Thursday

August 28, 2014

August 28, 2014

Total # Posts: 26,986

**Geometry**

Yup, I was so totally distracted by the second part of his post, that I completely missed and ignored the actual question. Another senior moment!!! but... wasn't that a great explanation?? reminds me of my teaching years, when during an exam a student replied to a certain ...
*August 6, 2014*

**Geometry**

both are variations of the relation cos 2A = cos^2 A - sin^2 A or cos 2A = 2 cos^2 A - 1 or cos 2A = 1 - 2sin^2 A We use this to either find trig ratios of double an angle or 1/2 an angle e.g. if we know sin 50° , I could now find ratios for 25° or 100° e.g. you ...
*August 6, 2014*

**math**

x^2 + 12x + 4 = 0 does not factor, so I will complete the square, easiest way for this one. x^2 + 12x + 36 = -4+36 (x+6)^2 = 32 x+6 = ±√32 = ±4√2 x = -6 ± 4√2
*August 6, 2014*

**math**

Must be mathemagics
*August 6, 2014*

**math**

Your post makes no sense to me How is this related to the binomial theorem? 32 ÷ 7 = 4 with a remainder of 4
*August 6, 2014*

**college algebra**

number of gallons of the 30% stuff --- x .3x + .14(60) = .2(60+x) 30x + 14(60) = 20(60+x) 30x + 840 = 1200 +20x 10x = 360 x = 36
*August 5, 2014*

**geometry**

I interpreted " two of its interior angles are 127 degrees and 135 degrees, and the remaining interior angles are 173 degrees each. " the wrong then. so I should have had 130 + 130 + 130 + 127 + 135 + 173(n-5) = 180(n-2) which gives 652 + 173n - 865 = 180n - 360 n = ...
*August 5, 2014*

**geometry**

But Damon's answer contradicts the sum of the inside angles property if n = 21 the sum of the interior angles = 127+135 + 19(173) =3949 which must be a multiple of 180
*August 5, 2014*

**geometry**

sum of interior angles of an n-gon = 180(n-2) 127 + 135 + 173(n-2) = 180(n-2) 262 + 173n - 346 = 180n - 360 276 = 7n n = 39.4.. , but n must be a whole number so the question is bogus. Check your wording and typing
*August 5, 2014*

**Math**

done
*August 5, 2014*

**algebra**

huh? I see no x in a^2 + b^2 = 2014
*August 5, 2014*

**Math**

If you want that sum to be less than 7000 x + x+2 + x+4 + x+6 + x+8 = 7000 5x = 6980 x = 1396 so 1396 + 1398 + 1400 + 1402 + 1404 = 7000 but you want the sum to be < 7000 so 1394 + ... 1402 = 6990 if you want the numbers to be less than 7000 6998 + 6996 + 6994 + 6992 + 6990...
*August 5, 2014*

**Math**

You have to give more information. It is not arithmetic , nor is it geometric I can make it a quadratic .... term(n) = 3n^2 - 10n + 10 and the three terms you gave me will match. so term(15) = 3(225) - 10(15) + 10 = 535 or a cubic or ....
*August 5, 2014*

**advance algebra**

ditto what Steve said in your previous post on this.
*August 5, 2014*

**math test review**

I do not understand your m<C=2m<b,m<A=6m<B. In our general usage of angles and sides, a capital letter usually stands for an angle, a small letter stands for the length of the opposite side to that angle, there also seems to be a missing equal sign. If you are ...
*August 4, 2014*

**math**

what is 2 more than p ? isn't it p+2 ? area = p(p+2) p^2 + 2p = 8 p^2 + 2p - 8 = 0 which factors to (p+4)(p-2) = 0 p = -4, which is not admissable or p = 2 so the table is 2 m by 4 m check: what is 2 x 4 ?
*August 4, 2014*

**math**

done! patience!, you posted the same question only about 8 minutes before this one.
*August 4, 2014*

