# Knights

Popular questions and responses by Knights
1. ## A probability question i think

In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally upward and to the right. How many ways are there for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard? Thanks in

2. ## help hexagon geometry

A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon? Express your answer as a common fraction. How is this

3. ## Trigonometry question?

Let ABCD be a square, and let M and N be the midpoints of BC and CD respectively. Find sin

4. ## Circles / Square

Alicia has a flat platter shaped like a square with a semicircle of diameter 10 inches on each edge. What is the number of inches in the side length of the smallest square that can contain the platter (which contains the square with the semicircles on each

5. ## geometry inequality triangles help if you can

Two sides of an obtuse triangle are 16 and 21. How many possible lengths are there for the third side, if it is a positive integer? i know that in an obtuse triangle a^2+b^2c but i tried plugging in and it wont work so couldyou guys help me? btw merry

6. ## Mathematics -- Geometry --

A bowling ball is a solid ball with a spherical surface and diameter 30 cm. To custom fit a bowling ball for each bowler, three holes are drilled in the ball. Bowler Kris has holes drilled that are 8 cm deep and have diameters of 2 cm, 2 cm, and 3 cm.

An equilateral triangle of side 14 centimeters is revolved about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone? Express your answer to the nearest whole number, without units. I have tried solving this but it

8. ## Bisectors in a Triangle

Let ABC have side lengths AB=13, AC=14, and BC=15. There are two circles located inside

9. ## Help please with reflection problem!?

A laser is shot from vertex A of square ABCD of side length 1, towards point P on BC so that BP = 3/4. The laser reflects off the sides of the square, until it hits another vertex, at which point it stops. What is the length of the path the laser takes?

10. ## Centroids and Triangles - determining perimeter?

Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of triangle ABC. I drew the diagram, but it doesn't really help....

11. ## Geometry - semicircle inside isosceles triangle

Isosceles triangle ABC has sides of length AB=AC=25 and BC=40 . Find the area of a semicircle inscribed in triangle ABC with diameter along BC . Please help I do not know how to start....

12. ## math problem triangle inequality help

Two sides of a triangle are 11 and 17. How many possible lengths are there for the third side, if it is a positive integer? I tried listing them all but I get confused...Please help thank you!

PLEASE HELP I REALLY NEED HELP. Each of the three circles in the figure below is externally tangent to the other two, and each side of the triangle is tangent to two of the circles. If each circle has radius three, then find the perimeter of the triangle.

14. ## Circle Geometry - chords in a circle

Let PQ, RS , and TU be parallel chords of a circle. The distance between chords PQ and RS is 4, and the distance between chords RS and TU is also 4. If PQ = 78 TU=50 , then find RS. how to do this? Draw some lines?

Find the maximum value of y/x over all real numbers x and y that satisfy (x-3)^2+(y-3)^2 = 6. It is a circle, but how do we even begin? As a matter of fact, how is there not only like 1 solution??

The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. Find the length of the median of the trapezoid. I don't get it... i got as far as the area is 40, and m (median) times the height is 40 as well... please help!

17. ## Analytic Geometry - lengths?

Square ABCD has sides of length 4, and M is the midpoint of CD . A circle with radius 2 and center intersects a circle with radius 4 and center A at points P and D . What is the distance from P to AD? Please help - I drew the diagram, but looks kinda

18. ## Analytic Geometry - Circles and Areas

Let R denote the circular region bounded by x^2+y^2 = 36. The lines x=4 and y=3 partition R into four regions R1, R2 ,R3 , and R4. Let [Ri] denote the area of region Ri. If [R1]>[R2]>[R3]>[R4] , then compute [R1]-[R2]-[R3]+[R4]. Could someone help me, I

19. ## Geometry - Circles and tangents

Two circles of radius 1 are externally tangent at Q . Let PQ and QR be diameters of the two circles. From P a tangent is drawn to the circle with diameter QR , and from R a parallel tangent is drawn to the circle with diameter PQ . Find the distance

20. ## analytic geometry/graphing problem

The vertices of a triangle are the points of intersection of the line y=-x-1, x=2 and y = 1/5x + 13/5. Find an equation of the circle passing through all three vertices. I don't understand how to solve this: should I set them all equal to find the

21. ## Graphing Circles - Finding the radius

A circle is tangent to the y-axis at the point (0,2) and passes through the point (8,0). Find the radius of the circle. I tried using distance formula but it doesnt work? Help please thanks.

