Answers created by maganbhai P.

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• How do you find the derivative of #cos(pi x)#?
  
• How do you write an equation for a circle whose diameter has endpoints of (-2, 4) and (4, 12)?
  
• How do you write an equation for a circle whose diameter has endpoints of (-2, 4) and (4, 12)?
  
• What is the derivative of #sin(arccos x)#?
  
• What is the derivative of #sin(arccos x)#?
  
• What is the scalar product of -2i+3j+4k and 5i-3j+3k, where I, j and k are the Cartesian unit vectors? answers given A,-15. B,-10. C, -7. D, 7. E, 10. ?
  
• How do you integrate #sqrt(4x² + 1)#?
  
• Find the integral of 4x/ (x^2 - 4 )(x-3) dx ?
  
• What is the sum of the geometric sequence -3, 18, -108, … if there are 7 terms?
  
• How do you integrate #sqrt(4x² + 1)#?
  
• How do you solve #\log_{3} ( 2x + 1) = \log_{3} ( 3x - 6)#?
  
• How do you solve #lim_x->pi/4 (tanx-cotx)/(x-pi/4)# ?
  
• How do you solve #log_5x=3#?
  
• How do you use the definition of a derivative to find the derivative of #f(x)=x^3-2x^2+5x-6#?
  
• Let #f(x)=1-x# and #g(x)= x^2# and #h(x)= 1/x#, how do you find #f(g(x))#?
  
• If #a^2 - 6b^2 - ab = 0#, what is value of #b/a# ?
  
• A triangle has corners A, B, and C located at #(4 ,5 )#, #(3 ,6 )#, and #(8 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
  
• How do you divide #(-18a+3a^3+9+6a^2)div(-3+3a)# using synthetic division?
  
• How do you solve #1-sin(theta)=cos2(theta)#?
  
• What is the equation of the line that passes through (#5, -2)# and #(3, 4)#?
  
• If #f(x) =x^(-1/3)#, what is the derivative of the inverse of f(x)?
  
• How do you solve this system of equations using the substitution method #x- y = 1 and 4x + 9y = - 87#?
  
• In triangle ABC, if #a = 8.75# centimeters, #c = 4.26# centimeters, and #m/_B# is #87°# what is the length of #b# to two decimal places?
  
• How do you divide #(x^4-2x^2+10)/(x-1)# using long division? What is the quotient and remainder?
  
• How do you use polynomial synthetic division to divide #(x^4-6x^2+9)div(x-sqrt3)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
  
• How do you show that #(3+sqrt2)/(5+sqrt8)# can be written to #(11-sqrt2)/17#?
  
• How do you evaluate #\frac{z ^ { 3} + 0z ^ { 2} - z + 42}{z - 7}#?
  
• How do you differentiate #f(x)= x^3 (1-3x^2)^4 # using the product rule?
  
• How do you divide #(x^3-8x+3)div(x+3)# using synthetic division?
  
• How do you divide #(x^3+15x^2+45x-25)div(x+5)# using synthetic division?
  
• If #alpha=(1/2)(-1+sqrt(-3)) and beta=(1/2)(-1-sqrt(-3))# then prove #alpha^4+(alphabeta)^2+beta^4=0#?
  
• How do you prove sin3θ = 3cos^2θ sinθ -sin^3θ ?
  
• Find y' in these 2 equations?
  
• Find y' in these 2 equations?
  
• If sin square theta-cos square theta=2-5cos theta then what is the value of theta?
  
• How do you use the chain rule to differentiate #log_(13)cscx#?
  
• Given #log_a 2 =4, log_a 3 =5#, and #log_a 11 = 8#, what is #log_a (33)/(2a^3)#?
  
• How do you solve the following system?: # 3x +2y =2 , 2x +y = -2#
  
• How do find the quotient of #(2x^3 − 3x 2 + x − 6) ÷ (x − 4)#?
  
• At least how many terms in the GP 20+28+36+.... is greater than 1000 ?
  
• How do you differentiate # f(x)=e^sqrt(1/x^2-x)# using the chain rule.?
  
• A triangle has corners at #(5 ,8 )#, #(2 ,6 )#, and #(7 ,3 )#. What is the area of the triangle's circumscribed circle?
  
• If #logx/(a^2+ab+b^2)=log y/(b^2+bc+c^2)=log z/(c^2+ca+a^2)# then find #x^(a-b)* y^(b-c)*z^(c-a)=#?
  
• How do you solve the system by graphing #y = 2x + 1# and #y = 2x - 2#?
  
• How do you write the expression as the sine, cosine, or tangent of the angle given #cos45^circcos120^circ-sin45^circsin120^circ#?
  
• IN any triangle ABC,#sinA-cosB=cosC# then angle B is?
  
• How do you solve #\frac { 1} { 2} ( 1+ \frac { 1} { x } ) - 2= \frac { 1- x } { x }#?
  
• What are the next three terms of the sequence 1, -3, 9, -27,…?
  
• The value of #sin20.sin40.sin60.sin80# is?
  
• How do you write the first five terms of the sequence #a_n=3n+1#?
  
• How do you simplify #(2-2i)^2#?
  
