MathDB

2013 General Problem 6

Source:

2/4/2013

Nick is a runner, and his goal is to complete four laps around a circuit at an average speed of 10 mph. If he completes the first three laps at a constant speed of only 9 mph, what speed does he need to maintain in miles per hour on the fourth lap to achieve his goal?

SMT 2013 Calculus #6

Source:

2/3/2013

Compute

\sum_{k=0}^{\infty}\int_{0}^{\frac{\pi}{3}}\sin^{2k} x \, dx

.

calculusintegrationtrigonometrygeometric series

2013 SMT Geometry #6

Source:

11/2/2014

ABCD

is a rectangle with

AB = CD = 2

. A circle centered at

O

is tangent to

BC

,

CD

, and

AD

(and hence has radius

1

). Another circle, centered at

P

, is tangent to circle

O

at point

T

and is also tangent to

AB

and

BC

. If line

AT

is tangent to both circles at

T

, find the radius of circle

P

.

geometryrectangle

SMT 2013 Algebra #6

Source:

2/3/2013

Compute the largest root of

x^4-x^3-5x^2+2x+6

.

algebrapolynomial

SMT 2013 Team #6

Source:

2/4/2013

How many distinct sets of

5

distinct positive integers

A

satisfy the property that for any positive integer

x\le 29

, a subset of

A

sums to

x

?

SMT 2013 Advanced Topics #6

Source:

12/31/2016

A positive integer

b\geq 2

is neat if and only if there exist positive base-

b

digits

x

and

y

(that is,

x

and

y

are integers,

0<x<b

and

0<y<b

) such that the number

x.y

base

b

(that is,

x+\tfrac yb

) is an integer multiple of

x/y

. Find the number of neat integers less than or equal to

100

.

2013Advanced Topics

6

Problems(6)