Answers edited by Ratnaker Mehta

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• How do you express #f(theta)=sin^2(theta)+6cot^2(theta)-8cos^4theta# in terms of non-exponential trigonometric functions?
  
• The length of a rectangular piece of carpet is 4 yards greater than the width. How do you express the area of the carpet as a function of the width?
  
• How do you solve #sqrt(x+6)-5=x+1# and find any extraneous solutions?
  
• How do you write the equation of a parabola in vertex form that has a focus at #(6,5)# and a directrix of #y=-1#?
  
• Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. How do you find the numbers?
  
• How do you find the exact value of #arccos(sin(3*pi/2))#?
  
• How do you evaluate #log_7 (-49)#?
  
• How do you determine algebraically the x coordinate of all points where the graphs of xy=10 and y= x+3 intersect?
  
• How do you simplify #(3+9i)/(3i)#?
  
• A chord with a length of #3 # runs from #pi/4 # to #pi/3 # radians on a circle. What is the area of the circle?
  
• Question #56a98
  
• How do you solve the following equation #sin 2x - sin x = 0# in the interval [0, 2pi]?
  
• Question #9adaf
  
• What is the limit of # ((1)+(3/x)+(5/x^2))^x# as x approaches infinity?
  
• How do you find the second derivative of #ln(x/2)# ?
  
• How do you show #cos (arctan x) = [ 1 / ( sqrt(1 + x^2))]#?
  
• What is the equation of a circle with center #(2, -3)# and radius of #3#?
  
• How do you determine #(d^y)/(dx^2)# given #1-xy=x-y^2#?
  
• How do you write the equation in point slope form given (8,7), (-2,-4)?
  
• How do you evaluate the limit #(sqrt(x+1)-2)/(x^2-9)# as x approaches -3?
  
• How do you prove #[(sin 3x) / sin x ] – [(cos3x) / cos x)] = 2#?
  
• What is the antiderivative of #x^3/(1+x^2)#?
  
• How do you integrate #int x^3sqrt(x^2-1)# using substitution?
  
• The mean of 3 numbers is 7. The mean of 4 other numbers is 8. The mean of 5 other numbers is 11. What is the mean of all 12 numbers?
  
• How do you find the slope given (0,5) and (-3, -4)?
  
• What's the derivative of #f(x) = (arctan (x/2)) + ((5x-1)/(2(x^2) + 4))#?
  
• How do you find the value of #sin(theta/2)# given #tantheta=2# and #0<theta<pi/2#?
  
• Question #4d43b
  
• Bradley is extending his rectangular living room. The original dimensions are 6 feet by 11 feet. If he extended his room by #x+8# feet, what is the new area? How many square feet of area did he add?
  
• Use the exponential growth model #P(t) = P_0e^(kt)#. The half-life of thorium-229 is 7,340 years. How long will it take for a sample of this substance to decay to 20% of its original amount?
  
• What is the limit of #(t^(1/3)-2)/(t-8)# as t approaches 8?
  
• Question #4f402
  
• How do you use the sum and difference identity to evaluate #sin((7pi)/12)#?
  
• How do you solve the equation on the interval [0,2pi) for #sin 3x = -sinx#?
  
• Question #64850
  
• How do you find the parametric equations of the line of intersection of the planes x+2z=0 and 2x-3y+4?
  
• How do you solve #1+ 6( 2x + 3) ^- 1+ 8( 2x + 3) ^- 2= 0#?
  
• Question #58346
  
• How do you simplify #(8i)(7-3i)#?
  
• How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-5,9) and midpoint M(-8,-2)?
  
• There are 15 students. 5 of them are boys and 10 of them are girls. If 5 students are chosen, what is the probability that there are at least 2 boys?
  
• How to find the distance from the point A(3,-5,5) to the line x = 2 + 3t , y= 1-2t, z= -1 + t ?
  
• How do you find the domain and range of #f(x) = -x^2 + 2x + 1#?
  
