Monday

August 3, 2015

August 3, 2015

Total # Posts: 6,757

**Geometry**

7 points are placed in a regular hexagon with side length 20. Let m denote the distance between the two closest points. What is the maximum possible value of m?
*March 12, 2013*

**Geometry**

In distinct odd-town, the inhabitants want to number their houses with 3-digit positive integers that are odd, which have all distinct digits. What is the maximum number of houses in odd-town?
*March 12, 2013*

**Algebra**

In a certain positive fraction \frac{a}{b} , the numerator is 2 less than the denominator. If the numerator and denominator are interchanged, the fraction is increased by 1 \frac{1}{15} . Find a + b .
*March 12, 2013*

**Algebra**

How many distinct prime factors does 100100 have?
*March 12, 2013*

**Calculus**

Given f(x) = x^4 + 6x^3 - 15x + 7, evaluate \displaystyle \lim_{h \to 0} \frac{f(1+h) - f(1-h)}{h}.
*March 12, 2013*

**Calculus**

a and b are integers that satisfy: \displaystyle \lim_{x \to 1} \frac{x-1}{x^2-ax+b} = -\frac{1}{3}. What is the value of a+b?
*March 12, 2013*

**Physics**

You launch a model rocket up into the sky. Right after launch the rocket is accelerating upwards at 10~m/s^2. What is the magnitude of the net force in Newtons on the rocket if the rocket has a mass of 0.1 kg?
*March 12, 2013*

**Algebra**

Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the value of a+b?
*March 12, 2013*

**Trigonometry**

ABC is a non-degenerate triangle such that 2\sin \angle B \cdot \cos \angle C + \sin \angle C = \sin \angle A + \sin \angle B, what is the value of \lfloor 100 \frac {AC}{AB} \rfloor ?
*March 12, 2013*

**Algebra**

If f(x) = 2x + 5 and g(x) = 8-3x^2, what is the value of f(g(4)) - g(f(4))?
*March 12, 2013*

**Algebra**

How many ordered pairs of solutions (a, b) are there to \frac{a}{b} - \frac{b}{a} - \frac{2}{a} - \frac{2}{b} = 0, where a and b are integers from -100 \leq a,b \leq 100?
*March 12, 2013*

**Algebra**

What is the sum of all the possible values of a for which 25x^2 + (a-15)x + 9 has exactly one distinct real root?
*March 12, 2013*

**Algebra**

Consider all three-digit numbers that are greater than the sum of the squares of their digits by exactly 543. What are the last three digits of the sum of these numbers?
*March 12, 2013*

**Algebra**

Find the largest possible real value of \sqrt{(x-20)(y-x)} + \sqrt{(140-y)(20-x)} + \sqrt{(x-y)(y-140)} subject to -40\leq x \leq 100 and -20\leq y \leq 200.
*March 12, 2013*

**Algebra**

Let \phi(n) be the Euler Phi Function. If 1 \leq n \leq 1000, what is the smallest integer value of n that minimizes \frac{\phi(n)}{n}?
*March 12, 2013*

**Algebra**

Suppose f(x) and g(x) are non-zero polynomials with real coefficients, such that f(g(x))=f(x)\cdot g(x). If g(2)=37, what is g(3)?
*March 12, 2013*

**Algebra**

Given the system of equations \begin{cases} x(x+y) &=& 9 \\ y(x+y) &=& 16 \end{cases} the value of xy can be written as \frac{a}{b} where a and b are positive coprime integers. Find a+b.
*March 12, 2013*

**Geometry**

Let S = \{ 1, 2, 3, \ldots 12\} and T_1, T_2, \ldots T_a be subsets of S such that T_i \not \subset T_j \, \forall i \neq j . What is the maximum possible value of a?
*March 12, 2013*

**Geometry**

Determine the largest positive integer N, such that given any N-gon (not necessarily convex), there exists a line (infinitely extended in both directions) that contains exactly 1 edge of the N-gon. The figure in blue is an example of a 20-gon that doesn't satisfy the ...
*March 12, 2013*