22. ## analytic geometry helps are appreciated

For some positive real number r , the line x+y=r is tangent to the circle x^2+y^2 = r. Find r. How do we do this? Set equal equations together??

A line with slope 6 bisects the area of a unit square with vertices (1,0), (0,0) , (1,1), and (0,1). What is the y-intercept of this line? I tried putting one point where the line intersects the square as (y,1), and the other as (x,0), and the y intercept

Find the largest real number x for which there exists a real number y such that x^2+y^2 = 2x+2y . I think it is a circle, but how am i supposed to figure this out??

25. ## analytic geometry helps are appreciated

A line with slope 3 is 2 units away from the origin. Find the area of the triangle formed by this line and the coordinate axes. How is this even going to be done? We are given little info but a bunch of variables. Could someone help please??

26. ## Help triangle angles!

Points D, E, and F are the midpoints of sides BC, CA, and AB of ABC, respectively, and CZ is an altitude of the triangle. If

27. ## double square root problem?

Hi I do not how to simplify the problem x^2 =40+12sqrt2 what would be x? BTW if you sqrt both sides it would be double square root so what then? how to simplify?

28. ## I am really struggling on this problem - geometry

Please help guys if you can, this is a really hard problem I am trying to solve Four circles of unit radius are drawn with centers (1,0),(0,1) ,(-1,0) ,(0,-1) and . A circle with radius 2 is drawn with the origin as its center. What is the area of all

29. ## Trigonometry - Cosine of angle

What is the cosine of the angle between two adjacent faces of a regular tetrahedron? (We define the angle between two intersecting planes as the angle between two intersecting lines, one in each plane, such that each line is perpendicular to the line at

30. ## Triangle inequality?

Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer? I tried using the triangle inequality but to no avail...how would I do this?

31. ## Circumcenter of Triangle in circle

Equilateral triangle ABC and a circle with center O are constructed such that BC is a chord of the circle and point A is the circumcenter of BCO in its interior. If the area of circle with center O is 48pi, then what is the area of triangle ABC? How to do

Two circles of different sizes are tangent at T. A is on the smaller circle, whereas B is on the larger one. Also, segment CD is tangent to the smaller circle, and crosses the goes through the larger circle and hits the other side at D. TD is a diameter,

33. ## Trigonometry - finding cos 36 given cos 72?

Please help, I know cos 72 degrees = (sqrt 5 - 1)/4. I need to know what cos 36 degrees is. How to do so?

34. ## slope and graphing

The lines y=5/12x and y=4/3 are drawn in the coordinate plane. Find the slope of the line that bisects these lines. How? Do we find the average? Do we build isosceles triangles?

35. ## Analytic geometry - finding point by intersect lin

I have a triangle ABC. The slope of AB is -1/ab, the slope of AC is -1/ac, and the slope of BC is -1/ac. My question is, I have 3 lines: Altitude from A to BC, altitude from B to AC, and altitude from C to AB. I know their slope because it is just

36. ## Analytic Geometry - Reflecting points over lines

Let P = (5,1), and let Q be the reflection of P over the line y = 1/2x + 2. Find the coordinates of Q. I don't understand how to start? Should we draw perpendicular lines? Analytic Geometry - Reflecting points over lines - Steve, Monday, March 4, 2013 at

37. ## Analytic Geometry - Reflecting points over lines

Let P = (5,1), and let Q be the reflection of P over the line y = 1/2x + 2. Find the coordinates of Q. I don't understand how to start? Should we draw perpendicular lines?

