Wednesday
May 25, 2016

# Posts by Reiny

Total # Posts: 34,785

Math
done, see above to your other post
March 8, 2016

algebra
simply sub t = 2 into your equation and do the math. at ground level, h = 0 0 = -16t^2 + 48t 16t^2 - 48t = 0 t^2 - 3t = 0 t(t-3) = 0 t = 0 ---> at the start it is at ground level or t = 3 state your conclusion
March 8, 2016

maths
amount of solid in the original sphere = (4/3)π(4^3) - (4/3)π(2^3) = (4/3)π(64-8) = 224π/3 This must become the volume of a cone (1/3)π(4^2)h = 224π/3 time 3/π 16h = 224 h = 14 cm
March 8, 2016

trig
you should know the expansions for cos(A+B) and for cos(A-B) cos(x-π/6) = cosxcos π/6 + sinxsin π/6 = (√3/2)x + (1/2)sinx cos(x+ π/6) = (√3/2)cosx - (1/2)sinx so .... cos(x - π/6) = 1 + cos(x + π/6) (√3/2)x + (1/2)sinx = 1 + (&#...
March 8, 2016

you would want: 3.75sin(733t) + 7.5 = 3.75sin[733(t+ 4π/3)] + 7.5 divide each term by 3.75, (how convenient ?) sin(733t) + 2 = sin[733(t+ 4π/3)] + 2 sin(733t) = sin[733(t+ 4π/3)] this can only be true if 733t = 733(t + 4π/3) OR 733(t+4π/3) = π - ...
March 8, 2016

Finite
what is 50( (1+.05/52)^208 - 1)/(.05/52) ?
March 7, 2016

Trigonometry
from 3cos^2 Ø -4sinØ =sin^2 Ø , why not replace the cos^2 Ø 3(1 - sin^2 Ø) - 4sinØ - sin^2 Ø = 0 .. 4sin^2 Ø + 4sinØ - 3 = 0 (2sinØ - 1)(2sinØ + 3) = 0 sinØ = 1/2 or sinØ = -3/2 which is...
March 7, 2016

algebra 1
let her monthly payment be P P( 1 - (1+.046/12)^-60)/(.046/12) = 8500 P = 158.85 total paid = 60(158.85) = \$9531.15
March 7, 2016

correction - Maths
surface area of earth which is land = (1/4)4πr^2 = π(6370)^2 = 127,476,091 km^2 =
March 7, 2016

John is wrong - precalc
John, you misread the question 2^(3x + 1) = 3^(x − 2) is not the same as 2 log(3x+1) = 3 log(x-2) then, log(3x +1) /log (x-2) ≠ log (3x + 1 -x +2) e.g. is log100/log10 = log(100-10) ??? LS = 2/1 = 2 RS = log 90
March 7, 2016

precalc
take logs of both sides and use log rules (3x+1)log2 = (x-2)log3 3log2 x + log2 = log3 x - 2log3 x(3log2 - log3) = -2log3 - lo2 x = (2log3 + log2)/(log3 - 3log2)
March 7, 2016

precalc
using our rules of logs , which you should have at your fingertips, log2 ( (x+17)/(x-2) ) = 1 so (x+17)/(x-2) = 2^1 solve for x , remember x> 2 for the log to be defined.
March 7, 2016

Math
They both would have run the same time. Let that time be t hrs. distance covered by zebra = 40t miles distance covered by lion = 50t miles The difference in their distances is 1000 ft or 1000/5280 miles 50t - 40t = 1000/5280 10t = 1000/5280 t = 100/5280 = .0189.. hrs = 1.13636...
March 7, 2016

