a) v⋅w = ,(b) ∥1v+1w∥= , (c) ∥4v−4w∥=
  
• How do you prove the statement lim as x approaches 4 for # (x^2) = 4# using the epsilon and delta definition?
  
• Question #adc16
  
• A weather rocket is launched straight up. Seconds into the flight, its velocity is 130m/s and it is accelerating at 19 m/s^2. At this instant, the rocket's mass is 59 kg and it is losing mass at the rate of 0.55 kg/s. What is the net force on the rocket?
  
• How do you solve #2/(3+x) = 25#?
  
• What is the difference between mole and molecule?
  
• Given #f(x)=x^2+1# with domain #{2,-1,0, 1,3}# what is the range?
  
• What are the applications of power series in electrical engineering?
  
• How do you implicitly differentiate #ln(x-y)=x-y #?
  
• How do you condense #ln(1+x^9)+1/2(ln(x)-ln(sin(x) #?
  
• How do you find the Integral of #sqrt(x^2 - 16)/ x dx#?
  
• How do you rewrite #((a^-2b^5)/c^-3)^-2# using a positive exponent?
  
• For #f(x)=2^x # what is the equation of the tangent line at #x=-5#?
  
• How do you translate into symbols: The difference between n and 14?
  
• What is acetylcholine classified as?
  
• How do you graph #x + y = –2#?
  
• How does genetics use the principles of probability?
  
• What is the domain and range of #y=2x-6#?
  
• What ions are present in NaCl, Na2CO3, MgSO4, and NH4Cl?
  
• What is #sqrt{-sqrt3 + sqrt (3 + 8 sqrt (7 + 4 sqrt3#?
  
• What is the binomial theorem?
  
• Question #ce2b6
  
• What is the angle between #<1 ,3,-8># and #< 4,1,5>#?
  
• The difference between the degree measures of two supplementary angles is 80°. What is the degree number of the larger angle?
  
• The girl's brother stands at the edge of the Golden Gate Bridge and throws a penny upwards at 29 m/s at an angle of 34°. How long does it take the penny to fall to the water, 227m below? How far from the base of the bridge does the penny hit the water?
  
• How do you simplify #1/(2+3i)# and write in a+bi form?
  
• What are synchronous machines?
  
• What is the angle between #<-1,-7,2 > # and #<-3,-5,1> #?
  
• What are the asymptotes for #(x^2+4x+3)/(x^2 - 9)#?
  
• Question #a8f63
  
• If #A= <6 ,9 ,-1 ># and #B= <-4 ,-1 ,4 >#, what is #A*B -||A|| ||B||#?
  
• How do you determine whether the function #f(x)=3x^5 - 20x^3# is concave up or concave down and its intervals?
  
• Question #4444b
  
• What is needed to produce an electromagnet?
  
• Is it correct to write #1^@=2pi/360^@#? Yes or no, and also why?
  
• What type of compound is CH3-CH2-CH3?
  
• How do you find the derivative of #lnxsqrt(x^2+1)#?
  
• What is the least squares regression model for the following data points?: (1,3), (2,6), (3,19), (2,7), (8,9), (10,25)
  
• How do you prove #cos 3 theta = 4 cos^3 theta - 3 cos theta#?
  
• A 2150 kg truck traveling north at 42 km/h turns east and accelerates to 61 km/h. (a) What is the change in the truck's kinetic energy? (b) What is the magnitude of the change in its momentum ?