Tuesday

September 2, 2014

September 2, 2014

Total # Posts: 27,020

**algebra**

I have a strong feeling you meant (x-4)(x+2)/( (x-3)(x+5) ) ≥ 0 I good and fast way is to look at the graph of y = (x-4)( (x+2)/(x-3)(x+5) ) http://www.wolframalpha.com/input/?i=y+%3D+%28x-4%29%28x%2B2%29%2F%28%28x-3%29%28x%2B5%29%29 It shows the graph to be above the x-...
*March 28, 2014*

**Geometry**

You are missing one of the dimensions of the floor, its length Once you have that, Cost = 105 ( 33 * 1/2 * ??)/27 units of money where ?? in your length we divide by 27 since there are 27 cubic feet in 1 cubic yard If the concrete is sold in whole cubic yards, you will have to...
*March 28, 2014*

**ALGEBRA**

the t of the vertex of your parabola is -b/(2a) = -20/-32 = 5/8 at t = 5/8 h = -16(25/64)+20(5/8) + 6 = 12.25 nope!
*March 28, 2014*

**math**

avg rate of change = (23500 - 8750)/(8 = ...
*March 27, 2014*

**Math**

treat it as two ordered pairs (t, c) where t is temperature and c is consumption so we have (90,220) and (76, 178) slope = (220-178)(/(90-76) = 42/14 = 3 so: c-220 = 3(t-90) c = 3t - 270+220 c = 3t - 50 check: if t = 90, c = 270-50 = 220 if t = 76, c = 228 - 50 = 178
*March 27, 2014*

**Math**

no, 26x^2 ≠ x√26 Whatever made you think so. let x = 4 26(4^2) = 26*16 = 416 xV26 = 4√26 = appr 20.4 is 416 = 20.4 ???? However, you could write 26x^ as (x√26)^2
*March 27, 2014*

**Math**

Imagine "opening up" a cylinder, what would you get? 2 equal circles + a rectangle whose length is the circumference of the circle and whose height is the height of the cylinder. so SA = 2π(6^2) + 2π(6)(20) = 72π + 240π = 312π = appr 980 No ...
*March 27, 2014*

**Math**

I assume you pick a card, then throw the die primes from 1-10 : 2,3,5,7 , so 4 of them primes on a die: 2 3 5, so 3 of them prob(2 primes) = (4/10)(3/6) = 1/5 prob(not 2 primes) = 4/5 odds in favour of getting two primes = (1/5) : (4/5 = 1 : 4
*March 27, 2014*

**2nd question - math help!!**

(x+y)^2-x-y = (x+y)^2 - (x+y) = (x+y)(x + y - 1)
*March 27, 2014*

**math help!!**

To make it easier to see, let 2x^2 - x = a so you have 2a^2 - 3a - 9 = (a-3)(2a+3) put the original back in = (2x^2 - x - 3)(4x^2 - 2x + 3) = (x + 1)(2x - 3)(4x^2 - 2x + 3)
*March 27, 2014*

**Math**

cosine law .... 5.4^2 = 6.2^2 + 3.6^2 - 2(6.2)(3.6)cosR cosR = 22.24/44.64 = .4982.. R = 60.1°
*March 27, 2014*

**Math**

direct application of the sine law: x/sin41 = 96/sin71 x = 96sin41/sin71 = ....
*March 27, 2014*

**Calculus Help Please!!!**

According to Newton's Law of Cooling T(t) = roomtemp + (37 - 20)e^(-kt) , where t is the time in hours and k is a constant so we get two equations: 32.5 = 20 + 17e^(-kt) ---> 12.5 = 17e^(-kt) and 30.3 = 20 + 17e^(-k(t+1)) ---> 10.3 = 17e^(-kt - k) divide them: 115/...
*March 27, 2014*

**Algebra**

did you try factoring both expressions? They factor quite easily. Then divide out the common factor, don't forget to state the restriction.
*March 27, 2014*

**trig**

Not sure what notation you are using when you say "blowing in at 53° " is North your 0° and you are going clockwise, or is 0° your positive x - axis and you are going counterclockwise ?
*March 27, 2014*

**Calculus**

just using ln a^b = b ln a ln (243^3/5 *32^4/5) = ln ( (3^5)^(3/5) * (2^5)^(4/5) ) = ln ( 3^3 * 2^4) = ln (27*16) = ln(432) 1/5 ln (243^3 * 32^4) = ln [ (243^3 * 32^4) ^(1/5) ] = ln (243^(3/5) * 32^(4/5) ) = .... = ln(432)
*March 27, 2014*