**Geometry**

Six standard six-sided die are rolled. Let p be the probability that the dice can be arranged in a row such that for 1\leq k \leq 6 the sum of the first k dice is not a multiple of 3. Then p can be expressed as \frac{a}{b} where a and b are coprime positive integers. What is ...
*March 12, 2013*

**Math**

72 strips of wood. 8 divide 4 equal 2, and it 1 inch wide. so 36 wide. so there 36 times 2 which is 72
*March 12, 2013*

**Physic**

An aluminum ring of radius 5.00 cm and resistance 2.00 10-4 Ω is placed around the top of a long air-core solenoid with 997 turns per meter and a smaller radius of 3.00 cm, as in the figure below. If the current in the solenoid is increasing at a constant rate of 267 A/s...
*March 12, 2013*

**Physic**

A pickup truck has a width of 78.9 in. If it is traveling north at 36 m/s through a magnetic field with vertical component of 33 µT, what magnitude emf is induced between the driver and passenger sides of the truck?
*March 12, 2013*

**Math**

you multiply each number by three and it will be your denominator
*March 12, 2013*

**science**

cell membrane
*March 12, 2013*

**English**

I urgently need to prepare these sentences for tomorrow. Could you please have a look at them? 1.If they told me to clean my room, I would. 2.You’d better take the keys in case I might still be out when you come back. 3. Would all this have happened if he hadn’t ...
*March 12, 2013*

**physics**

A string under a tension of 43.0 N is used to whirl a rock in a horizontal circle of radius 2.45 m at a speed of 20.9 m/s on a frictionless surface as shown in the figure below. As the string is pulled in, the speed of the rock increases. When the string is 1.00 m long and the...
*March 12, 2013*

**Government**

In which type of colony did strict governors anger the colonists? A. the royal colonies B. the proprietary colonies C. the charter colonies D. the informed colonies
*March 12, 2013*

**SCIENCE **

when a diorite partially melts, which element(1)............ decreases in the melt as a(2).......... magma forms. I have few options to choose from a)iron b)andesite c)rhyolite d)potassium f)basalt No one has
*March 12, 2013*

**accounting**

Lifo
*March 12, 2013*

**maths**

Find the largest possible value of sqrt[(x-20)(y-x)] + sqrt[(140-y)(20-x)] + sqrt[(x-y)(y-140)] if -40<=x<=100 and -20<=y<=200
*March 12, 2013*

**Probability**

The probability that it will take 5 or more flips of a fair coin before it lands on heads can be written as a/b , where a and b are coprime positive integers. Find a+b
*March 12, 2013*

**Chemistry**

I was given extra credit to find who Le Châtelier's High School Principal was. Not his PrincipLE, but his PrincipAL. My chemistry teacher told us only one student of his out of all these years came with the answer. Think outside of the box. Thanks.
*March 11, 2013*

**SCIENCE**

when a diorite partially melts, which element(1)............ decreases in the melt as a(2).......... magma forms. I have few options to choose from a)iron b)andesite c)rhyolite d)potassium f)basalt
*March 11, 2013*

**Math**

the median was 142 I forgot a number 142 is also on my list. thank you so much for your help
*March 10, 2013*

**Math **

Dr. Jane I came up with this: 127,128,129,139,139,139,141,143,144,145,146,147,148,152 Does this seem to work?
*March 10, 2013*

**math**

make up a set of 15 numbers with the following landmarks: maximum: 152 Range: 25 Mode: 139 Median: 142
*March 10, 2013*

**Geometry**

What is the minimum distance between any point on the circle x^2 + y^2 = 25 and the line y = -\frac{3}{4}x + \frac{75}{4} ?
*March 10, 2013*

**Geometry**

In the 2001 population census, information was collected about the number of people in each household, which is denoted by X. It is given that P(X=1) = 0.25, P(X=2) = 0.32, P(X=3) = 0.18, P(X=4) = 0.15, P(X=5) = 0.07, P(X=6) = 0.02 and P(X\geq 7) = 0.01. If R is the ...
*March 10, 2013*