38. ## Geometry - Dilation of a square

The preimage of square ABCD has its center at (8,-8) and has an area of 4 square units. The top side of the square is horizontal. The square is then dilated with the dilation center at (0,0) and a scale factor of 2. What are the coordinates of the vertex

39. ## analytic geometry helps are appreciated

Find the maximum value of y/x over all real numbers x and y that satisfy (x-3)^2+(y-3)^2 = 6. It is a circle, but how do we even begin? As a matter of fact, how is there not only like 1 solution??

40. ## analytic geometry helps are appreciated

Find the maximum value of y/x over all real numbers x and y that satisfy (x-3)^2+(y-3)^2 = 6. It is a circle, but how do we even begin? As a matter of fact, how is there not only like 1 solution?? No one has answered this question yet.

What is the area, in square units, of a triangle whose vertices are at (4,-1), (10,3) and (4,5) ? How to do this?

A laser is shot from vertex A of square ABCD of side length 1, towards point P on BC so that BP = 3/4. The laser reflects off the sides of the square, until it hits another vertex, at which point it stops. What is the length of the path the laser takes?

When a square of area 4 is dilated by a scale factor of k, we obtain a square of area 9. Find the sum of all possible values of k. I do not understand...it is not 3/2, as I was told, but I don't understand why? Help?

44. ## Geometry - Transformations and Dilations

When a square of area 4 is dilated by a scale factor of k, we obtain a square of area 9. Find the sum of all possible values of k. I do not understand...it is not 3/2, as I was told, but I don't understand why? Help?

A circle with radius 3 is inscribed in a isosceles trapezoid with legs of 10. Find the length of the smaller base. When I draw a diagram, calling the trapezoid ABCD with A and D at the bottom, I see that the length from where the altitude from B and C hits

46. ## I need help on a geometry cone/frustrum problem

A sphere with radius 3 is inscribed in a conical frustum of slant height 10. (The sphere is tangent to both bases and the side of the frustum.) Find the volume of the frustum. Could someone help me? I can't find the radius of the cone....

Let AB be the diameter of a circle, and let point P be a point on AB. Let CD be a chord parallel to AB. Prove that PA^2 + PB^2 = PC^2 + PD^2 It can be solved using geometry methods (no trig). Anyway, I figured out that PA^2 +PB^2 = 2OP^2 + 2OB^2. However,

48. ## Mock Trial

Hi all, I belong to a education group, and we practice Mock Trial. Where can I find a video of a real trial going on so I can learn from it? Thanks all and Happy New Year!

49. ## triangle inequality - altitudes help plz

hi guys ive be struggling on this problem for a couple of days, so please help if you can Problem:Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer? Thanks in advance

50. ## altitude triangle inequality

hi guys ive be struggling on this problem for a couple of days, so please help if you can Problem:Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer? Thanks in advance

The distance between two opposite vertices of the dodecagon is 2. Find the area of the dodecagon. first, what is the area of a dodecagon and second how to find it with just the distance between two oppositve vertices. i found that a dodecagon can be

52. ## Math could you help this is kinda hard and urgent

The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. Find the length of the median of the trapezoid. I tried figuring this out... by the way i got median times height is 40 and also notice that we are talking about the diagonals not

1. ## math

2/3x - 1/4 x = 500 8/12 - 3/12 = 500 5/12 x = 500 x = 1200

posted on April 13, 2013
2. ## maths- plseee urgently

plug in calc to get roughly 0.261496941........

posted on April 12, 2013

I tried to use outside sources for my answers but feel free to check on the internet for help.

posted on April 12, 2013

1. a 2. you are right 3. correct 4. thermal radiation you are correct 5. Best is Radiation Next is Conduction Last is convection (air) So false 6. An example of potential energy is a ball sitting at the top of a ramp, but not moving. It has potential

posted on April 12, 2013
5. ## algebra :( help me!!