**Calculus**

I agree with Damon's "huh" since ln (243^3/5 *32^4/5) = 1/5 ln (243^3 * 32^4)
*March 27, 2014*

**FINANCE**

choice A: pay 3100(.85) or 2635 now choice B: pay 12 payments of 270 present value of the 12 payments at a monthly rate of i = 270( 1 - (1+i)^-12)/i= 2635 hard to solve, let Wolfram do it for us (I changed the i to x, since Wolfram thinks i = √-1 ) http://www....
*March 26, 2014*

**math 2**

let E(x,y) be your point use ratios ... for the x: (x-3)/(11-3) = 3/8 8x-24 = 24 8x = 48 x = 6 for the y: (y-4)/(3-4) = 3/8 8y - 32 = -3 8y = 29 y = 29/8 E is (6,29/8)
*March 26, 2014*

**math**

y - 6 = .5x - 3.5 y = .5x - 3.6 + 6 y = .5x + 2.5
*March 26, 2014*

**math**

slope of AB = 4/-2 = -2 so slope of new line = +1/2 new line: y-6 = (1/2)(x-7) expand and doctor it up any way you want.
*March 26, 2014*

**argggh - Calculus**

messed up in my expansion volume should have been 4x^3- 120x^2 + 800x and V' = 12x^2 - 240x + 800 = 0 3x^2 - 60x + 200=0 to get x = 4.23
*March 26, 2014*

**Calculus**

First things first: width --- s length ---- 2s 2s^2 = 800 s^2 = 400 s = 20 so the piece of metal is 20 by 40 let the side of the square to be cut out be x so the width is 20-2x the length is 40-2x the height is x Volume = x(20-2x)(40-2x) = 2x^3 - 120x^2 + 800x d(Volume)/dx = ...
*March 26, 2014*

**Algreba**

What about it ?
*March 26, 2014*

**Calculus**

you should have recalled that sin (-x) = -sinx so that sin(-.1) could not have been positive. did you mean -.1 ?
*March 26, 2014*

**Math**

slope of new line must be -2 so y =-2x + b plug in the given point (2,-7) -7 = -2(2) + b -3 = b y = -2x - 3
*March 26, 2014*

**Calculus**

yes v(t) = h ' (t) = -16t + 5 so v(0) = -16(0) + 5 = 5
*March 26, 2014*

**math**

times 8 8B = 3(A-10) 8B = 3A - 30 8B+30 = 3A A = (8B+30)/3
*March 26, 2014*

**Math**

divide the fist equation by 2 to get y = 9x now plug that into the second: 9x - 6 = 2x 7x = 6 x = 6/7 then y = 9(6/7) = 54/7 x = 6/7 y = 54/7
*March 26, 2014*

**math**

I suspect that your equation is C = 6u^2 v (usually they would not separate factors of 6 and 2 like you did, and would have C = 12uv instead) Please confirm.
*March 26, 2014*

**Math**

prob(2dimes) = (8/14)(7/13) = 4/13
*March 26, 2014*

**Math**

consider the equation of the circle with centre (1,2) and radius 10 Its equation is (x-1)^2 + (y-2)^2 = 100 (7, 10) satisfies that equation, (7-1)^2 + (10-2)^2 = 100 6^2 + 8^2 = 100 36+64 = 100 100=100 so it is (7,10)
*March 26, 2014*

**College Calculus**

let Ø be the angle between them the angular velocity of the minute hand = 2π/60 rad/min = π/30 rad/min the angular velicity of the hour hand = 2π/(12(60)) or π/720 rad/min then, so dØ/dt = (π/30 - π/720) rad/min dØ/dt = 23&#...
*March 26, 2014*

**Math**

looks like a combination recursion let term(n) be the nth term, term(1) = 2 if n is odd: term(n) = 3term(n-1) if n is even: term(n)= term(n-1) - 2 so the next terms are: 26, 78, 76, 228, 226, 678 .....
*March 26, 2014*

**integer Math**

Since they gave the answer as 7 , I am taking a guess that they wanted √52
*March 26, 2014*

**Math**

x( 1.07^27 - 1)/.07 =25000 x(74.483823..) = 250000 x = $ 3356.43
*March 26, 2014*

