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Geometry and Topology

Geometry -- Rectangle

Q: If you have a string of Christmas lights that is 100 feet long, and, you want to hang it in the form of a rectangle that its length is twice its width or more; what is the range of the width? [Hint: This means that we need the lowest and highest values that the width can be.]

Geometry : Distance Function

Prove or disprove: If d0 and d1 are distance functions on S, s is > or = to 0 and t > 0 then sd0 +td1 is also a distance function on S.

Find the Volume of a Sphere with a Cylindrical Hole

#26 Please see the attached file for full problem description. (a) A cylindrical drill with radius r1 is used to bore a hole through the center of a sphere of radius r2. Find the volume of the ring-shaped solid that remains. (b) Express the volume in terms of height (h).

Finding Height of a Cone Given Radius and Volume

A soft- drink cup is in the shape of a right circular cone with a capacity of 250 millilitres. The radius of the circular base is five centimetres. How deep is the cup? (1 millilitre = 1 cubic centimetre). (Explain your answer).

Metric geometry

In the taxi-cab plane show that ifA=(-5/2,2),B=(1/2,2), C=(2,2), P=(0,0), Q=(2,1) and R=(3,3/2)then A-B-C and P-Q-R. Show that line segment AB~to line segment PQ,line segment BC~line segmentQR, line segment AC~line segment PR. Sketch an appropriate picture.

Circumference and Area of a Circle

Information is given about a circle in the following table. Fill in the missing entries of the table, and show how you come up with the answer. r=radius, d=diameter,C= circumference,A=area. Give answers to two decimal places. r d C A 231.04(symbol is pi)

Phase angle

Phase angle 15.18 degrees. What is this value in radians?

Calculating circumference

A circular well is 5 feet in diameter. What is the circumference of the circular plastic cover that fits exactly over the well (to the nearest hunderedth)

Volume of Ellipsoid

Find the volume of the ellipsoid formed by rotating the semi-ellipse (see attached word file) about the x axis.

Rotation Problem for Calc II

A)Find the center of mass with constant density of the region bound by y=x5, y=2-x4 and the y axis; b)Rotate it about the y axis and find its volume; c) Rotate it about the x axis and find its volume.

Area of a quadrilateral

What is the area of a quadrilateral with sides of length 16, 12, 15, and 25, and a right angle between the sides with lengths 16 and 12?

Geometric constructions

USING ONLY AN UNMARKED STRAIGHT EDGE AND A COMPASS CONSTRUCT THE FOLLOWING: (A) A RHOMBUS GIVEN: ONE SIDE AND ONE ANGLE (B) A PARALLELOGRAM GIVEN: TWO ADJACENT SIDES AND THE INCLUDED ANGLE (C) A PARALELLOGRAM GIVEN: THE DIAGONALS AND THE ANGLE BETWEEN THEM ********I NEED STEP-BY-STEP INSTRUCTIONS ON HOW TO CONSTRUCT

Proving a Set E is Compact

Please see the attached file for the fully formatted problems. Let lambda n be a real decreasing sequence converging to Prove E is compact if and only if = 0. I am assuming compactness here refers to the sequential compactness. This seems to make the most sense. Since this problem is an analysis problem, please be

Construct a geometric model using axioms

Construct a model that satisfies the following axioms. - 1. There exists at least 1 line. - 2. Every line of the geometry has exactly 4 points on it. - 3. Not all points of the geometry are on the same line. - 4. Each point of the geometry is contained in exactly 3 lines. - 5. Every pair of lines intersect and their interse

Maximum volume

Find the maximum possible volume of a rectangular box if the sum of the lengths of its 12 edges is 6 meters.

Transformation Geometry Proofs : Reflections

Please see the attached file for the fully formatted problems. Let l, m, n be distinct lines and P, Q, R be distinct points. Prove the following: (a) sigma l sigma m = sigma m sigma l if and only if l perpendicular to m. (b) sigma p sigma m = sigma m sigma p if and only if P E m. plus three more questions

Creating the formula to find the dimensions of a cube.

In Metric. Three college students are trapped in deep snow in northern Canada. To survive they must build an igloo using snow large enough for all of them to fit and small enough to not exceed their strength and stamina. Luckily one of them is a math major and quickly formulates the dimensions of the blocks they need to cu

Comparing Areas

Calculate AREA of Shape 1 then calculate the area of Re-arranged Shape 1. Did you get the same result? Why are they different? Please see the attached document.