• If sin A > 0 and tan A < 0, then A is in what quadrant?
  
• There were five people in group A, with a mean lQ of 100, and five in group B, with a mean IQ of 74. When Jack left group A for group B, both means increased, and the total of the two new means was 180. What Is Jack's IQ?
  
• The sides of a triangle measure 6 inches 8 inches, and 10 inches. The triangle has one 90° angle. What type of triangle is it?
  
• Segment #ST# has endpoints of #S(-2, 4)# and #T(-6, 0)#. What is the midpoint of segment #ST#?
  
• Question #e1c7e
  
• How do you find the equation of a circle whose center of this circle is on the line 2x-5y=9 and it is tangent to both the x and y axis?
  
• How do you differentiate # sin^2(x/2)#?
  
• How do you find the first and second derivative of #(ln(x^2-1))/x^2#?
  
• How do you evaluate #sec^-1(sec((5pi)/6))#?
  
• How do you solve #5+(sqrt(x+2))=8+(sqrt(x-7))#?
  
• How do you integrate #x/((x-1)(x^2+4)# using partial fractions?
  
• How do you find the x and y intercept of #4x + y = – 8#?
  
• What is the equation of the line that is normal to #f(x)=-e^x # at # x=-2 #?
  
• Suppose an experiment begins with 5 bacteria, and the bacteria population triples every hour. What would be the population of the bacteria after 6 hours?
  
• Question #f9011
  
• How do you evaluate the definite integral #int (2t-1)^2 # from #[0,1]#?
  
• What are all the possible rational zeros for #f(x)=2x^3-4x+8# and how do you find all zeros?
  
• How do you find the limit of #(1-sin(theta))/(1+cos(2theta))# as theta approaches pi/2?
  
• How do you integrate #(x^2-1)/(x^4-16)# using partial fractions?
  
• A circle has a center that falls on the line #y = 8/7x +2 # and passes through # ( 7 ,8 )# and #(3 ,9 )#. What is the equation of the circle?
  
• How do you find the exact value of #csc ((5pi)/6)# using the half angle formula?
  
• How do you simplify #(3sinx)/cos^2x*(cos^2x+cosxsinx)/(sin^2x-cos^2x)#?
  
• How do you integrate #{x(sqrt(1+x^2)} dx# from 0 to 1?
  
• How do you find the domain and range of #f(x)=1/(x+3)#?
  
• A line segment is bisected by a line with the equation # 4 y - 3 x = 2 #. If one end of the line segment is at #( 7 , 5 )#, where is the other end?
  
• Can you construct a triangle that has side lengths 8 m, 10 m, and 19 m?
  
• How do you find the limit of #sec3xcos5x# as x approaches pi/2 from the left?
  
• How do you find the 7th term of 2(sqrt{5}), 4(sqrt{5}), 6(sqrt{5}), ...?
  
• If #f(x)=1/(x+1)# how do you evaluate #(f(x+h)-f(x))/h#?
  
• There are 3 red and 8 green balls in a bag. If you randomly choose balls one at a time, with replacement, what is the probability of choosing 2 red balls and then 1 green ball?
  
• In a class of 300 students, 242 take math, 208 take science, and 183 take both math and science. How many students take neither math nor science?
  
• How do you integrate #e^x*cos(x)#?
  
• How do you implicitly differentiate #-1=(x+y)^2-xy-e^(3x+7y) #?
  
• How do you find the derivative of #Y= (e^x-e^-x)/(e^x+e^-x)#?
  
• Question #3e542
  
• Let #a,b,c,m# and #n# be integers such that #m<n# and define the quadratic function #f(x) = ax^2+bx+c# where #x# is real. Then #f(x)# has a graph that contains the points #(m,0)# and #(n, 2016^2)#. How many values of #n-m# are possible?
  
• How do you solve #3|2y-5|=27# and find any extraneous solutions?
  
• How do you solve #(e-2)/2=(e+2)/3#?
  
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