**Precalculus II**

don't you just love Wolfram http://www.wolframalpha.com/input/?i=plot+sec%5E2%28x%29%2B+3+tan%28x%29%3D5%2C+-2π+%3C+x+%3C+2π
*March 26, 2014*

**math**

Steve, that is really scary.
*March 26, 2014*

**math**

period of first = 2π/(12π) = 1/6 period of 2nd = 2π/(18π) = 1/9 1/3 is a factor of both, so the period = 1/3 verification: http://www.wolframalpha.com/input/?i=10+sin%2812+pi+t%29%2B4+cos%2818+pi+t%29
*March 26, 2014*

**Finance**

300( 1 - 1.01^-n)/.01 = 2000 300(1 - 1.01^-n) = 20 1 - 1.01^-n = 1/15 14/15 = 1.01^-n ln both sides and use rules of logs ln 14 - ln15 = -n ln 1.01 n = (ln 15 - ln 14)/ln 1.01 = 6.934 appr 7 months of course I could have used log 15 etc. and obtained the same result.
*March 26, 2014*

**math**

Who makes up these questions or what kind of strange paint is this? To paint a ceiling of that size should take about 1/2 gallon ( I know, I have too much time on my hand)
*March 26, 2014*

**Math**

number of adults --- A number of kids ----- C A + C = 35 12A + 7C = 315
*March 25, 2014*

**calcules**

Just noticed that both Damon and I answered a very similar question in the first of the Related Questions below http://www.jiskha.com/display.cgi?id=1268848081 I suggest you print it out , and change the numbers, and units.
*March 25, 2014*

**math**

solve 2 = e^(.07t) hint: take ln of both sides and use your log rules remember ln e = 1
*March 25, 2014*

**math**

what is 48000( 1.0105)^40 ?
*March 25, 2014*

**Trigonometry**

tan Ø = -√3 I know that tan 60 = +√3 and Ø could be in II or in IV in II , Ø = 180-60° = 120° or 2π/3 in IV, Ø = 360-60 = 300° or 5π/3
*March 25, 2014*

**Calculus**

let the number be x, and the sum as stated be S S = x^2 + 1/x dS/dx = 2x - 1/x^2 = 0 for a max/min 2x = 1/x^2 2x^3 = 1 x^3 = 1/2 x = (1/2)^(1/3) or the cube root of 1/2
*March 25, 2014*

**Math**

Brady, after all that work, you blew the final answer x+3x+6x = 180 10x=180 x = 10 but I called the angles x, 3x, and 6x so the angles are 18° , 54° , and 108° and of course 108° is the largest angle
*March 25, 2014*

**Math**

let the angles be x , 3x and 6x x + 3x + 6x = 180 take over ....
*March 25, 2014*

**Grade 12 Calculus**

I hope your function looks something like this: R(x) = (5000 - 100x)(30 + x) = 150000+ 5000x - 3000x - 100x^2 = -100x^2 + 2000x + 150000 this is a standard parabola opening dowwards , so it will have a maximum the x of the vertex is -b/(2a) = -2000/-200 = 10 So there should be...
*March 25, 2014*

**Trigonometry**

if sinx = -2/√5 in III y = -2, r = √5 , by Pythagoras, x^2 + 4 = 5 x = -1 in III cosx = -1/√5 tanx = sinx/cosx = (-2/√)/(-1/√5) = 2 sin 2x = 2sinxcosx = 2(-2/√5)(-1/√5) = 4/5 cos 2x = cos^2 x - sin^2 x = 1/5 - 4/5 = -3/5 tan 2x = 2tanx...
*March 25, 2014*

**math**

spent on perches --- x litter -------------- x -326 litter and perches combined = 2x - 326 nesting = 2(2x-326) 2x-326 + 2(2x - 326) = 4050 should be relatively easy to solve for x I get x = 838
*March 25, 2014*

**Algebra 2**

help with what? you didn't ask a question. your function simplifies to ... d(x) = 54x^10/(24x^8) = 4x^2 / 9 surely that wasn't your question, was it ?
*March 25, 2014*

**MATH**

so 2 + 4 + 8 + 16 + ... = 178 sum(n) = a(r^n - 1)/(r-1) 2(2^n - 1)/1 = 178 2^n - 1 = 89 2^n = 90 I know 2^6 = 64 2^7 = 128 2^8 = 256 So I agree with your answer , at the end of 7 you only have 128 but you need 178 so it must be the 8th month how did they come up with 10? ...
*March 25, 2014*