Math
unit digit --- x tens digit --- x-1 hundred digit --- 6 , to be between 600 and 700 Just translate the English into Math using my definitions: the sum of the digits = x + x-1 + 6 the 3-digit number = 600+10(x-1) + x 600 + 10(x-1) + x = 30(x + x-1 + 6) - 1 solve for x and all ...
March 7, 2016

math
amount = 600(1.05)^2 = ... how can you not be sure ?
March 7, 2016

math
with 3 girls: = C(10,3) x C(15,1) = .. with 4 girls = C(10,4) x C(15,0) = add them up
March 7, 2016

math
The two numbers: x and x+1 (x+1)^2 = x(x+1) solve for x
March 7, 2016

geometric progression
given: ar^4 = 48 ar^6 = (1/8)ar^3 8ar^6 = ar^3 8r^3 = 1 r = 1/2 back into ar^4 = 48 a(1/16) = 48 a = 768 series is 768 + 384 + 192 + 96 + 48 + 24 + 12 + .... Check: is the 5th term 48 ? YES is the 7th term 1/8 of the 4th ? is 12 =(1/8)(96) ?, YES My answer is correct
March 7, 2016

trig
sin 4x = sin 2x 2sin 2x cos 2x - sin 2x = 0 sin 2x(2 cos 2x - 1) = sin2x = 0 so 2x = 0, π, 2π, 3π, .. x = 0, π/2, π , 3π/2, 2π for 0≤x≤2π or cos2x = 1/2 2x = π/3, 2π-π/3, ..., the primaries x = π/6, 5π...
March 7, 2016

Math
Are you using tables, charts, or software?
March 6, 2016

trig plz help
You obviously have a diagram. Mark in all the given information. let the horizontal (adjacent to 46°21') be x ft What trig ratio involves opposite and adjacent?
March 6, 2016

trig
cot Ø = 4 then tan Ø = 1/4, and Ø is acute, thus in quadrant I Did you make a sketch of the triangle? recall that tanØ = y/x so y = 1, and x = 4 can you find r ? How is sinØ defined in terms of x, y, and r ? Did you know that cos 2Ø = ...
March 6, 2016

Probability
What is the definition of probability? So in your experiment in how many of the 500 cases did you get the required event ?
March 6, 2016

trig
recall that 1 + cot^2 x = csc^2 x as a variation of the Pythagorean identity so LS = (csc^2x+1)(csc^2 x-1)/cot^2x = (1 + cot^2 x + 1)(1 + cot^2 x -1)/cot^2 x) = 2 + cot^2 x = RS
March 6, 2016

algebra 2
What is wrong with my "final" equation. Why mess up a nice looking equation in factored form ?? your answer is correct, if you fix that typo in "-x.5x^2"
March 6, 2016

algebra 2
I will do mine using just a good ol' fashioned pencil and paper ... intercepts are -4, 2, and 5 so y = a(x+4)(x-2)(x-5) The a will stretch it and force it to go through (6,20) 20 = a(10)(4)(1) 20 = 40a a = 1/2 y = (1/2)(x+4)(x-2)(x-5) Well, what do you know, I didn't ...
March 6, 2016

calc 1
You haven't defined your x and y, so I can't answer the last part of your question. On my diagram, I have a right-angled triangle with a height of 1 m, a horizontal of x m and a hypotenuse of y m given: dy/dt = -1 m/s ( I made it negative, because the value of y will ...
March 6, 2016

Math
number of chain saws --- x number of chippers ----- y 7x + 3y ≤ 63 ---> time inequation profit = 190x + 220y we need integer values of x and y only possible cases from 7x + 3y = 63 : (0,21) , (3,14), (6,7), (9,0) for (0,21) profit = 0 + 4620 = 4620 for (3,14) profit...
March 6, 2016

