Questions asked by Ivy Liu

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• Find z (floor). Look at picture! Please?
  
• Find z (floor). Please? Add work and explanation.
  
• Find N? Please add work and explanation!
  
• What is the smallest positive integer n?
  
• Find the number of pairs of integers (x,y)?
  
• Find the amount of heat energy needed to convert 150 grams of ice at -15°C to ice at -63°C?
  
• Find the amount of heat energy needed to convert 400 grams of ice at -38°C to steam at 160°C? 1284440 Joules 246840 Joules 331056 Joules 159984 Joules
  
• What is the value of #a^2+b^2#?
  
• Find all ordered pairs of real numbers #(x, y)# such that #x^2y^2 + 2xy^2 + 5x^2 + 3y^2 + 10x + 5 = 0#?
  
• Let #r#, #s#, and #t# be the roots of the equation #x^3 - 2x + 1 = 0# in some order. What is the maximal value of #r^3 - s- t#?
  
• Use this equation to find the equilibrium constant?
  
• What is trichotillomania?
  
• Show that if a+b...........?
  
• Determine the minimum value of #a/(2b) + b/(4c) + c/(8a)# where #a,b,c# are positive real numbers?
  
• Where is the activation complex? IN PICTURE
  
• Factor 4x^3 - 9x^2 + 6x + 1?
  
• If #x# and #y# are positive numbers, what is the minimum possible value of #(x+y)(1/x + 1/y)# ?
  
• What is a and b and c on this graph?
  
• An equilibrium constant of 900 indicates?
  
• Which would not be affected by the addition of a catalyst?
  
• The reaction of charcoal (carbon) and oxygen is sped up by grinding the charcoal into a fine powder. This is an example of?
  
• If #A, B, C# and #D# are positive numbers such that #A + 2B + 3C + 4D = 8#, then what is the maximum value of #ABCD#?
  
• Suppose #0< a,b,c < 1# and #ab + bc + ca = 1#. Find the minimum value of #a + b + c + abc#?
  
• Find the smallest integer n?
  
• Label each element with an oxidation number?
  
• Find the maximum value of #2x + 2sqrt{x(1-x)}# when #0 \leq x \leq 1#?
  
• Prove that #\sqrt{ \frac{2x^2 - 2x + 1}{2} } \geq \frac{1}{x + \frac{1}{x}}#for #0 < x < 1.# ?
  
• What chemical is oxidized in the following reaction? Mg + 2HCl → MgCl2 + H2
  
• Assume that # 1a_1+2a_2+\cdots+na_n=1, # where the #a_j# are real numbers. As a function of #n#, what is the minimum value of #1a_1^2+2a_2^2+\cdots+na_n^2?#
  
• Let #x, y#, and #z# be real numbers such that #x^2 + y^2 + z^2 = 1.# Find the maximum value of #9x+12y+8z.#?
  
• For #x,y#, and #z# positive real numbers, what is the maximum possible value for \[ \sqrt{\frac{3x+4y}{6x+5y+4z}} + \sqrt{\frac{y+2z}{6x+5y+4z}} + \sqrt{\frac{2z+3x}{6x+5y+4z}}? \]
  
• Double Replacement Reactions: Complete and balance. Identify the precipitate (highlight it!!)?
  
• If f(a + b) = f(a) + f(b) - 2f(ab) for all nonnegative integers a and b, and f(1) = 1, compute f(1986). ???????
  
• Reaction Prediction?
  
• Use the solubility curve?
  
• Thermochemistry?
  
• Given the reaction: #NaOH(s) + H_2O(l) -> Na^"+"(aq) + OH^"-" (aq) + 10.6 kJ#, the heat of reaction, #ΔH#, is (positive/negative), the entropy, #ΔS#, is (positive/negative) and the reaction is (spontaneous/not spontaneous). Thermochem?
  
• If the equilibrium constant (K) = 100, this reaction favors the (reactants/products) and proceeds (very little/almost to completion). Equilibrium?
  
• If 20 mL of 1.0 M HCl is used completely to neutralize 40 mL of an NaOH solution, what is the molarity of the NaOH solution?
  
• The function f satisfies #f(x) + f(2x + y) + 5xy = f(3x - y) + 2x^2 + 1#for all real numbers x, y. Determine the value of f(10). ???
  
• Suppose that #x>0# we have #f(2x)= 5/(2+x)#. What is #2f(x)#?
  
• The function #f(x)# is defined for every positive integer #x# and satisfies the equation #f(x+y) = f(x)f(y) - f(xy) + 1# for all positive integers #x# and #y#. If #f(1) =2#, find #f(x)#?
  
• Find all functions #f: Z -> Z# such that #f(a + b) = f(a) f(b) + f(b)# for all #a,b#, and #f(1) = k-1#, where #k# is some integer greater than #1#?
  
• Suppose that x>0 we have f(2x)= 5/(2+x). What is 2f(x)?
  