**Geometry**

Martin's iPod has 24 songs on it. He wants to make a playlist consisting of three songs to dance to. Let N be the number of different playlists Martin can make. What are the last 3 digits of N?
*March 10, 2013*

**Calculus**

Evaluate \displaystyle \int_1^{10} \left(\sqrt{x} + 1\right)^3 dx - \int_1^{10} \left(\sqrt{x} - 1\right)^3 dx .
*March 10, 2013*

**Trigonometry**

If g(t) = 5t+1 and h(n) = 2(n - 7), what is the value of h(g(3))?
*March 10, 2013*

**Algebra**

Find the smallest positive integer N such that 13^N \equiv 1 \pmod{2013}.
*March 10, 2013*

**Physics**

You launch a model rocket up into the sky. Right after launch the rocket is accelerating upwards at 10~m/s^2. What is the magnitude of the net force in Newtons on the rocket if the rocket has a mass of 0.1 kg?
*March 10, 2013*

**Calulus**

Given \displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \frac{b\pi^2}{c}, where a, b and c are positive integers and b and c are coprime, what is the value of a + b + c?
*March 10, 2013*

**chemistry help !!!!!!!!!!!!!!!!**

a)A N6+ ion in its ground state absorbs an X-ray photon of energy 2.0000 keV. Explain what happens to the ion and why. b)Explain why the nitrogen ion N6+ is a hydrogen-like ion. Assuming the ion is for the major stable isotope 14N, state which sub-atomic particles it contains ...
*March 10, 2013*

**SCIENCE**

when a diorite partially melts, which element(1)............ decreases in the melt as a(2).......... magma forms. I have few options to choose from a)iron b)andesite c)rhyolite d)potassium f)basalt
*March 9, 2013*

**Geometry**

Given a 100 by 100 square grid, what is the most number of 1 by 51 rectangles that we can cut out of it?
*March 9, 2013*

**Geometry**

ABCDE is a regular pentagon. FAD is an equilateral triangle, such that points F and E are on the same side of line AD. What is the measure (in degrees) of \angle FAB?
*March 9, 2013*

**Geometry**

How many perfect squares less than 1000 end with the digit 6?
*March 7, 2013*

**Geometry**

What is the minimum distance between any point on the circle x^2 + y^2 = 25 and the line y = -\frac{3}{4}x + \frac{75}{4} ?
*March 7, 2013*

**Trigonometry**

\sqrt{i} in polar form can be written as r(\cos \theta + i \sin \theta), where r is a real number and 0 \leq \theta \leq \frac{\pi}{2}. What is the measure of \theta (in degrees)?
*March 7, 2013*

**Algebra**

Out on my street, there are a certain number of pigeons sitting on telephone poles. If there were exactly 2 pigeons sitting on each telephone pole, then 1 pigeon would have no space to sit on. If there were exactly 3 pigeons sitting on each telephone pole, then there would be ...
*March 7, 2013*

**Algebra**

Out on my street, there are a certain number of pigeons sitting on telephone poles. If there were exactly 2 pigeons sitting on each telephone pole, then 1 pigeon would have no space to sit on. If there were exactly 3 pigeons sitting on each telephone pole, then there would be ...
*March 7, 2013*

**Algebra**

Out on my street, there are a certain number of pigeons sitting on telephone poles. If there were exactly 2 pigeons sitting on each telephone pole, then 1 pigeon would have no space to sit on. If there were exactly 3 pigeons sitting on each telephone pole, then there would be ...
*March 7, 2013*

**Calculus**

Evaluate \displaystyle \lim_{x \to 0} \frac{e^{44x} - 1}{x^2+2x}.
*March 7, 2013*

**Algebra**

Alan and Bob are playing with numbers. Starting with the number n=1 they take turns performing arithmetic manipulations with n. Alan goes first and always multiplies n by 3. Bob adds 1 or 2 to the number n, depending on a coin toss. A number is called reachable, if it can ...
*March 7, 2013*