Probably mean because it is the average and thus in total the exact center of each group.

posted on April 12, 2013
6. ## interpersonal communication

Is there a question?

posted on April 12, 2013
7. ## math

a. factor would be if 2x+y * something else but it is not b. this is a factor beause it is 2x+y * something else c. sum of two terms because two terms are added d. yes it is a product because two terms are multiplied

posted on April 12, 2013
8. ## science

Yeah, that is true. But the standard definition for the atomic number is the proton, since electrons can vary. Quote "The atomic number is equal to the number of protons in an atom's nucleus. The atomic number determines which element an atom is." from

posted on April 11, 2013
9. ## math

a. false b. true c. true d. true

posted on April 11, 2013
10. ## math

3b(5b-8f) = 15b^2 - 24bf

posted on April 11, 2013
11. ## math

If it is 30 feet long, the other side is also 30 feet long. Thus, we have 30/15 + 1 = 16 saplings for one side. This, multiplied by 2 gives us 32 in all without the width. Now we only have 48-32 = 16 saplings left. Each side minus 2. Thus, we have x/2-1

posted on April 11, 2013
12. ## algebra1

distance = rate times time. Use the formula and plug in the constants and variables.

posted on April 11, 2013
13. ## math

a. False b. true c. true d. true

posted on April 11, 2013
14. ## science

EDIT - Damon is right, for number 4.

posted on April 11, 2013
15. ## Math

Um...are we given how many shares?

posted on April 11, 2013
16. ## Algerba 1

woops for the first I looked at it wrong... 3 * 10^10 xs 7 x 10^-4 = 21 x 10^6 = 2.1 x 10^7 And ma'm, I believe it is written in scientific notation...

posted on April 11, 2013
17. ## Algerba 1

1. 3 * 10^4 * 7 * 10^-4 7*3 = 21 10^4 * 10^-4 = 10^0 = 1 21 * 1 = 21 2.1 * 10^1 2. (5*10^4)^2= 25 * 10^8 = 2.5 * 10^9

posted on April 11, 2013
18. ## science

1. located in electron cloud 2. 8 3. protons 4. True. The closer the atoms are to the nucleus, the more energy it takes to move them between the levels. 5. True

posted on April 11, 2013
19. ## Math

For average grade of 90, must all add up to the average times the amount of tests. So, 90*5 = 450 x+ 93+ 82+91+88 = 450 x+(82+88) + (91+93) = 450 x + (170 + 184) = 450 x+ 354 = 450 x+4 + (350) = 450 x+4 = 100 x = 96

posted on April 11, 2013
20. ## chemistry

1. Usually sulfur smells like rotten eggs, but not the element sulfur, because sulfur is usually associated with hydrogen sulfide, which smells like rotten eggs too. 2. Probably aluminum sulfide if I had no other guess....also because no picture. 3.

posted on April 11, 2013
21. ## Math Geometery

No problem :D

posted on April 11, 2013
22. ## math

posted on April 11, 2013
23. ## math

we get 238 km in 15 days 30 days is 30/15 = 2 times that so must be 2 * 238 = 476

posted on April 11, 2013
24. ## math

Honestly, it is neither beneficial to any of us for you to continually post so many questions without an explanation of what you need. Anyways, 137 / 6 = firecrackers / duds 137/6 = 2466/x = firecrackers / duds 137/6 = 2466/x cross multiply to get 137x =

posted on April 11, 2013
25. ## Math Geometery

No. Imagine the center of the polygon. It can only have one point where the vertical line of symmetry hits the center of the polygon. So only one.