• For every pair of numbers a and b, the function f satisfies #b^2 f(a) = a^2 f(b)#. If #f(2)# does not equal 0, find the value of #[f(5) - f(1)] / f(2)#?
  
• Find all functions #f : R# \ #{-1} -> R# such that #[f(x)f(z)]/[y+1] = [f(y)f(z)]/[x+1]# whenever #x,y# and #z# do not equal #-1#?
  
• Let #f(t) = [t+ sqrt(3)]/[1 - tsqrt(3)]#. Prove that #f# is a cyclic function?
  
• The function #f : RR -> RR# satisfies #xf(x) + f(1 - x) = x^3 - x# for all real #x#. Find #f(x)#?
  
• Suppose that #f ( x )# and #g ( x )# are functions which satisfy #f ( g ( x ) ) = x^2# and #g ( f ( x ) ) = x^3# for all #x ≥ 1# . If #g ( 16 ) = 16# , then compute #log_2 g ( 4 ) #. (You may assume that #f ( x ) ≥ 1# and #g ( x ) ≥ 1# for all #x ≥ 1# .)?
  
• Suppose we have the following identity: #(px + (1-p)y)^2 = Ax^2 + Bxy + Cy^2.# Find the minimum of #max(A,B,C)# over #0 leq p leq 1#?
  
• If #y = x + 1/x#, then write the equation #x^4 + x^3 -4x^2 +x +1 = 0# in terms of #y#?
  
• Find all order pairs #(x,y)# such that #2x^4 +5x^3 y +45xy^3 = 34x^2 y^2 + 18y^4# and #2x - 3y =7#?
  
• Find all solutions to the equation #7^2a = 45(7^a) + 4 (7^2)#?
  
• If #a# and #b# are integers such that #x^2 -x-1# is a factor of #ax^3 + bx^2 +1#, then find b?
  
• Let p(x) be a fourth degree polynomial with a leading coefficent 2 such that p(-2) = 34, p(-1) = 10, p(1) = 10, and p(2) = 34. Find p(0)???
  
• Solve for all complex numbers z such that #z^4 + 4z^2 + 6 = z#?
  
• Let #f(m,1) = f(1,n) = 1# for #m geq 1#, #n geq 1#, and let #$f(m,n) = f(m-1,n) + f(m,n-1) +...# ?
  
• Compute #1/[r-1] + 1/[s-1] + 1/[t-1]# given that #r,s# and #t# are the rootes of #x^3 -2x^2 +3x -4 = 0#?
  
• Let p(x) be a degree 2 polynomial such that p(1) = 1, p(2) =3, amd p(3) = 2. The p(p(x)) =x has four real solutions. Find the only such solution that is not an integer?
  
• Find all a, b such that #a^2 9^b = 4# and #a/3^b =18#?
  
• Find an equation whose graph is a parabola with directrix y= -1 and vertex (1,3)?
  
• Find an equation whose graph is a horizontally opening parabola that passes through (20, -3), (12,1), and (33,-2)?
  
• Find the vertex, axis of symmetry, and graph the parabola? x = 5y^2 -20y +23
  
• Find the equation, center, foci, and the lengths of the major & minor axes from #x^2 +2y^2 -12y +4x+2=0#?
  
• A chord of a circle is a line segment whose endpoints are on the circle. Find the length of the common chord of the two circles whose equations are #x^2 + y^2 =4# and #x^2 +y^2 -6x +2 = 0#?
  
• The lactus rectum of a parabola is a line segment passing through the focus of the parabola......?
  
• Find axis of symmetry and vertex of #x=5y^2 -20y +23#?
  
• Factor #9a^5 -4a^3 -81a^2 +36# completely over the a) intergers c) reals b) rationals d) complex numbers ??
  
• Find all ordered pairs #(x,y)# such that #x-xy^3 =7# and #xy^2 -xy =3#?
  
• Factor each of the following as completely as possible over the reals? a) #a^3 (c-b) + b^3 (a-c) + c^3 (b-a)# b) #a^4 (c-b) + b^4 (a-c) + c^4 (b-a)#
  
• Find 2 positive integers greater than 1 whose product is #6^6 + 8^4 + 27^4#?
  
• Simplify the expression below?
  
• Put the following statements in the correct order for the events of the sliding filament theory?
  
• Solve #4sin^2(x) -3 = 0# for #[0,2pi)#????
  
• Vector addition?? Please see below!
  
• Put the following statements in order?
  
• Determine the angle between c= <5, -4> and d= <12, 7>. Please use right triangles!?
  
• Schedules of reinforcement?
  
• Parametric equation problem?
  
• Polar coordinates?
  
• Parametric?
  
• Which of the following is NOT the same point in polar coordinates as (3, -1.236)? (-3, 1.906) (3, -7.518) (3, 5.047) (-3, 1.236)
  
• To estimate the size of a lake, Leah starts at one end of the lake and walks 90 meters. Then, she turns 100 degrees and walks another 84 meters to the end of the lake. Please draw a diagram of this situation. Also, how long is the lake?