### Geometry

Would like more details and explanations as to how the attached graph is solved. Create a graph with four odd vertices. See attached file for full problem description.

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Would like more details and explanations as to how the attached graph is solved. Create a graph with four odd vertices. See attached file for full problem description.

Formalizing Proofs. See attached files for full problem description.

51. Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. Describe and sketch the surface. 4. z = 4 - x^2 8. x^2 ? y^2 = 1

Please see the attachment for the proper formatting and related diagrams. 1. DEF and GHI are complementary angles and GHI is eight times as large as DEF. Determine the measure of each angle. 2. If line p and q are parallel, find the measure of angle 2 3. (Using ABC, find the following: a) The length of s

R is bounded below by the x-axis and above by the curve y=2cosx, 0 <= x <= Pi/2. Find the volume of the solid generated by the revolving R around the y-axis by the methods of cylindrical shells.

1) Show that for n less than or equal to 4, any Latin square of order n can be obtained from the multiplication table of a group by permuting rows, columns, and symbols. Show that this is not true for n=5 2) If n is an order for which mutually orthogonal Latin squares exist, does every Latin square of order n have an orthogo

Find the dimensions of the trapezoid of greatest area with longer base on the x axis and its other two vertices above the x axis and on the graph of 4y = 16 - x^2. keywords: trapezium, trapezoids

The symmetric difference of two sets A and B, denoted by A Δ B, is defined by A Δ B = ( A - B ) U ( B - A ); it is thus the union of their differences in opposite orders. Show that A Δ ( B Δ C ) = ( A Δ B ) Δ C.

1. Show that affine algebraic sets satisfy the axioms for the closed sets of a topology, i.e. show that the intersection of an arbitrary collection of algebraic sets is algebraic and the union of two algebraic sets is algebraic.

Find the dimensions of a rectangle that has an area equal to its perimeter.

An outfielder throws a ball at a speed of 75 mph to the catcher who is 200 feet away. At what angle of elevation was the ball thrown? See attached formula.

Find the volume of the solid generated by the revolution of a curve around an axis

The width of an open box is half its height and its surface area is 75 cm3. Find the dimensions to maximize its volume. Indicate which of the following functions satisfies the conditions of the mean value theorem on the given interval.

Find the equation of the tangent plane to the surface xy + yz + zx = 3 at the point (1,1,1)

Find the area of the parallelogram with vertices (1,2,2), (1,3,6), (3,8,6), and (3,7,3)

Given P is any point in the interior of the rectangle ABCD. Show BP^2 + PD^2 = AP^2 + CP^2. Is the result the same when P in the exterior of the rectangle? keywords: vertex

The region in the first quadrant bounded by the graphs of y = x and y = x^2/2 is rotated around the line y=x. Find (a) the centroid of the region and (b) the volume of the solid of revolution.

Using the method of cylindrical shells to find the volume of the solid rotated about the line x=(-1) given the conditions: y=x^3 -x^2;y=0;x=0.

A guy wire (a type of support used for example, on radio antennas) is attached to the top of a 50 foot pole and stretched to a point that is d feet from the bottom of the pole. Express the angle of inclination as a function of d.

I need to find the dimensions of a box to fit a #5 size soccer ball that weighs 14 to 16 ounces and has a circumference of 27 to 28 inches. Then I need to find the amount of wrapping paper I would need to wrap the above box.

Find an equation of the tangent plane to the parametric surface x = -1rcos(theta), y = -5rsin(theta), z = r at the point (-1sqrt(2), -5 sqrt(2), 2), when r = 2 and theta = pi/4.

Sketch the graph of the following functions. Find all vertical and horizontal asymptotes of the graph of each function. Determine intervals of increasing and decreasing, determine concavity, and locate all critical points and points of inflection. Show all special features such as cusps or vertical tangents. See attached file

A) Let z1 and z2 be two points on a circle C. Let z3 and z4 be symmetric with respect to the circle. Show that the cross ratio (z1,z2,z3,z4) has absolute value 1. b)Let ad-bc=1, c not zero and consider T(z)=(az+b)/(cz+d). Show that it increases lengths and areas inside the circle|cz+d|=1 and decreases lengths and areas outsid

1. a) Let z1,z2,z3,z4 lie on a circle. Show that z1,z3,z4 and z2,z3,z4 determine the same orientation iff (z1,z2,z,3,z4)>0 b) Let z1,z2,z3,z4 lie on a circle and be consecutive vertices of a quadrilateral. Prove that |z1-z3|*|z2-z4|=|z1-z2|*|z3-z4|+|z2-z3|*|z1-z4|

Volume of a solid generated by the rotating the region formed by the graphs - y= x^2 , y =2, x = 0

Projective Geometry Problem 1 i. Prove that a set of four points in a projective plane P (i.e. dim P = 2) form a projective frame if and only if no three of the points are collinear, i.e. no three lie on the same projective line. ii. Find a necessary and sufficient condition for five points to form a projective frame in a t

Verify the divergence theorem (∫∫ (F.n) ds = ∫∫∫ (grad.F) dV) for the following two cases: a. F = er r + ez z and r = i x + j y where s is the surface of the quarter cylinder of radius R and height h shown in the diagram below. b. F = er r^2 and r = i x + j y + k z where s is the surface of th

I have a circle with a circumference of 160' with an additonal circumference 12' outside of that. I need to know the length of the second circumference. Does that make sense?

Problem: Find the volume of the solid that is generated by rotating the region formed by the graphs of y = 2x^2 and y = 4x about the line x = 3.

Refer to circle A at right, which has radius 12. 1. Find the circumference Full problem in attached file.