Thursday
August 25, 2016

# Posts by Reiny

Total # Posts: 35,552

Math
smallest angle --- x the other is ------ x+45 third ------ 2x - 5 solve for x: x + x+45 + 2x-5 = 180
May 2, 2016

Trigonometry
easier than it looks: cos^-1(radical3/2), means you want the angle Ø so that cosØ = √3/2 of course you should recognize that as a ratio form our 30-60-90 triangle, and Ø = 30° for tan^-1 (-√11/√5), construct a triangle in quadrant II ...
May 2, 2016

Probability and statistics
prob(choosing child) = 6/12 = 1/2 prob(non-child) = 1- 1/2 = 1/2 prob(exactly one child in choosing two) = C(2,1) (1/2)(1/2) = 1/2 or If C stands for choosing child and N stands for non-child we have these cases: CC -- prob = (1/2)(1/2) = 1/4 CN -- 1/4 NC --1/4 NN -- 1/4 so ...
May 2, 2016

Math
The least perimeter is obtained when you have a square let the side be s s^2 = 32 s = √32 = 4√2 so the least perimeter is 8√2 by Calculus: let the width be x then the length is 32/x P = 2x + 2y = 2x + 64/x P' = 2 - 64/x^2 = 0 for a min of P 2 = 64/x^2 x^2...
May 2, 2016

Math
Well, your homework is poorly stated. Here is an example of what Steve is saying: suppose the width is .1 ft then the length = 39/.1 or 390 ft perimeter = 2(390) + 2(.1) = 780.2 ft check: area = .1(390) = 39 suppose the width is .001 ft then the length is 39/.001 or 39000 ft ...
May 2, 2016

Geometry
3 small ones of 5 in diameter v = 3((4/3)π(2.5)^3) = 125π/2 = 62.5π = appr 196.35 one of diameter 8 v = (4/3)π(4^3) = 256π/3 = appr 268.08 hemisphere of radius 5 = (1/2)(4/3)π(5^3) = 250π/3 = appr 261.8
May 2, 2016

Probability and statistics
we can build our 5 digit number using 5 different numerals all possible numbers = 5! or 120 In all of these, the lead digit, the 10-thousand digit, can be occupied by the "9" 24 times, the "8" 24 times, etc. The value of those 24 9's would be 24(90000...
May 2, 2016

Gr 11 Functions
(1+tanx)^2 ≠ (1-sinx)(1+sinx) RS = 1 - sin^2 x = cos^2 x and cos^2 x is certainly not equal to (1+tanx)^2 try x = 45° (1+tan45)^2 = (1+1)^2 = 4 cos^2 (45°) = (1/√2)^2 = 1/4 no wonder you got nowhere with your work. check the question, or check your typing.
May 2, 2016

Correcion - math
Sarim's solution above makes absolutely no sense consider this one: http://www.jiskha.com/display.cgi?id=1462219074
May 2, 2016

maths
I know that the cost of coffee has gone up, but \$2000 per kg ???? I will assume that you meant \$22.00, (even that is too high) anyway..... let the cost of the mix be \$x per kg 8(20) + 12(22) = x(8+12) 20x = 424 x = \$21.20
May 2, 2016

math
looks for every increase of 1 unit in the x's the corresponding y decreases by 5 so slope = -5 y = -5x + b at x = -2, y = 9 9 = -5(-2) + b b = -1 function rule: y = -5x - 1
May 2, 2016

Math
I have no idea what your line 42pi C=pi*d=pi.pi*42=42pi. is supposed to say or mean. Are you saying the C = 42π ?? in that case the radius would be 21 units and the answer is in exact form now if we use the approximation of 22/7 for π we get C = 42(22/7) = 132 42&#...
May 2, 2016