**Math**

first tell me what you got for your inverse matrix
*March 25, 2014*

**Geometry B**

x^2 + y^2 − 2x + 2y − 1 = 0 , notice how we indicate exponents complete the square x^2 + y^2 − 2x + 2y = 1 x^2 - 2x + 1 + y^2 + 2y + 1 = 1+1+1 (x-1)^2 + (y+1)^2 = 3
*March 25, 2014*

**math**

http://www.wolframalpha.com/input/?i=y+%3D+1%2F%283-x%29 asymptote at x = 3
*March 25, 2014*

**discrete mths**

(white, red) ----> 12 13 14 15 16 (5 of them ----> 23 24 25 26 (4 of them) ----> 34 35 36 (3 of them) ----> 45 46 (2 of them) ----> 56 just one so 5+4+3+2+1 = 15 prob(your event) = 15/36
*March 25, 2014*

**algebra 2**

complete the square ... y = -4(x^2 - (3/4)x .....) - 6 , (we usually don't say +-6 to adding a negative 6 ) = -4(x^2 - (3/4)x + 9/64 - 9/64) - 6 , ( take 1/2 of 3/4 to get 3/8, now square that ----> 9/64 = -4( (x - 3/8)^2 - 9/64) - 6 = -4(x-3/8)^ + 9/16 - 6 = -4(x - 3/8...
*March 25, 2014*

**Trigonometry**

http://www.wolframalpha.com/input/?i=y%3D2sin%28x-2pi%2F3%29 for x-intercepts, y = 0 2sin(x-2pi/3) = 0 sin(x-2pi/3)=0 but sin 0 = 0 and sin π =0 and sin 2π = 0 so x - 2π/3 = 0 and x -2π/3 = π and x - 2π/3 = 2π x = 2π/3 or x = π + 2...
*March 24, 2014*

**math**

amount in B ---- x amount in A -----x - 8000 .04x + .08(x-8000) = 1040 times 100 4x + 8(x-8000) = 104000 I am sure you can finish it
*March 24, 2014*

**Algebra**

-5 + 2x^2 = -6x 2x^2 + 6x - 5 = 0 x = (-6 ± √(36 - 4(2)(-5))/4 = (-6 ± √76)/4 = (-6 ± 2√19)/4 = (-3 ± √19)/2
*March 24, 2014*

**Implicity**

1 + 4x dy/dx + 4y (1) = 2y dy/dx 1 + 4y = 2y dy/dx - 4x dy/dx dy/dx(2y - 4x) = 1 + 4y dy/dx = (1+4y)/(2y-4x)
*March 24, 2014*

**Calculus A**

I will assume you meant: h(x) = x^2 + 5x + 4/(x-1) h ' (x) = 2x + 5 - 4/(x-1)^2 = 0 for max/min 2x + 5 = 4/(x-1)^2 (2x+5)(x^2 - 2x + 1) = 4 2x^3 - 4x^2 + 2x + 5x^2 - 10x + 5 = 4 2x^3 + x^2 - 8x + 1 = 0 hard to solve, Wolfram has this http://www.wolframalpha.com/input/?i=2x...
*March 24, 2014*

**math**

after 1st round 7 people receive email after 2nd round 7^2 or 49 receive email after 3rd round 6^3 or 343 receive email after 4th round 7^4 or 2401 receive email after 5th round ...........16807 receive email number receiving email in 5th round = 7^5
*March 24, 2014*

**math**

correct, so .....
*March 24, 2014*

**math**

what is √(300^2 + 50^2 ) ?
*March 24, 2014*

**Maths**

in groups of 4 with 2 left over: 6 10 14 .... 94 98 102 106 110 114 in groups of 5 with 1 left over : 6 11 16 21 .....96 101 106 111 116 .... looks like 106 or 4a + 2 = 5b + 1 4a = 5b - 1 a = (5b-1)/4 but 5b+1 > 100 5b > 99 b > 99/5 or 20, 21, ... let b = 21, then a= ...
*March 24, 2014*

**Algebra 1 Answer Evaluation**

check by expanding your answer, you will see that the first one is wrong you probably meant a^3 - 5a^2 + 2a -10 , says by grouping, so do that ... = a^2(a-5) + 2(a-5) = (a-5)(a^2 + 2)
*March 24, 2014*

**Algebra**

17*w*(2w+4) = 2720 2w^2 + 4w = 160 w^2 + 2w + 1 = 80+1 , I completed the square (w+1)^2 = 81 w+1 = ± √81 w = -1 ± 9 = 8 or some negatiave, which I will reject the width = 8 inches
*March 24, 2014*