Calculus / Rates of Change
ok, let's go with your definitions: height: --- h base --- 1.5h area ---- a given: d(a)/dt = 9 cm/s find dh/dt, when h = 12 (I see variables a for area and h for height. So I will need an equation that contains a and h) a = (1/2)base x height a = (1/2)(h)(1.5h) = .75h^2 d(...
March 6, 2016

trig plz help
tan (3x) = -1 I know that 3x must be in quadrants II or IV and I know that tan 45° = +1 or tan π/4 = 1 so 3x = π - π/4 OR 3x = 2π - π/4 3x = 3π/4 or 3x = 7π/4 x = π/4 or x = 7π/12 now the period of tan 3x is π/3 so adding ...
March 6, 2016

trigonometric
let the height of the mountain be h ft let the distance from the base of the mountain to its vertical line h be x ft (inside the mountain) You have two right-angled triangles. From the first: tan25 = h/(x+600) h = (x+600)tan25 From the 2nd: tan 20 = h/(x+1400) h = (x+1400)...
March 6, 2016

trig gauss jordan
lots of writing... Here is a neat page http://www.gregthatcher.com/Mathematics/GaussJordan.aspx tell it you have 3 rows and 4 columns, then enter the values Notice it takes it all the way to the matrix 1 0 0 ? 0 1 0 ? 0 0 1 ? you only have to go as far as 1 x x x 0 1 x x 0 0 1...
March 6, 2016

trig help
centre is the midpoint of the vertices: C(-1,1) our a value is 6, and we don't know b but we know b/a = 1/3 b/6 = 1/3 3b = 6 b = 2 (x+1)^2 / 36 - (y-1)^2/4 = 1 or (x+1)^2 - 9(y-1)^2 = 36 verification: http://www.wolframalpha.com/input/?i=plot+(x%2B1)%5E2+-+9(y-1)%5E2+%3D+36
March 6, 2016

mat
nice graph, what about it ? http://www.wolframalpha.com/input/?i=f(x)%3D5sin%5E2x-8cos%5E5x
March 6, 2016

Math
Perfect for this page ... http://davidmlane.com/hyperstat/z_table.html click on above prob = .1587 multiply that by 8000
March 6, 2016

algebra
rate of sailing in still water , assuming the lake has no current ---- x km/h rate of sailing in river against current -- x-2 km/h time in river = 6/(x-2) time in lake = 15/x the difference in those times is = 1 form the equation and solve for x hint: I would multiply each ...
March 6, 2016

#2 7(2p − 1) just expand, takes 1 step = 14p - 7 ----> C #3, 1.8c + 5.4cd, common factor is 1.8c, one step = 1.8c( 1 + 3d)
March 6, 2016

1.C -- correct 2.D -- wrong 3 Idk. - wrong 4.C -- wrong 5.A -- wrong 6.D -- wrong I think you were just guessing, hoping that now I would do them for you. Why not show your steps to get these answers, that way I can help you.
March 6, 2016

March 6, 2016

Math
What is your choice and why ?
March 6, 2016

trig/ellipse equation
the major axis is vertical, and a = 5, b = 6 , and centre is (-1,-2) equation: (x+1)^2/25 + (y+2)^2/36 = 1
March 6, 2016

math
but it said the tens digit is less than 9, your is 9 how about 78?
March 6, 2016

Math
I made a sketch, and let RS = PS = x then QP = 3x Draw RC || SP to meet QP at C Then CP = x and QC = 2x PCRS is now a ||gram, making angle QCR = 60° In triangle RCQ, by the cosine law: QR^2 = (2x)^2 + x^2 - 2(x)(2x)cos60° = 5x^2 - 4x^2 (1/2) = 3x^2 QR = √3 x In ...
March 6, 2016

math
I will assume you meant: "largest volume" Obviously the "bose" must be a cube. Sketch a cross-section I see a square in a circle, with a diameter of 2. let each side of the cube be x then x^2 + x^2 = 2^2 2x^2 = 4 x^2 = 2 x = √2 The "bose" is...
March 6, 2016