Algebra
yes, the new vertex will be (4,-1) proof: f(x-2) = (x-2)^2 - 4(x-2) + 3 = x^2 - 4x + 4 - 4x + 8 + 3 = x^2 - 8x + 15 = g(x) vertex of g(x) = -b/(2a) = 8/2 = 4 g(4) = 4^2 - 8(4) + 15 = -1 vertex is (4,-1)
May 2, 2016

calculus
a) let the top right vertex be (x,y) then the area = 2xy A = 2xy = 2x(16-x^2) = 32x - 2x^3 dA/dx = 32 - 6x^2 = 0 for a max of A 6x^2 = 32 3x^2 = 16 x^2 = 16/3 x = 4/√3 , then y = 16 - 16/3 = 32/3 so the rectangle has a base of 2(4/√3) = 8/√3 and a height of ...
May 2, 2016

calculus
sum(1) = 1^3/1^4 = 1 or 4/4 sum(2) = (1 + 8)/16 = 9/16 sum(3) = (1+8+27)/81 = 36/81 = 4/9 or 16/36 sum(4) = (1+8+27+64)/256 = (1+8+27+64)/256 = 100/256 = 25/64 sum(5) = (1+8+27+64+125)/625 = 225/625 = 9/25 = 36/100 I noticed I can change my numerator to (n+1)^2 for sum(n) and ...
May 2, 2016

calculus
recall that tan^2 A +1 = sec^2 A and d(tanA)/dA = sec^2 A so ∫ tan² x/3 dx = ∫ sec^2 (x/3) - 1 dx form 0 to π = [3 tan (x/3) - x] from 0 to π = 3tan π/3 - π -(3tan 0 - 0) = 3 √3 - π
May 2, 2016

maths
volume of cube = (5.5 cm)^3 = 166.375 cm^3 then our cylinder's height would increase by h , such that π(49)h = 166.375 h = 1.081 cm (note that the 9 cm depth of water did not enter the picture)
May 2, 2016

Calculus
let the water level have a radius of r ft let the height of the water be h ft by ratio: r/h = 5/12 12r = 5h ---> r = 5h/12 V = (1/3)π r^2 h = (1/3)π(25h^2/144)(h) = (25/432)π h^3 dV/dt = (25/144)π h^2 dh/dt plug in our given stuff 1 = (25/144)π(64) ...
May 2, 2016

Calculus
dy/dt = 2ax dx/dt + dx/dt dy/dt = dx/dt(2ax + 1) but dy/dt = dx/dt , so 1 = 2ax + 1 2ax = 0 x = 0 then y = b at the point (0,b)
May 2, 2016

Calculus
did you make your sketch ?? let the length of the man's shadow be x ft let the distance he is from the lightpost be y by ratios: 6/x = 15(x+y) 6x + 6y = 15x 6y = 9x 2y = 3x 2dy/dt = 3dx/dt but dy/dt = 3 so 6 = 3 dx/dt dx/dt = 2 His shadow is lengthening at 2 ft/s but he is...
May 2, 2016

Math
your def: a*b= a+b-ab = first + last - product of first times last (a*b)*c = (a+b-ab)*c = a+b-ab + c - ac - bc + abc = a+b+c - ac - ab - bc + abc a*(b*c) = a*(b+c - bc) = a+b+c-bc - ab - ac + abc = a+b+c - ac - ab - bc + abc = (a*b)*c so the operation is associative -5*8 = -5+...
May 2, 2016

calculus too hard help
let's try this: let y = x^x lny = xlnx y'/y = x(1/x) + lnx dy/dx = y(1 + lnx) = x^x + x^x(lnx) let u = x^x^x , the x's are staggered ln u = x ln(x^x) u'/u = x(x^x + x^x(lnx))/x^x) + ln(x^x) argghhhh!! I was looking for a pattern. What am I not seeing ????
May 2, 2016

calculus too hard help
second last line should have been 532 = 5^9 = 1953125
May 2, 2016

calculus too hard help
y=x^x^x^x... take ln of both sides ln y = ln(x^x^x^x... ) ln y = x ln(x^x^x^x... ) lny = x ln(y) 1 = x well, that got me nowhere. are the x's staggered upwards or on the same level? e.g 532 = 5^8 = 390625 but (5^3)^2 = 5^6 ≠ 5^8
May 2, 2016

maths
r = 50 volume of full tank = (4/3)π(50)^3 = ... so half of that is .....
May 2, 2016

