Answers created by Salvatore I.

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Question #1a166
What is the maximum value of $\frac{3 - cos x}{1 + cos x}$ $(3-cosx)/(1+cosx)$ for $0 < x < (2 π)$ $0< x < (2pi)$ ?
How do you differentiate $H (x) = {(x + x^{- 1})}^{3}$ $H(x)=(x+x^-1)^3$ ?
How do you find the exact value of $\frac{sin 2 θ}{1 + cos 2 θ} = 4$ $(sin2theta)/(1+cos2theta)=4$ in the interval $0 \leq θ < 2 π$ $0<=theta<2pi$ ?
A cone has a height of $9 c m$ $9 cm$ and its base has a radius of $8 c m$ $8 cm$ . If the cone is horizontally cut into two segments $2 c m$ $2 cm$ from the base, what would the surface area of the bottom segment be?
How do you calculate ${tan}^{- 1} (- \frac{1}{2})$ $tan ^-1 (-1/2)$ ?
How do you determine all solutions for the equation $2 {sin}^{2} θ = 1 - sin θ$ $2sin^2theta=1-sintheta$ in the domain $0^{\circ} \leq θ < 360^{\circ}$ $0^circ<=theta<360^circ$ ?
How do you evaluate $arctan (\frac{2}{5})$ $arctan(2/5)$ ?
How do you use the remainder theorem to find the remainder for each division $(x^{3} - x + 6) \div (x - 2)$ $(x^3-x+6)div(x-2)$ ?
How do you convert $r (2 + cos θ) = 1$ $r(2 + cos theta) = 1$ into cartesian form?
How do you find the derivative of $sin (x cos x)$ $sin(x cos x)$ ?
A line segment has endpoints at $(1, 6)$ $(1 ,6 )$ and $(5, 2)$ $(5 ,2 )$ . The line segment is dilated by a factor of $4$ $4$ around $(2, 1)$ $(2 ,1 )$ . What are the new endpoints and length of the line segment?
Circle A has a radius of $1$ $1$ and a center at $(3, 3)$ $(3 ,3 )$ . Circle B has a radius of $3$ $3$ and a center at $(6, 4)$ $(6 ,4 )$ . If circle B is translated by $< - 3, 4 >$ $<-3 ,4 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?
How do you divide $\frac{8 g^{3} - 6 g^{2} + 3 g + 5}{2 g + 3}$ $(8g^3-6g^2+3g+5)/(2g+3)$ ?
How do you use the angle sum or difference identity to find the exact value of $cos (\frac{7 π}{12})$ $cos((7pi)/12)$ ?
A triangle has sides A, B, and C. Sides A and B are of lengths $7$ $7$ and $4$ $4$ , respectively, and the angle between A and B is $\frac{π}{6}$ $pi/6$ . What is the length of side C?
Differential Calculus Word Problem?
How do you find the value of $cot (\frac{2 π}{3})$ $cot ((2pi)/3)$ using the double angle or half angle identity?
How do you find the volume of a solid that is enclosed by $y = 3 x^{2}$ $y=3x^2$ and y=2x+1 revolved about the x axis?
How do you determine dy/dx given $x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}$ $x^(2/3)+y^(2/3)=a^(2/3)$ ?
What is the slope of the tangent line of $r = θ cos (\frac{θ}{4} - \frac{5 π}{3})$ $r=thetacos(theta/4-(5pi)/3)$ at $θ = \frac{π}{3}$ $theta=(pi)/3$ ?
A parallelogram has sides with lengths of $24$ $24$ and $9$ $9$ . If the parallelogram's area is $54$ $54$ , what is the length of its longest diagonal?
What is the derivative of $sec ((x^{2}) + 3 x)$ $sec((x^2)+3x)$ ?
How do you solve $7 e^{x} = 9 - e^{- x}$ $7e^{x} = 9- e^{- x}$ ?
Question #bcaa7
How do you write the following in trigonometric form and perform the operation given $\frac{3 + 4 i}{1 - \sqrt{3} i}$ $(3+4i)/(1-sqrt3i)$ ?
How do you find the sum of the geometric series $1/16+1/4+1+...$ to 7 terms?
How do you find $f^{-1}(c)$ if $f(x)= 5x + 8 x^{11}$ ; c = -13?
How do you integrate $f(x)=3^xe^(-x+1)$ using the product rule?
Question #3e769
How do you simplify the expression $cos(arctan(x/5))$ ?
How do you find the 4rd root of $81e^(60i)$ ?
How do you convert $4sqrt3-4i$ to polar form?
How do you find all solutions to $x^4-i=0$ ?
How do you graph the polar equation $r^2=9sin2theta$ ?
If $A= <4, 3 ,-1 >$ and $B= <9 ,7 ,6 >$ , what is $A*B -||A|| ||B||$ ?