Physics ?? - Maths
sounds like Physics to me
March 6, 2016

algebra
a=3/8, r = 2 term8 = ar^7 = (3/8)(2^7) = ....
March 6, 2016

Calculus
area = πr^2 d(area)/dt = 2πr dr/dt given: dr/dt = -4 inches/hr find d(area)/dt when r = 108 inches d(area)/dt = 2π(108)(-4) inches^2/hr = appr 2714.3 inches^2/h if you had said 3:00 am, the time would have been 3 hrs, and the radius would have shrunk by 12 ...
March 6, 2016

trigonometry
See my previous comment http://www.jiskha.com/display.cgi?id=1457256421
March 6, 2016

Maths
let height of tower be h m let height of "flay" pole be f m two right-angled triangles: tan40 = h/10 h = 10tan40 tan 50 = (h+f)/10 h+ f = 10tan50 continue
March 6, 2016

I will let the y-axis be the axis of symmetry So the vertex is (0,24) so the equation must be y = a(x-0)^2 + 24 y = ax^2 + 24 but we have two points at the top of the tower, (84,??) and (-84,??) Unless I am misreading the question, we are missing information. How high are the ...
March 6, 2016

trigonometry
This and your previous questions have all been the same type. You have shown no effort on your part or indicated where your difficulties lie. Did you just want us to simply do them for you ?
March 6, 2016

trigonometry
You have a triangle with sides 8(24) km and 8(28) km, and the contained angle of (180 - 38°15; - 51°45') between them Just use the cosine law
March 6, 2016

Math
Euler's formula: V-E+F=2 14-E + 21 = 2 -E = -33 E = 33
March 6, 2016

trigonometry
I see a right-angled triangle with a horizontal side of 10 km and its opposite angle 40°20' for original position SL tan 40°20' = 10/SL SL = 10/tan40°20' = 11.7776.. km for final position LS' sin40°20' = 10/LS' you finish it, and state ...
March 6, 2016

linear equations
√(5-x) = x+1 To be defined, 5-x ≥ 0 -x ≥ -5 x ≤ 5 also since √anything yields a positive result, x+1≥0 x≥-1 so -1 ≤ x ≤ 5 To solve, square both sides 5-x = x^2 + 2x + 1 x^2 + 3x - 4 = 0 (x+4)(x-1) = 0 x = -4 or x = 1 ...
March 6, 2016

x = ±√( (4-8p)/4) square it x^2 = (4-8p)/4 x^2 = 1 - 2p x^2 + 2p = 1 x^2 + 2p + p^2 = 1+p^2 , I completed the square (x+p)^2 = 1+p^2 x+p = ±√(1+p^2) x = -p ± √(1+p^2) since 1+p^2 is always positive , x will always be real to have equal ...
March 6, 2016

Calculus Derivatives
y' = x(1/x) + lnx = 1 + lnx y'' = 1/x ---> yup, you had that concave up when 1/x > 0 or x> 0 concave down when 1/x < 0, or x < 0 yes, you got it!
March 5, 2016

math
the sheet of paper is 324 cm by 172 cm The tempation is to say: area of whole paper = 55728 cm^2 area of 1 envelope = 216 so we have 55728/216 or 258 envelopes. BUT, not so fast ..... If we lay the length of the envelope along the long side of the large sheet, we can get 324/...
March 5, 2016

Calculus
Found this youtube for you He is doing dx/√(x^2+a^2) so for yours a^2 = 16, a = 4 https://www.youtube.com/watch?v=MWfA85-Mb50 Have fun
March 5, 2016

Math
prob(good) = .9 prob(bad) = .1 you want prob(6 of 7 to be good) = C(7,6)(.9)^6 (.1) = .. you push the buttons
March 5, 2016

Math
value of \$1.00 at end of 1 year: Bank A : amount = (1 +.0479/12)^12 = ... Bank B : amount = (1 + .048/4)^4 = .. compare the results
March 5, 2016