Math
with no restrictions, number of 4 digit permutations are 10x10x10x10 = 10,000 as you stated but , if we exclude the 9, we have only 9 numerals to play with number of 4 digit phone number endings = 9x9x9x9 = 6561 (now, a nicer question would have been: of those 4 digit endings...
May 2, 2016

Maths
sin(2Ø + π/3) = 1/2 we know sin (π/6) = 1/2 , (sin 30° = 1/2) so 2Ø + π/3 = π/6 OR 2Ø + π/3 = 5π/6 (sin30° = 1/2 and sin150° = 1/2) case1: 2Ø + π/3 = π/6 2Ø = π/6 - π/3 = -π/6...
May 2, 2016

Math
do you want something like this ? RR --> (4/12)(3/11) = 1/11 RG --> (4/12)(8/11) = 8/33 GR --> (8/12)(4/11) = 8/33 GG --> (8/12)(7/11) = 14/33 note that 1/11 + 8/33 + 8/33 + 14/33 = 1
May 2, 2016

Math
We have similar triangles Juan is 6' 1" = 73 inches so we can say: 73 inches/5 m = x inches/12 m notice we have the same units in each ratio, so 73/5 = x/12 5x = 12(73) x = 175.2 inches x = 14.6 ft = 14 ft and 7.2 inches
May 2, 2016

MATH
1 m^2 = 1.1959905 yards^2 so 76000 m^2 = 90895.278 yards^2 cost = 80(90895.278) = \$7,271,622.24 (In reality, the cost would be found in terms of Euros/m^2. )
May 2, 2016

Math
A marathon is 42.195 km = 42,195 m time = 42195/1.8 = 23441.666.. seconds = 6.5116 hrs or 6 hours and 31 minutes or 1.8 m/s = 64800 m/h = 6.48 km/h rate = 42.195/6.48 hours = 6.5116 hrs as above or 1.8 m/s = 180 cm/s = 70.866.. inches/s = 5.90551... ft/s ,(stored in calculator...
May 2, 2016

maths
"u" is not an English word, however "you" is one. let the number of bikes be b let the number of tricycles be t 2b + 3t = 19 integer solutions (b,t) are (8,1) , (5,3) , (2,5) for 2b + 3t = 23 integer solutions are: (10,1) , (7,3) , (4, 5) , (1, 7)
May 2, 2016

Math
depends on the rate of exchange. The current rate is \$1 CND = \$.80 US so \$76025 CND = \$60820 US So which is the better offer ?
May 2, 2016

math
Since positions of the board are stated, we are dealing with a permutation, so the number of boards = 30(29)(28)(27) = ....
May 2, 2016

Math
Are your two models supposed to be in a ratio equal to the ratio of the height of the two buildings? The buildings do not have the same shape, so we can't make a ratio comparison between their volumes. The wording of the first two Related Questions below deal with the ...
May 2, 2016

Maths (Need Help)
given line: 8y = 2x+ 3 y = (2/8)x + 3/8 y = (1/4)x + 3/8 The slope of the given line is 1/4 a) find the slope of AB and show it is equal to -4 b) midpoint of AB = ( (3+2)/2 , (-1+3)/2 ) or ( 5/2 , 1) --- show that ( 5/2 , 1) satisfies the given equation by subbing it in to see...
May 2, 2016

Finance
if left alone: amount = 500(1.055)^8 = .... if \$150 is take out, amount = 350(1.055)^8 - ... take the difference between the two answers
May 2, 2016

Math
Instead of taking 10% off, think of what would be left after you do that 100% - 10% = 90% <-----> 1 - .10 = .90 e.g. suppose your car costs R122 000, take 10% which is R12 200 off R122 000 - R 12 200 = R 109 800 - now take 90% or .9 of 122 000, that would also be 109 800...
May 2, 2016

Exponential Modeling
Having done a few of these kind of problems for you, it is time for you to tell me what you got for this one
May 1, 2016

Exponential Modeling
what is 100(1.32)^10 ??
May 1, 2016

Exponential Modeling
if the rate of increase is linear, then rate = (1.25 - .10)/(2012-1972) = 1.15/40 = .02875 or appr 3 cents a year
May 1, 2016