**Math**

general equation of a conic: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 we can eliminate the xy term by finding the angle of rotation Ø , so that tan (2Ø) = B/(A-C) and replacing the x and y with a new X and Y, so that x = XcosØ - YsinØ and y = XsinØ...
*March 24, 2014*

**Algebra**

If x=-4 and x = -1 are zeros to one or more of the given functions, then dividing them by both x+1 and x+4 should yield a remainder of zero. I divided x+1 into each of the given functions (I used synthetic division), each yielded a remainder. So x+1 did not divide into any of ...
*March 24, 2014*

**good catch , Calcules**

yup, looked over my work and found an error in my SA substitution. SA = 2(4xy) +2(x)(4x) + 2(xy) .... = 10x(231/x^2) + 8x^2 ---->10x(231/(4x^2)) + 8x^2 to produce your answers
*March 23, 2014*

**Calcules**

let the height be x then the width is 4x , (the height is 1/4 of the width, this way I have no fractions ) let the length be y volume = (x)(4x)(y) = 4x^2 y 4x^2 y = 231 y = 231/(4x^2) SA = 2(4xy) +2(x)(4x) + 2(xy) = 8xy + 8x^2 + 2xy = 10xy+8x^2 = 10x(231/x^2) + 8x^2 = 2310/x...
*March 23, 2014*

**MATH HELP!!**

from the 2nd: 2c + 6d = -34 c + 3d = -17 c = -3d-17 plug into the 1st: 3(-3d-17) - 7d = -3 -9d - 51 - 7d = -3 -16d = 48 d = -3 then c = -3(-3) - 17 = -8 c = -8 , d = -3
*March 23, 2014*

**Algebra II**

double the 2nd c - 6d = 16 add to the first 3c = 30 c = 10 back into the 1st 20 + 6d = 14 6d = -6 d = -1 c = 10 , d = -1
*March 23, 2014*

**algebra 2**

what is 3500(1.025) ?
*March 23, 2014*

**trig**

sin(anything) lies between -1 and +1 so -18sin(71π t) lies between -18 and +18 then p lies between 83-18 and 83+18 or between 65 and 101 period of your function = 2π/(71π) = 2/71 min or appr 1.69 seconds 1.69 seconds = 1 beat 1 second = 1/1.69 beats 60 seconds...
*March 23, 2014*

**maths**

distance along flight path = (3/4)(220) = 165 km measured horizontally: cos 25° = x/16 x = 165cos28 = 49.54 km
*March 23, 2014*

**Math**

Just noticed that Steve answered the same question when you reposted it just a few entries above this Please avoid reposting the same question, especially when it still shows near the top of the list of questions like it did here. It avoids unnecessary duplication of solutions.
*March 23, 2014*

**Math**

vector ab = (-3,4,1) vector dc = (3, -4, -1) = vector cd since their magnitude is the same, and they simply have opposite direction they must be equal and parallel So the figure is a parallogram vector cb = (0,-2,6) area = cross product of ab and cb = (-3,4,1) x (0,-2,6) = (26...
*March 23, 2014*

**Math**

loan at 2.8% --- $ x loan at 4.5 % ---- $ 31000-x solve for x .... .028x + .045(31000-x = 1024.40 times 1000 28x + 45(31000-x) = 1024400 etc
*March 22, 2014*

**Algebra**

Just noticed a typo (sticking 3 key) <taking the first 3 I got: a = 5.5 , b=-12.5 , c = 12> should say: taking the first 3 I got: a = 53.5 , b=-12.5 , c = 12 btw , I did not show how I solved those 3 equations in 3 unknowns, I used a webpage for that http://www.1728.org/...
*March 22, 2014*

**Algebra**

I did the usual analysis and found the first differences to be 145, 250, 358, and 465 and the second differences to be 105, 108, and 107 which appear to be relatively constant at appr 106, so I suspect a quadratic. let N = ad^2 + bd + c, where d is the number of days, and N is...
*March 22, 2014*

**Math (help)**

So the punch contained 1 gal of fruit juice and 1 gal of ginger ale, for a total of 2 gallons percentage of fruitjuice = 1/2 * 100% = 50% I have no clue how they get 25%, did you check the wording of the problem?
*March 22, 2014*