**Algebra**

what is the smallest positive integer N such that 13^N \equiv 1 \pmod{2013}
*March 7, 2013*

**Algebra**

The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers.
*March 7, 2013*

**Geometry**

Circles \Gamma_1 and \Gamma_2 intersect at 2 distinct points A and B. A line l through A intersects \Gamma_1 and \Gamma_2 at C and D, respectively. Let M be the midpoint of CD. The line MB intersects \Gamma_1 and \Gamma_2 again at E and F , respectively. If MA=129, MB =156 and...
*March 7, 2013*

**Geometry**

ABCD is a convex quadrilateral satisfying AB=BC=CD, AD=DB and \angle BAD = 75^\circ. What is the measure of \angle BCD?
*March 7, 2013*

**Geometry**

Two of the heights of a triangle are 63 and 147 . Given that the third height is also an integer, what is the maximum possible value for the third height?
*March 7, 2013*

**math**

I don't understand
*March 7, 2013*

**math**

thank you, Ms.sue
*March 7, 2013*

**math **

Mike is saving money for a new bike that costs $180.00. If m represents the amount of money he has saved so far, which expression represents the amount of money, in dollars, he still needs to save? a. 180 + m b. 180 - m c. 180 ' m d. 180 . m
*March 7, 2013*

**physics**

I child with a mass of 20kg,hops on a merry go round with moment of intertia of 1000kg and radius of 7m.if it takes the child time T to move 360degrees ,relative to the ground at 6m away from the center,what is the angle covered relative to the ground
*March 7, 2013*

**Chemistry**

A 1.00 kg gold bar at 1010 K is dropped into 0.750 kg of sand at 25 °C. Assuming no heat is lost to the atmosphere, what is the final temperature of the sand?
*March 7, 2013*

**Chemistry**

A 1.00 kg gold bar at 1010 K is dropped into 0.750 kg of sand at 25 °C. Assuming no heat is lost to the atmosphere, what is the final temperature of the sand?
*March 7, 2013*

**Calculus**

Given that \displaystyle \int_0^4 x^3\sqrt{9+x^2} dx = a, what is the value of \lfloor a \rfloor?
*March 7, 2013*

**Physics**

You launch a model rocket up into the sky. Right after launch the rocket is accelerating upwards at 10~m/s^2. What is the magnitude of the net force in Newtons on the rocket if the rocket has a mass of 0.1 kg?
*March 7, 2013*

**Geometry**

ABCD is a convex quadrilateral satisfying AB=BC=CD, AD=DB and \angle BAD = 75^\circ. What is the measure of \angle BCD?
*March 7, 2013*

**Geometry**

A circle \Gamma cuts the sides of a equilateral triangle ABC at 6 distinct points. Specifically, \Gamma intersects AB at points D and E such that A, D, E, B lie in order. \Gamma intersects BC at points F and G such that B, F, G, C lie in order. \Gamma intersects CA at points H...
*March 6, 2013*

**Geometry**

Let G be a rectangular grid of unit squares with 3 rows and 8 columns. How many self-avoiding walks are there from the bottom left square of G to the top left square of G?
*March 6, 2013*

**Physics**

What must the critical angle be if light transmits from diamond into water?
*March 6, 2013*

**Physics**

A racquet ball with mass m = 0.224 kg is moving toward the wall at v = 14.8 m/s and at an angle of è = 27° with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to ...
*March 6, 2013*

**math**

simpplify. (3x)^3 (note use positive exponents only.) my answer is 27x^3
*March 5, 2013*

**language**

Those trees have (fewer, less) fruit on them.
*March 5, 2013*

**language**

Of the 2 swimmers, Dana is the (more better, best, better)
*March 5, 2013*

**Algebra**

What is \left \lfloor ( 3 + \sqrt{5} ) ^3 \right \rfloor?
*March 4, 2013*

**math**

please display graph of 2x=1 (if can be) thanks
*March 4, 2013*

**Algebra**

What are the sum of the roots of f(x) = x^2 - 16x + 63?
*March 4, 2013*

**Algebra**

The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers.
*March 4, 2013*

**Algebra**

Find the number of integer quadruples (a,b,c,d) with 0\leq a,b,c,d \leq 100, such that a and b are the roots of the quadratic equation x^2-cx+d=0, while c and d are the roots of the quadratic equation x^2-ax+b
*March 4, 2013*