Exponential Modeling
huhh??? value at end of year 1 = 25000(.65) = 16250 value at end of year 2 = 16250(.65) = 10562.50 value at end of year 3 = 10562.50(.65) = 6865.63 or in 1 step value = 25000(.65)^3 = 6865.63 So much for you little trick, it is blatantly wrong.
May 1, 2016

Algebra 1
It is not exponential the way you typed it. If you meant y = 15,000(1.07)^x , which is what I suspect ... A is certainly not the one B is out since that would be linear C. 2 = 1.07)^x log2 = xlog1.07 x = log2/log1.07 = 10.24 so that is a correct choice so far D 3 = 1.07^x x = ...
May 1, 2016

math
Assuming they play all 5 games, to get 5 points in 5 matches, it could be DDDDD --- arranged in 1 way WDDDL --- arranged in 5!/3! or 20 ways WWDLL--- arranged in 5!/(2!2!) or 30 ways Prob(win) = 1/3 prob(draw) = 1/6 prob(loss) = 1/2 prob(DDDDD) = (1/6)^5 = 1/7776 prob(WDDDL...
May 1, 2016

algebra tricky q
Just translate to Math number of breads --- b milk ---------------- 2b cereal ------------- b+1 meat -------------- b+1 now for the cost: 70(2b) + 60b + 50(b+1) + 150(x+1) = 1000 140b + 60b + 50b + 50 + 150b + 150 = 1000 400b = 800 b = 2 2 loaves of bread 4 cartons of milk 3 ...
May 1, 2016

math
First let arrange the 10 boys. This can be done in 10! ways Now there are 9 places in this arrangement where we can place a girl, but we only have 6 girls. So we have to choose 6 of those 9 places to insert the single girls. There are C(9,6) or 84 ways of doing so But we can ...
May 1, 2016

Trigonometry
2nd part I will make a similar substitution let x/2 = y, then we have prove: tany + coty = 2cscy LS = siny/cosy + cosy/siny = (sin^2 y + cos^2 y)/sinycosy but (2sinycosy = siny) = 1/((1/2)siny) = 2cscy = 2csc(x/2) = RS
May 1, 2016

Trigonometry
let x/2 = Ø , then your equation becomes sinØ - cosØ = ±√(1 - sin 2Ø) we know that if LS = RS , then (LS)^2 = (RS)^2 LS = sinØ - cosØ (LS)^2 = (sinØ - cosØ)^2 = sin^2 Ø - 2sinØcosØ + cos^...
May 1, 2016

diameter
No They are chargint \$40 per <b<square yard, so we are dealing with area, not circumference Area = πr^2 = π(48)^2 = 2304π feet ^2 = 256π yards^2 cost = \$40(256π) = \$32,169.91 or appr \$32,170 Your answer of only \$105.90 should have sounded totally...
May 1, 2016

calculus
or using discs V π∫ y^2 dx from x= 0 to 4 = π∫x dx from x = 0 to 4 = π[ (1/2)x^2] from 0 to 4 = π(16/2 - 0) = 8π
May 1, 2016

Calculus
May I suggest two excellent videos from the Khan Academy The first develops the standard method of finding the area https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/area-polar-graphs/v/formula-area-polar-graph And the second just about matches your ...
May 1, 2016

Calculus
So at 2:00 pm the first ship would be 5 nautical miles directly south of the second ship. Let the time passes since 2:00 pm be t hours So the two ships form a right-angled triangle, with a horizontal side of 10t nmiles and a vertical of (5+5t) nmiles Let the distance between ...
May 1, 2016

math
Effectively, you have all the numbers form 100 to 999 , (can't start with 0 or else we have a 2 digit number) There would be 999-100 + 1 = 900 of them or using the standard permutation method choices for 1 digit = 9 choices for 2nd digit = 10 choices for 3rd digit = 10 ...
May 1, 2016