How do you find the polar equation for $3x-2y=1$ ?
How do you find the derivative of $g(t)=t^2 2^t$ ?
The sum of two consecutive even integers is -102. What are the two integers?
How do you solve $(x-4)/(x+3)>0$ ?
How do you solve the quadratic with complex numbers given $8x^2-4x+5=0$ ?
How do you simplify $n!(n+1)$ ?
What is the center and radius of the circle with equation $x^2 + y^2 – 8x – 20y + 80 = 0$ ?
How do you find the antiderivative of $f(x) = 1 / (5cos^2(5x))$ ?
A triangle has sides A, B, and C. Sides A and B are of lengths $3$ and $9$ , respectively, and the angle between A and B is $pi/6$ . What is the length of side C?
A triangle has two corners with angles of $( pi ) / 3$ and $( pi )/ 6$ . If one side of the triangle has a length of $1$ , what is the largest possible area of the triangle?
How do you find the volume bounded by $y=e^x$ and the lines y=0, x=1, x=2 revolved about the y-axis?
A line segment has endpoints at $(7 ,8 )$ and $(3 ,5 )$ . If the line segment is rotated about the origin by $(3 pi)/2$ , translated vertically by $-2$ , and reflected about the y-axis, what will the line segment's new endpoints be?
What is the vertex form of $y= (x-14)(3x+4)-x^2+2x$ ?
How do you find the area between $y=x^2$ and $y=8x$ ?
What is the instantaneous velocity of an object moving in accordance to $f(t)= (sin2tcost,tant-sect )$ at $t=(13pi)/12$ ?
A circle has a center that falls on the line $y = 8/7x +2$ and passes through $( 2 ,1 )$ and $(3 ,6 )$ . What is the equation of the circle?
Twice the sum of 3 times a number and 60 is 155 greater than the opposite of the number. What is the number?
Question #57267
Without solving, how do you determine the number of solutions for the equation $sintheta=sqrt3/2$ in $0<=theta<2pi$ ?
How do you simplify the expression $(1+costheta)(csctheta-cottheta)$ ?
How do you find the slope of a tangent line to the graph of the function $f(x)= -3x^2+2$ at (3, -25)?
An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the lengths of the top. The prism's height is $15$ , the cap's height is $8$ , and the cap's radius is $9$ . What is the object's volume?
A circle's center is at $(7 ,4 )$ and it passes through $(8 ,2 )$ . What is the length of an arc covering $( pi ) /6$ radians on the circle?
How do you find the exact solutions to the system $x^2+y^2=36$ and $y=x+2$ ?
Question #40e1d
How do you find the Vertical, Horizontal, and Oblique Asymptote given $(8x-48)/(x^2-13x+42)$ ?
A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 14, respectively. The angle between A and C is $(17pi)/24$ and the angle between B and C is $(pi)24$ . What is the area of the triangle?
How do you compute the 9th derivative of: $arctan((x^3)/2)$ at x=0 using a maclaurin series?
What are the three consecutive odd integers with a sum of 117?
What is the Cartesian form of $r = -sintheta+4csc^2theta$ ?
Juan read for 5/6 of an hour. Larissa read for 10/12 of an hour. Who read for a longer period of time?
How do you solve the system of equations $8x - 7y = - 5$ and $- 4x + 3y = 1$ ?
A line segment is bisected by a line with the equation $- 6 y + 2 x = 4$ . If one end of the line segment is at $( 4 , 8 )$ , where is the other end?
How do you evaluate $e^( ( pi)/4 i) - e^( ( 5 pi)/4 i)$ using trigonometric functions?
How do you find the roots of $4x^3-12x^2-x+3=0$ ?
How do you solve the system of equations $-5x + y = 18$ and $5x + 5y = - 30$ ?
Two corners of an isosceles triangle are at $(9 ,2 )$ and $(4 ,7 )$ . If the triangle's area is $64$ , what are the lengths of the triangle's sides?
How do you use the first and second derivatives to sketch $f(x) = (x+1)e^x$ ?
What is the equation of the line tangent to $f(x)=x^2/e^x-x/e^(x^2)$ at $x=0$ ?
How do you find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle?
How do you find parametric equations for the path of a particle that moves around the given circle $x^2 + (y – 2)^2 = 4$ clockwise, starting at (2, 2)?
What are the points of inflection, if any, of $f(x)=x^(1/3)e^(3x)$ ?
The base of a triangular pyramid is a triangle with corners at $(2 ,5 )$ , $(6 ,3 )$ , and $(7 ,8 )$ . If the pyramid has a height of $15$ , what is the pyramid's volume?
What is the net area between $f(x) = 1/sqrt(x^2+2x+1)$ and the x-axis over $x in [2, 4 ]$ ?