**math**

I assume you meant: If b is a positive integer < 200 a/b = 2/9 9a = 2b a = 2b/9 So b must be a multiple of 9 to have a as an integer the smallest value of b is 9 and the largest value of b is 198 so we have: 9 18 27 .... 180 189 198 to find out how many terms are in this ...
*August 4, 2014*

**MA 1310**

rewrite it in the more general form as y = (1/4) cos 3(x + 7/3) compared to y = a cos k(Ø + p) the amplitude is 1/4 the period is 2π/3 the phase shift is 7/3 to the left for your equation in the original form a common mistake would be to state that the sphase shift...
*August 4, 2014*

**geometry**

should be 19 cm^3 x/19 = 3^3/2^3 x/19 = 27/8 8x = 513 x = 64.125 cm^3
*August 4, 2014*

**math 4**

Value of loan = $300 let the monthly rate be i then 34*(1- (1+i)^-10)/i = 300 hard to solve this type of equation but I have some methods and it gave me i = appr .02343 so the annual rate compounded monthly is 28.1 % check: 34(1 - 1.02343^-10)/.02343 = = 299.9988 , not bad I ...
*August 4, 2014*

**Ha ha - algebra**

got me, ( I think 15/60 = 1/3 in non-metric) anyway... Thank you Steve
*August 4, 2014*

**algebra**

15/60 or 1/3 chose an hour lunch with no breaks for in 500 people we would expect 1/3 of 500 or 167 to choose the above option
*August 4, 2014*

**math**

let Jim's distance be x miles then John's distance is 3-x miles Jim's time = x/4 John's time = (3-x)/5 when they meet, they will both have paddled the same time so ... x/4 = (3-x)/5 5x = 12 - 4x 9x = 12 x = 12/9 miles so Jim's time = (12/9) /4 = 1/3 hour or...
*August 4, 2014*

**geometry**

radius of base = 3√3 height^2 + (3√3)^2 = (6√3)^2 find the height, now you have everything needed in the formula for the volume of a cone
*August 4, 2014*

**math**

follow the same steps I just showed you in your previous post. Let me know what you got
*August 4, 2014*

**math**

let f(x) = 4x^2 - 3x - 8 and use the Remainder Theorem, f(a) = 4a^2 - 3a - 8 = 2 4a^2 - 3a - 10 = 0 (a-2)(4a + 5) = 0 a = 2 or a = -5/4 the 2nd is done the same way: f(3) = 81 + 9m + 3n + 5 = 128 9m + 3n = 42 3m + n = 14 f(-1) = -3 - m - n + 5 = 4 -m-n = 2 add them: 2m = 16 m...
*August 4, 2014*

**Math**

balance owing = 22000-5500 = 16500 We don't know the rate, but if the monthly rate is i , then 16500 = 406.69(1 - (1+i)^-48)/i Did some alternate numerical calculations and found n = .007083333.. which makes it an annual rate of 8.5% compounded monthly So balance owing ...
*August 3, 2014*

**algebra**

Number(Ipad or Car) = number(Ipad) + number(carss) - number(Ipads and cars) = 65 + 45 - 15 = 95 which leaves 5 unaccounted for from the 100 so .... a) 95 owned either Ipad or car b) 5 owned neither or you could get the same result by constructing a Venn diagram
*August 3, 2014*

**math**

In your text or in your notes you should find the following relationship between (r,Ø) and (x,y) x = rcosØ -->cosØ = x/r y = rsinØ --> sinØ = y/r r^2 = x^2 + y^2 and tanØ = y/x so in r = 1/(sinØ + cosØ) r(sinØ...
*August 3, 2014*

**Proof: math**

amount at end of t = 2 = 500(1.015)^8 = 563.25 add additional payment of 273.14 = 836.39 amount of that after 3 more years = 836.39(1.015)^12 =999.9986.. not bad, eh?
*August 2, 2014*

**oops - math**

I miscounted on my "time line" should have been: 500(1.015)^20 + x(1.015)^12 = 1000 ... x = $273.14
*August 2, 2014*