**Math**

66 2/3 of 39 = (200/3)(39) = 7800/3 = 2600
*March 22, 2014*

**Math**

If you have consecutive values of x, like in both your cases, in general if the first differences in the y's are constant, you have a linear function if the 2nd differences in the y's are constant, you have a quadratic function, (as your case above) if the 3rd ...
*March 22, 2014*

**Math**

I took first differences and got 2.8 , 8.4 , 14, and 19.6 second differences yielded: 5.6 , 5.6 , 5.6 which tells me that the relationship is a quadratic function. so let y = ax^2 + bx + c, giving us 0 = c 2.8 = a + b + c 11.2 = 4a + 2b + c we know c = 0 so if we double the ...
*March 22, 2014*

**math**

sinhx = (e^x - e^-x)/2 and coshx = (e^x + e^-x)/ , by definition. then: 5coshx + 3sinhx = 4 5(e^x + e^-x)/2 + 3(e^x - e^-x)/2 = 4 5e^x + 5e^-x + 3e^x - 3e^-x = 8 8e^x + 2e^-x = 8 times e^x 8 (e^x)^2 + 2 = 8e^x a quadratic, let a = e^x 8a^2 - 8a + 2 = 0 4a^2 - 4a + 1 = 0 (2a - ...
*March 22, 2014*

**maths**

The correct answer to your question is: It is a quadratic equation. If you want the solution ... it factors: (3x-1)(3x + 2) = 0 x = 1/3 or x = -2/3
*March 22, 2014*

**precal**

from sin 2x = 1/2 2x = π/6 or 2x = π-π/6 = 5π/6 x = π/12 or 5π/12 but the period of sin 2x is π so we get 2 more solutions: x = π/12 + π = 13π/12 or x = 5π/12 + π = 17π/12 in [ 0 , 2π] x = π/12 , 5π...
*March 21, 2014*

**Math - PreCalc (12th Grade)**

First of all , I am sure you meant: s(t) = 2t^2 + 3t s(2) = 2(4) + 3(2) = 14 s(4) = 2(16) + 3(4) = 44 total distance = 44-14 = 30 m total time = 4-2 seconds = 2 seconds average velocity = total distance / total time = 30 m/2 seconds = 15 m/s
*March 21, 2014*

**Math - PreCalc (12th Grade)**

very similar to http://www.jiskha.com/display.cgi?id=1395410253
*March 21, 2014*

**Math - PreCalc (12th Grade)**

Use you "sense" of numbers to see what happens to the fractions as n gets larger. (I think your last term should read 15/(3n^2) or else it becomes large as n gets large) e.g. look at 5/n suppose n = 100,000, then 5/n = .00005 , which is close to zero suppose n = 1,...
*March 21, 2014*

**Math and Music**

Perhaps you will find it fascinating to see the relationshipe between music and the Fibonacci Numbers and the Golden Ratio ( google Fibonacci numbers to see thousands of webpages, here is probably one of the best: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/...
*March 21, 2014*

**arithmetic**

interest = 2000(1.0155)^20 - 2000 = 720.37 or "appr" $ 720
*March 21, 2014*

**Math - PreCalc (12th Grade)**

spread = 5-2 = 3 if cut into n pieces, each base = 3/n endpoint of 1st rectangle = 2 + 3/n endpoint of 2nd rectangle = 2 + 2(3/n) ... endpoint of kth rectangle = 2 + k(3/n) = 2 + 3k/n f(2+3k/n) = 2(2 + 3k/n) + 1 = 5 +6k/2 I see you have two other questions above that follow ...
*March 21, 2014*

**MATHS**

Steve's answer and mine seem to contradict each other, but we defined x differently. Steve defined x as his usual time, so the answer of 7.5 is correct for his usual time I defined x to be the usual speed, and got x = 2/15 so to go 1 km would take 1/(2/15) = 15/2 = 7.5 , ...
*March 20, 2014*

**MATHS**

usual speed --- x km/h time at usual speed to go 1 km = 1/x hrs time at 3/4 his normal speed = 1/(3x/4) = 4/(3x) 4/(3x) - 1/x = 2.5 times 3x 4 - 3 = 7.5x 7.5x = 1 x = 1/7.5 = 2/15 km/h
*March 20, 2014*

**Trigonometry**

r^2= 7^2 + (-3)^2 = 58 r = √58 since (7,-3) is in IV, cosØ = 3/√58 secØ = √58/3 cotØ = -7/3
*March 20, 2014*

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