Exponential Modeling
what is 100(1.24)^5 ?
April 30, 2016

Calculus
My sketch shows the following: M is the man's position 16 m off shore A is the point on the shore perpendicular to M B is the point where he wants to go, AB = 30 Let P be the optimum point between A and B, let AP = x, then PB = 30-x distance in water = MP MP = (x^2 + 256...
April 30, 2016

Math
In your sketch , draw a perpendicular from the vertex to the base. You now have 2 identical right-angled triangles. let the base for each be x units (your whole base would then be 2x) by simple trig, cos 67.5° = x/10 x = 10cos67.5 = 3.8268.. , Use your calculator for this ...
April 30, 2016

MATH
a = 11 d = 3 term(n) = a + (n-1)d 83 = 11 + (n-1)(3) 72 = 3n - 3 3n = 75 n = 25 83 is the 25th term check: term(25) = a + 24d = 11 + 24(3) = 83
April 30, 2016

Math
did you make your sketch? On mine I labeled the top of the pole as P and it bottom as Q. I marked the bird on the tree as A Draw a horizontal from A to meet PQ at R let PR = x, then PQ = 10.65+x In triangle ARQ tan60° = 10.65/AR AR = 10.65/tan60 Triangle ARP is right-...
April 30, 2016

algebra
Volume = (4/3)π (1.9)^3 = 28.7309... SA = 4π (1.9)^2 = 45.36459... ratio of V : SA = 28.7309.../45.36459... = .63333... in general , ratio of volume/SA = (4/3)πr^3/(4πr^2) = (1/3) r using our values above ratio vol. / SA = (4/3)π(1.9)^3 / (4π (1.9...
April 30, 2016

Algebra
This question makes absolutely no sense to me. You say that you already have a pool . Are you going to change it?? How deep is the pool to be? Will people be able to stand with their heads above water? Is the pool circular? That way you would have the largest surface area, but...
April 30, 2016

Math
factors of 40 : 2,4,5,8,10,20 but only 5, 8, 10 fall within our domain So numbers which are even OR a factor of 40 are: 5,6,8,10,12,14 --> 6 of them prob(of your event) = 6/10 = 3/5
April 30, 2016

Math
1.8 m = 180 cm length = 18900/180 cm = .. make sure you express above in metres.
April 30, 2016

geometry
sketch a cross-section, and complete the right-angled triangle let the radius be r r^2 = 10^2 + 15^2 r = √325 depth of water = 10 + √325 = ...
April 30, 2016

math
final value = \$60(.8)(.9)(1.55) = \$66.96
April 30, 2016

math
original fraction : x/y new fraction : (.5x)/(.75y) = (2/3) (x/y) so the new fraction is 2/3 of the old one, thus it was decreased by 1/3
April 30, 2016

math
According to your wording: - you wanted the percentage increase , so my answer is correct 3.5/.432 = 8.102 so the new price is 810% of the old one, but the increase is 710% e.g. suppose the cost of a coat went from \$100 to \$120 so it increased by 120%, but the percentage ...
April 30, 2016

math
number of dozen in the bucket = 450/12 = 37.5 so cost price per dozen = 16.20/37.5 = .432 So they bought them at \$ 0.432 per dozen and sold them at \$3.50 per dozen percentage increase = 3.5/.432 - 1 = 7.102 or 710%
April 30, 2016

consumer math
I will assume you are using compound interest and the monthly rate is .13/12 or i = .0108333... n = 15 payment = p p( 1 - 1..0108333..^-15)/.0108333... = 1380 I get p = 100.17
April 30, 2016

Maths
I see that you corrected your post, and inserted a time of 2 hours So go back to my previous reply to the same question, replace t with 2 and repeat the steps. (or just plug t=2 into my answer for x)
April 30, 2016

Maths
"how far are apart" ? After what time ? Let the time passed since they left be t hours My diagram shows a triangle with sides 5t and 7.5t and an angle of 134° between those sides. If the distance between them is x, by the cosine law: x^2 = (5t)^2 + (7.5t)^2 - 2(...
April 30, 2016

