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## #1 Re: Help Me ! » amc problems » 2013-11-07 12:41:37

i'm pretty much sure it gets to the main pic

## #2 Re: Help Me ! » amc problems » 2013-10-27 15:30:16

got another question: The triangle ABC shown is a right triangle. The semicircles have the sides of the triangle as diameters. The areas of two of the semicircles are shown. What is the area of the third semicircle?

the image is the one in the search

## #3 Re: Help Me ! » amc problems » 2013-10-27 15:26:57

the picture is here: http://classroom.artofproblemsolving.com/latex/e/4/4/e44183c89cddb01c6e653eb0a08526a673fb8717.png

## #4 Help Me ! » amc problems » 2013-10-25 11:41:55

mathstudent2000
Replies: 8

1. A cube is sliced with one straight slice which passes through two opposite edges. The result is two solids, as shown. The area of the largest face on one of these two solids is 242\sqrt {2} square units. What was the exact surface area of the original cube?

2. A rectangle contains two circles of radius 6 that are each tangent to the rectangle in exactly 3 points. If the distance between the centers of the circles is 10, what is the area of the rectangle?

3. The rectangle below has height 8 and width 9. What value of k would make the shaded triangle's area 12\frac12% of the rectangle's area?

4. A 4" by 6" by 8" rectangular solid is cut by slicing through the midpoint of three adjacent edges. What is the number of inches in the sum of the lengths of the edges of the tetrahedron that is cut?

5. A cube of volume 27 has 1 x 1 square holes drilled through the center of each face and passing through the center of the cube. What is the volume of the figure that remains?

6. The circle is inscribed in a square with sides 8 cm. What is the area of the shaded part in square centimeters? Express your answer in terms of \pi.

## #5 Re: Help Me ! » mathcounts/amc problems » 2013-09-06 10:56:20

i got the rico problem now but the pillot problem i'm still not sure how to do with the strategy

ok no problem

ok no problem

## #8 Re: Help Me ! » mathcounts/amc problems » 2013-09-05 12:23:19

i solved all except for no. 2 and no.3

## #9 Re: Help Me ! » mathcounts/amc problems » 2013-09-05 10:45:19

did you get the other ones?

## #10 Help Me ! » mathcounts/amc problems » 2013-09-02 12:47:02

mathstudent2000
Replies: 12

1. Maria normally spends half an hour driving to work. When her average speed is ten miles per hour slower than usual, the trip takes ten minutes longer. How many miles does she drive to work?

2. Mr. Pillot always rides his bicycle to work, and he begins his ride at the same time every day. If he averages 10 miles per hour, he arrives at work 2 minutes late, but, if he averages 15 miles per hour, he arrives 1 minute early. How many miles does Mr. Pillot ride to work? Express your answer as a decimal to the nearest tenth.

3. Rico can walk 3 miles in the same amount of time that Donna can walk 2 miles. Rico walks a rate 2 miles per hour faster than Donna. At that rate, what is the number of miles that Rico walks in 2 hours and 10 minutes?

4.For a particular value of k, one root of the equation 5x^2 + kx = 4 is x=2. What is the other root?

(A "root" is a value that makes the equation true, so x=2 is a root of the equation x+3=5.)

ok got it

## #12 Re: Help Me ! » mathcounts/amc problems » 2013-09-02 12:38:24

ok

it means a box in which a unknown number is placed

## #13 Help Me ! » mathcounts/amc problems » 2013-09-02 05:51:04

mathstudent2000
Replies: 6

1. How many sets of 3 primes sum to 20?

2. An old book listed that 72 turkeys were bought for $\square.\square\square each, at a total cost of$\square 67.9\square. What was the cost of each turkey, if each \square stands for a digit that was unreadable in the old book?

Note: The \square digits are not all the same.

3. A number has three distinct digits. The sum of the digits equals the product of the digits. How many three-digit numbers satisfy this condition?

thanks

## #15 Help Me ! » trig problems » 2013-09-01 10:05:10

mathstudent2000
Replies: 15

1. What is the sine of an acute angle whose cosine is 7/25?

2. I'm standing at 300 feet from the base of a very tall building. The building is on a slight hill, so that when I look straight ahead, I am staring at the base of the building. When I look upward at an angle of 54 degrees, I am looking at the top of the building. To the nearest foot, how many feet tall is the building?

3. If A is an acute angle such that \tan A + \sec A = 2, then find \cos A.

4. In triangle GHI, we have GH = HI = 25 and GI = 30. What is \sin\angle GIH?

5. In triangle GHI, we have GH = HI = 25 and GI = 40. What is \sin\angle GHI? (Note: This is NOT the exact same as the previous problem!)

## #16 Re: Help Me ! » analystic geometry problems » 2013-08-23 15:46:33

ok, thanks, i think the easiest is the distance formula one

## #17 Help Me ! » analystic geometry problems with proofs » 2013-08-23 15:45:33

mathstudent2000
Replies: 4

1. Let A = (1,2), B = (0,1), and C = (5,0). There exists a point Q and a constant k such that for any point P, PA^2 + PB^2 + PC^2 = 3PQ^2 + k. Find the point Q and the constant k. What is the significance of point Q with respect to triangle ABC?

2. In triangle ABC, AB = AC, D is the midpoint of \overline{BC}, E is the foot of the perpendicular from D to \overline{AC}, and F is the midpoint of \overline{DE}. Prove that \overline{AF} is perpendicular to \overline{BE}.

## #18 Re: Help Me ! » hockey stick identity proof » 2013-08-23 15:44:21

yes please, but i don't know how to

## #19 Re: Help Me ! » analystic geometry problems » 2013-08-23 15:43:10

Thanks i now know how to do 1 and 3 but i still don't really get no. 2, can you please explain how to do it

## #20 Help Me ! » analystic geometry problems » 2013-08-21 12:42:49

mathstudent2000
Replies: 5

1. Points A and B are in the first quadrant, and O = (0,0) is the origin. (A point is in the first quadrant if both coordinates are positive.) If the slope of \overline{OA} is 1 and the slope of \overline{OB} is 7, and OA = OB, then compute the slope of \overline{AB}.

2. The line y = (3x + 7)/4 intersects the circle x^2 + y^2 = 25 at A and B. Find the length of chord \overline{AB}.

3. The lines y = \frac{5}{12} x and y = \frac{4}{3} x are drawn in the coordinate plane. Find the slope of the line that bisects these lines.

## #21 Re: Help Me ! » hockey stick identity proof » 2013-08-21 12:18:08

how do you substitute it

## #22 Re: Help Me ! » hockey stick identity proof » 2013-08-21 12:16:29

never mind i didn't get it

i think i got it

## #24 Re: Help Me ! » hockey stick identity proof » 2013-08-17 11:41:29

i didn't know how to do it

## #25 Re: Help Me ! » hockey stick identity proof » 2013-08-17 04:51:53

In class we studied the identity (r) combination (r) + (r+1) combination (r) +(r+2) combination (r) + ... + (n) combination (r) = (n+1) combination r+1 We also took a glimpse at (r) combination (0) + (r+1) combination (1) +(r+2) combination (2) +... +(n) combination (n-r) = (n+1) combination (n-r). We will now take a closer look at this second identity.

(a) Confirm that the second identity works for n=5, r=2 and for n=7, r=3.

(b) What is the relationship between the first and second identities?

(c) Prove the second identity above algebraically without using what you learned in Part b. (In other words, prove it without the help of the hockey stick identity we studied in class).

(d) Prove the second identity above with a block-walking argument.