Algebra
are we solving √(8-3x) + √(6x-1) = 7 - 2√(9x-24) ???? I tested it in Wolfram, and there is no "real" solution, so I won't even try. http://www.wolframalpha.com/input/?i=%E2%88%9A(8-3x)+%2B+%E2%88%9A(6x-1)+%3D+7+-+2%E2%88%9A(9x-24) notice that ...
March 5, 2016

math
factors of 1440 2x720 3x480 4x360 5x288 6x240 8x180 9x160 10x144 12x120 15x96 16x90 18x80 20x72 24x60 30x48 32x45 36x40 ---> that's all of them values of n^2-1 1,3,8,15,24,35,48,63,80,99,120,143,168,195,288,325,360,399,440,483,529,575,624,675,728 the largest of these ...
March 5, 2016

math
values of n+1 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,.... multiples of 4n+1 5,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81,85,89,93,97,101,... let 4n+1) = k(n+1) k = (4n+1)/(n+1) , so k has to be whole number if n=2 , 9/3 = 3 --> k = 3 if n=3, 13/4 ≠ ...
March 5, 2016

Algebra
speed of slower --- x km/h speed of faster ---- x+2 km/h 20/x - 20/(x+2) = 20/60 = 1/3 times 3x(x+2) , the LCD 60(x+2) - 60x = x(x+2) x^2 + 2x - 120 = 0 (x+12)(x-10) = 0 x = 10 or x = -12, the ladder is silly The slower one went 10 km/h, and the faster went 12 km/h check: 20/...
March 5, 2016

Math
width --- x length --- (6/5)x (6/5)x^2 = 480 x^2 = 400 x = √400 = 20 picture is 20 inches by 24 inches
March 5, 2016

Did you mean simple interest? if so, PRT = I 52600(.05)T = 1261 T = 1261/(.05(52600)) = .4795 years or 175 days check: 52600(.05)(175/365) = 1260.96 or \$1261
March 5, 2016

Calc Derivatives
you should say y = (4x-3)/(3x^(1/2)) or f(x) = (4x-3)/(3x^(1/2)) dy/dx =[ 3x^(1/2) (4) - (4x-3)(3/2)x^(-1/2) ]/(9x) = 0 for a max/min 12x^(1/2) = (3/2)(4x-3)/x^(1/2) 12x = (3/2)(4x - 3) 24x = 12x - 9 12x=-9 x = -3/4 , but x ≥0 or else x^(1/2) is undefined. There are no ...
March 5, 2016

math ples help
using these log rules: log(ab) = loga + logb log(a/b) = loga - logb log( a^n) = nloga Rewrite 2log8/6 + 2^2log3 - 2log12 as log(64/36) + 4log3 - log144 = log(64/36) + log81 - log144 = log ( (64/36)(81)/144) = log 1 = 0
March 5, 2016

Math
The simple proportion for your similar triangles: h/48 = 5/12 12h = 240 h = 20 or by straight logic: The mirror is 4 times the distance away from the pole as she is from the mirror. So the flage pole is 4 times her height, or 20 ft " Find the geometric mean of the pair of...
March 5, 2016

math
Ok ... RS = sinx/√(1+cosx) * √(1-cosx)/√(1-cosx) , you did that = sinx √(1-cosx) /(√( (1+cox)(1-cosx) ) = sinx √(1-cosx)/√(1 - cos^2 x) = sinx √(1-cosx)/√sin^2 x = sinx √(1-cosx)/sinx = √(1-cosx) = LS
March 5, 2016

math
solve for m, the number of miles .09m + 57.98 = .14m + 49.98 9m + 5798 = 14m + 4998 ...
March 5, 2016

Math
Make a Venn diagram Label it P and B, for pepperoni and banana put 5 in the intersection of both circles - of the 25 who like pepperoni, 5 are already counted, so put 20 in the P circle apart from the intersection. - of the 31 who like banana peppers, 5 are already counted, so...
March 5, 2016