**Algebra**

x and y satisfy 2^x = 5 and 5 ^ y = 64. What is the value of xy?
*March 4, 2013*

**Algebra**

How many integer values of x are there such that |x-3| + 5 < 16 ?
*March 4, 2013*

**Algebra**

Alan and Bob are playing with numbers. Starting with the number n=1 they take turns performing arithmetic manipulations with n. Alan goes first and always multiplies n by 3. Bob adds 1 or 2 to the number n, depending on a coin toss. A number is called reachable, if it can ...
*March 4, 2013*

**Geometry**

How many ordered triples (a, b, c) of positive integers are there which satisfy the equation a + b + c = 10 ?
*March 4, 2013*

**Algebra**

Find the number of integer quadruples (a,b,c,d) with 0\leq a,b,c,d \leq 100, such that a and b are the roots of the quadratic equation x^2-cx+d=0, while c and d are the roots of the quadratic equation x^2-ax+b.
*March 4, 2013*

**Geometry**

ABC is a right triangle with AB = 2, BC = 8\sqrt{3} and AC = 14. What is the value of \sec \angle BAC?
*March 4, 2013*

**Calculus**

Given that \displaystyle \int_0^4 x^3\sqrt{9+x^2} dx = a, what is the value of \lfloor a \rfloor?
*March 4, 2013*

**Geometry**

A 12 by 12 by 12 cube has all its faces painted blue. It is then broken down to 1728 individual 1 by 1 by 1 cubes. The probability that a randomly chosen 1 by 1 by 1 cube has exactly 2 faces painted blue is \frac {a} {b} , where a, b are coprime. What is the value of a+ b?
*March 4, 2013*

**Algebra**

How many integers from 1 to 19999 have exactly 15 divisors?
*March 4, 2013*

**Algebra**

Alan and Bob are playing with numbers. Starting with the number n=1 they take turns performing arithmetic manipulations with n. Alan goes first and always multiplies n by 3. Bob adds 1 or 2 to the number n, depending on a coin toss. A number is called reachable, if it can ...
*March 4, 2013*

**Algebra**

The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers.
*March 4, 2013*

**Hard physics**

Two equal point charges of 5 µC are on the horizontal axis. One charge is at -10 cm, the other is at +10 cm.? These two charges don't move, they are STUCK, take the potential to be zero at infinity. Find the potential at the following coordinates: (0,0) cm, (0,10)cm...
*March 3, 2013*

**algebra**

rachel and rosa each invested the same amount of money in bonds. Rachel got an 8% return on her money and rosa got a 9% return. If rosa's annual interest was $500 more than rachel's, how much did each invest? Do i need a chart for this problem?
*March 3, 2013*

**Chemistry**

what is the percent by mass of NaCHO3 in a solution containing 12g NaCHO3, dissolved in 450mL of water?
*March 3, 2013*

**Geometry**

Sandy has a long list of 100 suitors. She decides to label them according to if they are tall, dark or handsome. She finds that each of her suitors fall into at least one of the categories, and 65 of them are tall, 76 of them are dark and 53 of them are handsome. If 20 of the ...
*March 2, 2013*

**Physics**

train car with mass m1 = 521 kg is moving to the right with a speed of v1 = 7.9 m/s and collides with a second train car. The two cars latch together during the collision and then move off to the right at vf = 5.1 m/s. 1)What is the initial momentum of the first train car? I ...
*March 1, 2013*

**Geometry**

Luis has a simple calculator that has buttons for the digits 0 through 9, each of the 4 basic operations (+, - ,*,/ ), and an '=' button. Luis pushes a digit followed by the '+' sign, followed by another digit, followed by the '-' sign, followed by ...
*March 1, 2013*