Questions asked by Valour J.

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• On an interval #[a,b]#, #f# is a continuous function. If #f(a)<0# and #f(b)>0#, then there exists a constant #c\in [a,b]# such that #f(c)=0# by which theorem?
  
• Use the second fundamental theorem of calculus to calculate #F(x)=int_-3^x(t^2+3t+2)dt#?
  
• Which of the following statements is true?
  
• Please explain any one of them in detail? Thanks!
  
• The function #f# is defined by #f(x)=(x-1)(3+x)#, #x>b-1# #f(x)=-x+1#, #x<=b-1# and is continuous at #b-1#. What is #b#?
  
• If #Delta ABC# is drawn such that #m/_BAC=30^circ#, #AB=7#, #BC=4#. How many triangles can be drawn with this information?
  
• Determine whether Rolle's Theorem can be applied to #f# on the closed interval #[a,b]#. If Rolle's Theorem can be applied, find all the values of #c# in the open interval #[a,b]# such that #f^'(c)=0#?
  
• Does the answer to #(log_b5)(log_5b)# depend on the value of b? (a). Yes (b). No (c). Not enough information to answer
  
• If #A# and #B# are two events such that #P(A)ne0# and #P(B|A)=1#, then?
  
• What is the value of #k#, where #k=(1+1/n)^n#, given #n# is equals to number of seconds in one year? (a). #e# (b). 2.7 (c). 2 (d). 2.75
  
• Is #log(x*x*x)=2log(x)+log(y)# ?
  
• Can you find any point that is equidistant from three collinear points? Please help me choose from the last two options?
  
• Jon is asked to clean a circular radioctive area of radius r. If by the end of each day he cleans half the area that he started with on that day, how much area would have been cleaned at the end of the twentieth day?
  
• What is the radius of the incircle of a triangle whose sides are 5, 12 and 13 units?
  
• If a liquid from a completely filled spherical container of inner radius #r# is poured into a cube shaped container, what would be the dimensions of the cube in terms of the radius of the sphere?
  
• If #f(a+b-x)=f(x)#, then #int_a^bxf(x)dx# is equal to?
  
• Given that #sin(b)=-2/3#, and that #b# is in the third quadrant, what is the value of #tan(2b)#..?
  
• In one 15 square mile area of woods, there were five dears. In a different section that was 21 square miles, there were seven. Find the deer per square mile?
  
• A new born child grows at a rate of #4/sqrtt# pounds per month for the first 12 months (#t>0#). How many pounds does the child gain between the 1st and 4th month?
  
• Suppose A is the arc on the unit circle that connects #(1,0)# to #(-12/13, 5/13)# and passes through #(0,-1)#. Let #u# be the measure of the angle that subtends this arc. Find the value of #sin(u)#?
  
• Let, # f(x)=x^2-5x # and #g(x)=8-x#, find #(fg)(7)=?#
  
• How many critical points does the function #f(x)=(x-2)^5(x+3)^4# have?
  
• Out of 786 students surveyed, 582 of them hate smoking cigaretes. Find the confidence interval corresponding to 96% degree of confidence?
  
• Find the quotient and write the result in a+bi form? #(16(cos240^\circ+isin240^\circ)) /(8(cos90^\circ+isin90^\circ))#
  
• I would like someone to clarify this sentence for me. "It was too directly bound to its own anguish to be anything other than a cry of negation, carrying within itself the seeds of its own destruction." I would like to have the simplified explanation?
  
• A non zero value of #c# such that the solution set for the inequality #x^2+2cx-6<0# is the open interval is #(-3c,c)# is?
  
• In the equation #Q=Ae^{pt}#, can the term #e^p# be replaced by #x^y#, where both #x# and #y# are rational numbers?
  
• Please state the domain of this function?
  
• Please help, I am stuck?
  
• Anybody, please help me. This is a piecewise function?
  
• Can anybody help me write the equation of this graph. How can I do it myself?
  
• Can anybody help me write the equation of the function from the graph? Thanks
  
• #y=f(x)# is given. Graph, #y=f(3x)-2# and #y=-f(x-1)#?
  
• The graph of #y=g(x)# is given below. Sketch an accurate graph of #y=2/3g(x)+1# on same set of axes. Label the axes and at least 4 points on your new graph. Give the domain and range of the original and the transformed function?
  
• How can I write down the function from the graph?
  
• Prove that?
  
• Prove by induction? Thanks :)
  
• Prove by induction, 2? Thanks :)
  
• Part #e).#, #\ \ f).#, and #\ \ g).#. Please correct the step if you find any mistake in the previous steps? Thanks :)
  
• Given #\ \ f(x)=1/2x^4-x^3+x-3\ \ #... Show the equation?
  
• I need help with part #\ \ b)...#?
  
• Can you help?
  
• How many grams of #\text{NH}_4\text{OH}# do I need to make #400\ \text{mL}# of a #0.45\ \text{M}# solution of #\text{NH}_4\text{OH}#...?
  
• A group of twenty female and twenty male students are in a room. If eight of the #40# are selected at random and put in a row for a picture, what is the probability that the eight are of the same gender?
  
• Alice randomly selects a permutation of #(1, 2,\cdots\ \cdots\ , 74, 75).# What is the probability that she selects a permutation where #75# precedes 7?# ##" "## # (Note: In the permutation #[1, 4, 5, 6, 3, 2], 4# precedes #2#.)
  
• Question is lengthy so I've attached the screenshot. Can you help? It's probability.
  
• Let #\ \ h(x,y)=x^3-6x^2-3y^2\ \ #. Find all critical points of #\ \ f\ \ #? Then classify each as either a relative maximum, minimum, saddle point, or neither.