Maxima, Stationary Points
If (9*x^6+28*x^4+51*x^2-88*x-10)/(3*x^2+2)^2 is the derivative of some function and you want to find max/min, you would set the above equal to zero that would leave you with 9x^6 + 28x^4 + 51x^2 - 88x - 10 = 0 I am not at all familiar with your software, but my favourite math ...
March 5, 2016

math
How good are you at sketching 3-D diagrams? I let P be the point directly below plane A, and I now have 4 triangles, each in their own plane. Redraw each with a side view: right-triangle ABP , right angle at P right-triangle ACP, right angle at P triangle BCP , (on ocean floor...
March 5, 2016

trigonometry
sinx/secx = 1/tanx+cotx , is not true but sinx/secx = 1/(tanx+cotx) is true LS = sinx(1/cosx) =sinxcosx RS = 1/(sinx/cosx + cosx/sinx) = 1/( (sin^2 x + cos^2 x)/(sinxcosx) ) = 1/(1/sinxcosx)) = sinxcosx = LS
March 5, 2016

college algebra
let the three numbers be x x+2 x+4 2x - (x+2) = 20 x = 22 largest is x+4 = 26
March 5, 2016

MATH
Make a sketch, (it won't be to scale!) You will have an isosceles triangle with an angle at the earth of 31 minutes of angle. Draw in a perpendicular which would be 360,000 km If the radius of the moon is r, I see it as tan (0°15'30") = r/360000 r = 360000(tan...
March 5, 2016

Math
let the two numbers be 3x and 4x 3x+10 = 4x - 10 solve for x
March 5, 2016

Allgebra
let the two numbers be x and y (x+y)/2 = 17 x+y = 34 --> y = 34-x √(xy) = 8 xy=64 x(34-x) = 64 x^2 - 34x = -64 x^2 - 34x + 289 = 289-64 ---> I completed the square (x-17)^2 = 225 x-17 = ±15 x = 32 or x = 2 if x = 32, y = 2 if x = 2, y = 32 , (called ...
March 5, 2016

Algebra
in a harmonic progression, the reciprocals of its terms form an arithmetic progression. so if the third term of the HP is x then 1/a , 1/b, and 1/x form an AP that is, 1/b - 1/a = 1/x - 1/b 2/b - 1/a = 1/x (2a - b)/(ab) = 1/x x = ab/(2a - b)
March 5, 2016

Algebra
"one third of a one third of a point is deducted" - why not just say say: " 1/9 of a point is deducted for an incorrecte answer" ?? number correct --- x number incorrect --- 72-x x - (1/9)(72-x) ≥ 60 x - 8 + (1/9)x ≥ 60 (10/9)x ≥ 68 x &#...
March 4, 2016

maths
1/x + 1/(x+6) = 1/(40/3) = 3/40 times 40x(x+6) 40(x+6) + 40x = 3x(x+6) 3x^2 - 62x - 240 = 0 t = (62 ± √6724)/6 = 24 or -3/1/3 , but x > 0 so x = 24 tom alone can do it in 24 hrs, John alone can do it in 30 hours check: at combined time, time of job = 1/(1/24+1/...
March 4, 2016

probability
prob(zero people leave tip) = C(6,0)(.7)^0 (.3)^6 = .000729 prob(1 person leaves tip) = C(6,1)(.7)(.3)^5 = .010206 prob(2 persons leave tip) = C(6,2)(.7)^2 (.3)^4 = .059535 prob(3 persons leave tip) = C(6,3)(.7)^3 (.3)^3 = .18522 prob(4 people leave tip) = C(6,4)(.7)^4 (.3)^2...
March 4, 2016

Calculus with Analytical Geometry
you are looking for the vertex of h = -16t^2 + 1000t + 20 the t of the vertex is -1000/-32 = 31.25 seconds for that value of t, h = 15645 ft
March 4, 2016

Math Algebra Intermediate
ay - a^6 y^6 = ay(1 - a^5 y^5) Much Ado About Nothing, as Shakespeare would say.
March 4, 2016

