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A. Radius = height

A cylindrical container open at the top with a mirfmum surface area at a given volume. What is the relationship of its radius to height? A. Radius = height B. Radius = 2height C. Radius = height/2 D. Radius = 3 height

C. equal to the other

When two lines are parallel, the slope of one is: A. equal to the negative of the other B. equal to the reciprocal of the other C. equal to the other D. equal to the negative reciprocal of the other*

D. equal to the negative reciprocal of the other

When two lines are perpendicular, the slope of one is: A. equal to the negative of the other B. equal to the reciprocal of the other C. equal to the other D. equal to the negative reciprocal of the other

B. (0, -a/a16)

find the centroid of the solid generated when the area bounded by the first quadrant arc of x^2 + y^2 = a^2 and the fourth quadrant arc of 2x - y = 2a and x = 0 is revolved about x = 0. A. (0, a/3) B. (0, -a/a16)* C.(0, -a/3) D. (0, -a/4)

B. (11,-20)

The segment from (-1,4) to (2,-2) is extended three times its own length. The terminal point is: A. (11,-18) B. (11,-20) C. (11,-24) D. (-11,-20)

B. Concentric

Two circles with different radius but with the same center re called___circles. A. Eccentric B. Concentric C. Symmetric D. Tangent

A. Hyperbola

The general equation of the conic is Ax^2 +Bxy +Cy^2 +Dx +By +F=0. fI B^2 - 4AC > 0, the equation describes a A. Hyperbola B. Circle C. Parabola D. ellipse

B. square root (x" + y") + y = C

Solve [y - square root of (x* + y")]dx + xdy = 0 A. square root (x" + y" + y) = C B. square root (x" + y") + y = C* C. square root (x" -y") + y = C D. square root (x + y) + y = C

D.（1⼟ 7）/5

Solve the equation 5z" + 2z + 10 = 0 A. 1 - i, 1 - 2i B. 1 + i, 1 - 2i C. 1 + i, 1 - 2i D.（1⼟ 7）/5

С. у2 = сх

Solve the equation y' = y/2x. A. y2 = cx3 В. у = сх2 С. у2 = сх D. y = cx

C. xy" - (y') 3- y' = 0

Determine the differential equation of the family of circles with center at the y-axis. A. yx" - (y')3 - x' = 0 B.yx''ー（x')3ーy=0 C. xy" - (y') 3- y' = 0 D.yx" - (x')3 - y' = 0

B. 4 units

Determine the radius of the sphere whose equation is x2 + y2 + z2 - 2x + 8y + 16x + 65 = 0. A. 5 units B. 4 units C. 3 units D. 6 units

B. In 4

Evaluate the integral of 1/x - y) dxdy with inner bounds of 2y to 3y and outer bounds of 0 to 2. A. In 2 B. In 4* C. In 1/2 D. In 3

D. 2 sqrt. of 2

Find the minimum distance from the point (4, 2) to the parabola y2 = 8x. A. 3 sqrt. of 3 B. 2 sqrt. of 3 C. 3 sqrt. of 2 D. 2 sqrt. of 2

D. Point of inflection

It is a point in a polynomial curve where the concavity cannot be determined and the second derivative of y wrt x is equal to zero. A.Maximum point B.Minimum point C. Critical point D. Point of inflection

A. g(x) =cx

Listed below are functions each denoted g(x) and each involving a real number , constant c > .1 fI f(x) = 2*. which of these functions yield the greatest value for f(g(x), for all x > 1? A. g(x) =cx B. g(x) = c/x C. g(x) = c - x D. g(x) =x/C