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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