Math
i = .042/12 = .0035 n = 30(12) = 360 PV =.8(260000) = 208,000 let the payment be P P( 1 - 1.0035^-360)/.0035 = 208000 P = \$1017.16
March 4, 2016

Math
S(1) = 2 by the formula: S(1) = 1(1 + 3)/2 = 2 S(2) = 2+5 = 7 by the formula: S(2) = 2(1+6)/2 = 7 S(3) = 2+5+8 = 15 by formula: S(3) = 3(1+9)/2 = 15 seems to work.
March 4, 2016

math
let the two numbers be x and x+1 4x + x(x+1) = 36 x^2 + 5x - 36 = 0 (x+9)(x-4) = 0 x = 4 or x = -9, but x>0 x = 4 the two numbers are 4 and 5
March 4, 2016

Algebra 2
(log5 16^3 )(log11 6^2 = log x 3(log16/log5)(2)(log6/log11) = logx 6(log16/log5)(log6/log11) 6(1.28724...) = logx 7.72346... x = 10^7.72346.. x = appr 52,900,679 I was using the log properties: log a^n = n loga , and log a b = logb/loga
March 4, 2016

algebra 1b
typo: don't know where my 20 came from. should have been: quarters ---- x nickels ----- 16-x solve for x: 25x + 5(16-x) = 220
March 4, 2016

algebra 1b
quarters ---- x nickels ----- 20-x solve for x: 25x + 5(20-x) = 220
March 4, 2016

math
let the total be x make a Venn diagram of two intersecting circles, and place 27 in the intersection. In the exclusive parts of the two circles place (3/4)x - 27 and (4/7)x - 27 then: (3/4)x-27 + 27 + (4/7)x-27 = x (3/4)x + (4/7)x-27 = x multiply each term by 28, the LCD 21x...
March 4, 2016

Math
Was that supposed to say KL = 14 ? I will assume that, since N does not enter the picture elsewhere. Let's find angle K, the largest angle. 18^2 = 14^2 + 16^2 - 2(14)(16)cosK 448cosK = 128 cosK = 2/7 K = appr 73.4° area = (1/2)(14)(16)sinK = 112(.9583..) = appr 107.33 ...
March 3, 2016

Geometry
in any rhombus, the diagonals right-bisect each other. illustration: midpoint of PR = (0,0) midpoint of QS = (0,1/2) oops, something is not right the figure is not a rhombus, I think S should be (1,-2) then midpoint of QS is also (0,0) and the two diagonals would bisect each ...
March 3, 2016

typo at end - statistics
Last line of previous post should have been: number of ways = 4x36 = 144
March 3, 2016

statistics
a) consider each couple as one unit, so you are just arranging 3 units. Number of ways = 3! = 6 b) I don't understand the question c) for the men to sit together, we could have MMMWWW **** WMMMWW WWMMMW WWWMMM Number of ways to do *** = 3x2x1x3x2x1=36 but each of the other...
March 3, 2016

Calculus Related Rates
let the distance between them be x ft after a time of t seconds, distance of the northbound person = 4t ft distance of the other person = 5t ft They walk at an angle of 45° to each other. By the cosine law: x^2 = (4t)^2 + (5t)^2 - 2(4t)(5t)cos45 = 41t^2 - 40t^2 (√2/2...
March 3, 2016

Algebra
so you have an arithmetic series with a = 30,000 , d = 2300 sum(10) = (10/2)(60000 + 9(2300) ) = 403,500
March 3, 2016

mathematics
The way you typed it, all is good, the expression would be real and defined for all values of x but... if you meant: 5x+4÷√(8-4x) , then we have two concerns 1. to be real, 8-4x ≥ 0 -4x ≥ -8 x ≤ 2 2. to be defined: 8-4x ≠ 0 -4 ≠ -8 x...
March 3, 2016