Calculus
Make a sketch and draw in the rectangle. Let the top-right point be P(x,26-x^2) and the bottom-right point be Q(x, x^2 + 2) So the width of the rectangle is 2x and the height is 26-x^2 - x^2 - 2 = 24 - 2x^2 area = 2x(24-2x^2) = 48x - 4x^3 d(area)/dx = 48 - 12x^2 = 0 for a max ...
April 29, 2016

Math
2x - 1 = x+3 x = 4 , then y = 7 the solution is (4,7) which is not listed The wording is poor. "No solution" implies that there is no answer to our intersection, but there is! It should have said "none of the above"
April 29, 2016

Algebra
let's rephrase the question. For what values of k will the quadratic x^2 - kx + k^2 = 0 have 2 solutions when b^2 - 4ac > 0 k^2 - 4(1)(k^2) >0 -3k^2 > 0 k^2 < 0 any number squared is always positive, so there is no value of k for which the graph will cross the ...
April 29, 2016

Geometry
cosine law: DE^2 = 70^2 + 50^2 - 2(70)(50)cos54° = .. carry on
April 29, 2016

math
number of men --- x number of men --- 3x men wearing glasses = (3/5)x number of women wearing glasses = (1/3)(3x) = x x - (3/5)x = 120 times 5 5x - 3x = 600 2x = 600 x = 300 people at concert = x + 3x = 4x = 1200
April 29, 2016

College Algebra
#1 4 - 3(x+1) = 2x 4 - 3x - 3 = 2x -5x = -1 x = -1/-5 = 1/5 #2 15x^2=x=2 , assuming you meant 15x^2 + x=2 since the = and + sign are on the same key 15x^2 + x - 2 = 0 which factors to (3x-1)(5x+2) = 0 x = 1/3 or x = -2/5 by formula: x = (-1 ± √121)/30 = 1/3 or -2/...
April 29, 2016

@Steve
Thanks Steve Had an inkling thats what he was doing, but then it was contradicted in how he worked the last one. btw, was it overkill in my solution to http://www.jiskha.com/display.cgi?id=1461944692 Almost gave up on it, but found some clues on a webpage.
April 29, 2016

College Algebra/pre-calculus
#1 How did you get -2 ?? log 6^(1/36) = (1/36) log 6 = appr .0216 #2 ln(1/e^4) = ln1 - ln e^4 = 0 - 4lne = 0 - 4(1) = -4 #3 log 7^1 = log 7 = appr .845 #4 log 4^64 = 64 log4 = appr 38.532 #5 log 10^8 = 8log10 = 8 #6 --- the only one you got right
April 29, 2016

Trigonometry
One of my all-time favourite topics in Math is the Golden Ratio of (1 + √5)/2. I happen to know that cos 36° = (1+√5)/4 Notice also that in a regular pentagon , we have interior angles of 108° , and if we draw in some diagonals, we have all kinds of 36, 72 ...
April 29, 2016

Math
When they meet, they both would have traveled the same time. Let that time be t hrs so 60t + 80t = 210 140t = 210 t = 1.5 hrs take over
April 29, 2016

algebra
given: 8l = 15w then w = 8l/15 Perimeter = 2l + 2w 2l + 2(8l/15) = 230 times 15 30l + 16l = 3450 46l = 3450 l = 75 then w = 8(75)/15 = 40 the yard is 40 ft by 75 ft check: is 15(40) = 8(75) ??? YES is 2(40) + 2(75) = 230 ?? , YES
April 29, 2016

Math
Your question makes no sense. Must be reach a certain amount before withdrawing?
April 29, 2016

Math
correction: on this good earth of ours the equation would be h(t) = -16t^2 + 35t + 1 I assume you had a typo. the t of the vertex (instead of the normal x) = -b/2a = -35/-32 so h(35/32) = -16(35/32)^2 + 35(35/2) + 1 = appr 20.14 (exact answer is 1289/64)
April 29, 2016

College Algebra Help?!
number of choices = C(20,2) x C(32,2) = 190(496) = 94240 ways
April 29, 2016

Math (Probability)
1) prob(r,r) = (12/20)(8/13) = 24/65 ----> B 2) prob = (6/20)(2/19) = 3/95 ----> C 3) you want (1/2)^12 = 1/4096 ----> A
April 29, 2016