• How do you prove #sinx/(1-cosx) + (1-cosx)/sinx = 2csc x#?
  
• What are the center and foci of the ellipse described by #x^2/9 + y^2/16 =1#?
  
• What are the center and foci of the ellipse described by #x^2/9 + y^2/16 =1#?
  
• How do you multiply (x-1)(x+1)(x+2)?
  
• How do you simplify #6^2 / (6^-4 x 5^1)^-2#?
  
• How do you divide #(8v^5+43v^4+5v+20)div(v+4)# using synthetic division?
  
• What is the derivative of this function #y=cot^-1(sqrt(x-1))#?
  
• How do you find the integral of #arccos(x)x#?
  
• How do you solve #2 ln (7x) = 4#?
  
• #a# i s The arithmetic mean of two positive numbers #b and c# . #G_1# and #G_2# are the geometric mean between the same positive numbers #b and c# so prove that #G_1^3+G_2^3#=#2abc# ?
  
• Can you Solve [(2)^2 cos^2(x) - √(3) cos(x) = 0] on the interval 0˚< x < 360?
  
• How do you convert #-3+1i# to polar form?
  
• How can #(sin^2(-x))/(tan^2(x))# equal to #cos^2x#?
  
• What is the area of a parallelogram with vertices (2,5), (5, 10), (10, 15), and (7, 10)?
  
• For what value of k will the equation #12x^2-10xy+2y^2+11x-5y+k=0# represent a pair of lines?
  
• How do you solve #log(x^2+4)-log(x+2)=2+log(x-2)#?
  
• How do you divide #(2x^3+2x^2+4x+4)/(x^2+8x+4)#?
  
• How do I evaluate the integral #intsqrt(54+9x^2)dx#?
  
• What is the derivative of #e^(-x)#?
  
• How do you find all the real and complex roots of #3x^2 - x + 2 = 0#?
  
• How do you evaluate #(4x^{-12}y^{10})(6x^{4}y^{3})#?
  
• Find the area of the parallelogram whose vertices are (-5,3) (8,6) (1,-4) and (14,-1) ?
  
• How do solve the following linear system?: # x+2y=1 , 3x-y=3 #?
  
• How do you simplify #(8n-3)/(n^2+8n+12)-(5n-9)/(n^2+8n+12)#?
  
• If #A= <3 ,1 ,-2 ># and #B= <4 ,-2 ,3 >#, what is #A*B -||A|| ||B||#?
  
• If nth term of a series is 1/2 ×n(n+1) then find the sum of n terms of the series ?
  
• How do you integrate #int sin(lnx) dx#?
  
• If #A = <5 ,2 ,-5 >#, #B = <6 ,5 ,3 ># and #C=A-B#, what is the angle between A and C?
  
• Prove #|(1,a,a^2,a^3+bcd),(1,b,b^2,b^3+cda),(1,c,c^2,c^3+dab),(1,d,d^2,d^3+abc)|=0#?
  
• If #0<= aplha,beta <= 90# and #tan(alpha+beta)=3# and #tan(alpha-beta)=2# then value of #sin(2alpha)# is?
  
• Prove #|(1,cosx-sinx,cosx+sinx),(1,cosy-siny,cosy+siny),(1,cosz-sinz,cosz+sinz)| =2*|(1,cosx,sinx),(1,cosy,siny),(1,cosz,sinz)|#?
  
• How could I turn 2sin5xcos3x into a sum of trig functions?
  
• Solve for x in #|(3+x,5,2),(11-3x,17,16),(7-x,14,13)| = 0#?
  
• Show that #|(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=-2(a^3+b^3+c^3-3abc#?
  
• The sum of two numbers is 37. Their product is 312. What are the numbers?
  
• How do you find the mean, median, and mode of the following frequency distribution table?
  
• How do you find the exact value in radians without using a calculator #cos^-1 (1/2)#?
  
• How do you solve #2/(x+1) + 5/(x-2)=-2#?
  
• How do find the quotient of #(10b^2 + b - 1)/(2b + 3)#?
  
• How do you integrate #int x/sqrt(4x^2+4x+-24)dx# using trigonometric substitution?
  
• How do you evaluate the expression #tan(u-v)# given #sinu=3/5# with #pi/2<u<p# and #cosv=-5/6# with #pi<v<(3pi)/2#?
  
• How do you integrate #int (x^2-1)/sqrt(x^2+9)dx# using trigonometric substitution?
  
• How to use the limit definition (Riemann sum) to evaluate the following integral ?
  
• How do you solve #\sqrt { 2a + 5} - 2\sqrt { 2a } = 1#?
  
• How do you divide #(x^2 + 7x – 6) / (x-6) # using polynomial long division?
  
• How do you solve #\frac { 4x + 3} { 15} - \frac { 2x - 3} { 9} = \frac { 6x + 4} { 6} - x#?
  
• How do you use the sum or difference identities to find the exact value of #sin165^circ#?
  
• Are the set of points A (3, 0), B(-2, 10), C(0, 5) are collinear?
  
• What is the orthocenter of a triangle with corners at #(1 ,3 )#, #(6 ,9 )#, and (2 ,4 )#?
  
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