MathDB

Problems(5)

2015 Algebra #7

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7/1/2022
Compute the minimum value of x4+2x3+3x2+2x+10x2+x+1\frac{x^4+2x^3+3x^2+2x+10}{x^2+x+1} where xx can be any real number.
2015Algebra Test
2015 Advanced #7

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7/8/2022
What is the largest integer nn such that nn is divisible by every integer less than n3\sqrt[3]{n}?
2015Advanced Topics Test
2015 Guts #7

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7/28/2022
The Yamaimo family is moving to a new house, so they’ve packed their belongings into boxes, which weigh 100 kg100\text{ kg} in total. Mr. Yamaimo realizes that 99%99\% of the weight of the boxes is due to books. Later, the family unpacks some of the books (and nothing else). Mr. Yamaimo notices that now only 95%95\% of the weight of the boxes is due to books. How much do the boxes weigh now in kilograms?
2015Guts Test
2015 Geometry #7

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7/1/2022
In a rectangle ABCDABCD, two segments EGEG and FHFH divide it into four smaller rectangles. BHBH intersects EGEG at XX, CXCX intersects HFHF and YY, DYDY intersects EGEG at ZZ. Given that AH=4AH=4, HD=6HD=6, AE=4AE=4, and EB=5EB=5, find the area of quadrilateral HXYZHXYZ.
2015Geometry Test
2015 Team #7

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8/3/2022
Nine identical spheres of radius rr are packed into a unit cube. One sphere is centered at the center of the cube and is tangent to the other eight spheres, each of which is located in a corner of the cube and is tangent to three faces of the cube. Compute the radius of the spheres rr.
2015team test