Algebra
So we need the vertex of the parabola h(t) = -16t^2 + 293t + 7 the t of the vertex is -b/(2a) = -293/-32 = 293/32 seconds or in 9.15625 seconds plug that into h(t) = ... = appr 1348.4 ft your next two questions have just been answered
April 29, 2016

sails math
amount of the 70% solution --- x L amount of the 45% solution--- 300-x L .70x + .45(300-x) = .65(300) time 100 70x + 45(300-x) = 65(300 70x + 13500 - 45x = 19500 25x = 6000 x = 240 So 240 L of the 70% stuff, and 60 L of the 45% stuff check: .7(240) + .45(60) = 195 .65(300) = ...
April 29, 2016

alg
f(x) = 4(x^2 - 6x + 9 - 9) + 20 = 4( (x-3)^2 - 9) + 20 = 4(x-3)^2 - 36 + 20 = 4(x-3)^2 - 16
April 29, 2016

math
1. π --- irrational √3 --- irrational √2 --- irrational 1.333.... = 4/3 ---- Rational 2. If n is your symbol for π then your choice if a) is correct
April 29, 2016

math
yes, notice that 300, 400, and 500 is simply a multiple of 3,4, 5 3,4,5 would form the smallest right-angled triangle with integer sides.
April 29, 2016

math
Just good ol' Pythagoras .... L^2 = 300^2 + 400^2 L = .....
April 29, 2016

Math Help
Wolfram shows that x = -π/12 and π/36 are intersection values and the region forms a closed area. area = ∫(cos 12x - sin 6x) dx from -π/12 to π/36 = (1/12)sin 12x + (1/6)cos 6x | from -π/12 to π/36 = .. take over
April 29, 2016

Error - Geometry
This question makes no sense. You don't have a right-angled triangle , since 6^2 + 4^2 ≠ 7^2 from sinA = 6/7 , A = appr 59° from cosA = 4/7, A = appr 55° Which one is it ?
April 29, 2016

math
avg vel = total distance / total time find the time from 2:00 pm to 5:45 pm, write it as a decimal and go for it.
April 28, 2016

Algebra
ummmhh, if the points don't form a straight line, then the function is not linear.
April 28, 2016

math
I don't see any choices. y = 2x^3 - 4x + 1 dy/dx = 6x^2 - 4 at x = -1, dy/dx = 6-4 = 2 y = -2 + 4+1 = 3 so we have slope = 2, point is (-1,3) equation of tangent: y - 3 = 2(x + 1) dress it up to whatever form you need.
April 28, 2016

math
those codes don't work here, I read that as: C(x) = x^2 + 2 R(x) = 2x^2 - x equate them: 2x^2 - x = x^2 + 2 x^2 - x - 2 = 0 (x-2)(x+1) = 0 x = 2 or x = -1 if x=2, y = 6 if x = -1, y = 3 you had (2,-6) , don't see how you got y = -6 C(x) can never be negative, you are ...
April 28, 2016

geometry
Assuming that the peak of the house is in the centre of the width. tanØ = 40/15 = 8/3 Ø = appr 69°
April 28, 2016

Math
since both are expressed as y = ... we can equate them: x^2 + 2x = 3x + 20 x^2 - x - 20 = 0 (x-5)(x+4) = 0 x = 5 or x = -4 if x = 5, y = 3(5) + 20 = 35 if x = -4, y = 3(-4) + 20 = 8 x=5, y = 35 x = -4, y = 8 check: http://www.wolframalpha.com/input/?i=solve+y%3Dx%5E2%2B2x,++y%...
April 28, 2016

Alias robert
a = 2 v = 2t + c, where t is in seconds when t=0, v = 0 , (it started from rest) 0 = 0 + c, c = 0 v = 2t s = t^2 + k when t = 0, s = 0 , (hasn't gone anywhere) after 10 seconds v = 20 m/s s = 100 m now goes for 20 s, at 20 m/s, covering 400 m so it can covered 500 m, and ...
April 28, 2016