posted on April 11, 2013
26. ## math

8A = 7B A + 14 = B 8A = 7(A+14) = 8a = 7A + 7*14 A = 7*14 A = 7*7*2 = 49*2 = 98 mph B = 98+14 = 112

posted on April 11, 2013
27. ## math

1/1/55+1/30 = 1/ (17/330) = 330/17 min

posted on April 11, 2013
28. ## History

Fetterman massacre. In December 1866, the Native American allies attacked and defeated a United States unit in what the whites would call the Fetterman Massacre (or the Battle of the Hundred Slain), which resulted in the most U.S. casualties of any Plains

posted on April 5, 2013
29. ## Maths

sin 30 = 1/2 thus, we get 3/2 - 2cos 60 cos 60 = 1/2 thus we get 3/2 - 2/2 = 1/2 tan45 = 1 so the equation is just 4cos60 - 2cos60 cos 60 = 1/2, as previously mentioned thus, we get 2 - 1 = 1..... btw...I think you can just plug these functions into your

posted on April 5, 2013
30. ## math

I agree. Please explain what you came up with and how far you have gotten before posting 10 questions in a row.

posted on April 5, 2013
31. ## geometry

We are not given the area, perimeter, or any other info to solve for x....Now if LMNO was a rhombus, that would be different.

posted on April 5, 2013
32. ## maths-

We are not given any other lengths or angles. It is impossible to determine the area of the triangle. x^2+y^2 = 65 we need to find 2xy

posted on April 5, 2013
33. ## algebra 1

1 hour = 60 minutes 1 minute = 60 seconds so one hour = 3600 seconds this is 3600/8 = 450 times of the given. So in one hour, the car runs 450 * 40 = 18000 feet. 18000 / 5280 = roughly 3.4 miles To the nearest whole number, the car goes at 3 miles per

posted on April 5, 2013
34. ## Maths

multiply all by abcd to get bcd+acd+abd+abc = abcd.

posted on April 5, 2013
35. ## Government senior college ikoyi

Basically the inradius of the equilateral triangle. The formula for that is inradius * semiperimeter (half the perimeter) = area We know that the formula for calculating the area of a equilateral triangle is s^2 sqrt 3 /4 so we get 100sqrt3 as the area of

posted on April 5, 2013
36. ## Math

posted on April 4, 2013
37. ## Math

6 * 1 1/2 meters of cloth = 6 * 3/2 = 9 meters of cloth. a meter is roughly a yard. so we need about 9 yards. However, a yard is a bit less than a meter, so to make sure, buy 10 yards of cloth.

posted on April 4, 2013
38. ## Science

btw this is from wiki answers

posted on April 4, 2013
39. ## Science

Your body needs oxygen in order to efficiently break down glucose and process it into your cell's primary energy source (ATP). As you do more intense exercise, you need more energy and therefore more oxygen. Your blood carries oxygen from the lungs to your

posted on April 4, 2013
40. ## Math

No you don't. FALSE, you find a common denominator, keep that denominator, and add the numerator.

posted on April 4, 2013
41. ## math ugh.

20/20 - 9/20 = 11/20 Then, since the ratio between male and female is 11/20 / 9/20 = 11/20 * 20/9 = 11/9, we can use this to figure the amount of males. multiply by 2160 (number of females) to get 2640.

posted on April 4, 2013
42. ## Math

Could you please stop repeatedly posting a quadrillion questions and perhaps ask why you don't get the problem maybe? Anyway, False because many even numbers are negative.

posted on April 4, 2013
43. ## math ugh.

since 9/20 were female, 11/20 were male 11/9 * 2160 = 2640 males.

posted on April 4, 2013
44. ## Math

I believe I answered the question, just find the probability of 7 failures ( a 6/7 chance each time) 3 successes (a 1/7 chance each time) Then multiply.

posted on April 4, 2013
45. ## Math

True....I said that in a previous response.

posted on April 4, 2013
46. ## Math

I answered this kind of question before, so I won't get into detail. Before I showed that subtracting a negative number will move you right. It follows that adding one will move you left. Thus, TRUE.

posted on April 4, 2013
47. ## Math

np

posted on April 4, 2013
48. ## art

emotionalism

posted on April 4, 2013