**math**

500(1.015)^20 + x(1.015)^16 = 1000 1.268985... = 326.572.. x = $257.35
*August 2, 2014*

**maths**

height/100 = tan 60° height = ..... ?
*August 2, 2014*

**math**

for Tia: distance = 29-75(t-1) for Kathie: distance = ..... (what do you think)
*August 2, 2014*

**Math**

log (10A)/(7B^2) = log(10A) - log(7B^2) = lof 10 + logA - (log7 + 2logB) = 1 + logA - log7 - 2logB
*August 2, 2014*

**college math**

From a Physics point of view, this question is really flawed. First of all, it should be -16t^ (gravity works downwards, not upwards) Secondly, at the moment of jettison of the tanks, the tank still has an upwards velocity, so there should be term in t after the -16t^2 anyway...
*August 2, 2014*

**College math**

-In45=3.80666249 this statement is false should say: In45=3.80666249 then e^3.80666249 = 45 again, I will assume you meant: Log sub.B T^5=W , I read that as: logB T^5 = W by definition: T^5 = B^W
*August 2, 2014*

**College math**

yes it is 1: y = x^3 - 27 ----> x = y^3 - 27 2: x = y^3 - 27 y^3 = -x - 27 y = (-x - 27)^(1/3)
*August 2, 2014*

**College math**

follow same steps as I showed you
*August 2, 2014*

**College math**

Inverse: step 1. switch the x and y variables y = 5/(x+3) -----> x = 5/(y+3) step 2: solve this new equation for y xy + 3x = 5 xy = 5-3x y = (5-3x)/x I was able to find the inverse, but both the original and the inverse have restrictions, so it is not a one-to-one function ...
*August 2, 2014*

**Greg/kat - calculus**

Please stick to one name done in previous post
*August 2, 2014*

**Precalculus**

All you want is the linear equation passing through the two points (0,20000) and (5,10000) slope = (10000-20000)/(5-0) = -2000 So if we let t be the time V = -2000t + 20000 the rate of depreciation is $2000/year
*August 2, 2014*

**Math**

well! , just set 164t - 16t^2 = 400 -16t^2 + 164t - 400 = 0 4t^2 - 41t + 100 = 0 (t-16)(4t - 10) = 0 t = 10 or t = 10/4 or 2.5 seconds So it will reach that height first at 2.5 seconds, (and again after 10 seconds on its way back down)
*August 2, 2014*

**Math**

As you can see from the many similar questions, this poorly worded question comes up again and again with just a change of numbers We must assume that the width is the same for the kitchen and the dining room let the dining room be x by x area of dining room = x^2 area of ...
*August 2, 2014*

**math**

let the mileage be m 65 + .7m < 114 + 0m .7m < 49 m < 70 so for m> 70 miles, company A is cheaper check: if m = 50 company A charges $114 company B charges 65 + .7(50) = 100 if m = 71 company A charges $114 company B charges 65+.7(71) = $114.70 . which is more btw...
*August 2, 2014*

**math**

assuming neither of the two given sides is the hypotenuse, make a sketch to see that tan B = 960/490 angle B = appr 63°
*August 2, 2014*

**math**

if GP , then (2x-4)/4 = (21x+2)/64 128x-256 = 84x + 8 44x = 264 x = 6 check: 4, 8, ... , 64, 128 YUP, common ratio of 2
*July 30, 2014*

**typo - Math**

In all that lengthy typing, I just noticed an error. When I stated De Moivre's Theorem, it should of course have been: then z^n = r^n( cos (nØ) + i sin (nØ) ) I did use it correctly in my work.
*July 30, 2014*

**Math**

How did I get 171.9 ? from tanØ = -1/7 I know that the tangent is negative in II and IV by the CAST rule but <-7,1> ends up in quadrant II so I took tan-inverse of 1/7 to get 8.13° , had it been in quad I in quad II we have 180-8.13 = appr 171.9
*July 30, 2014*

**Math**

Jane, you will have to be able to change a complex number from standard form to trig form in general a + bi = (√(a^2 + b^2) [cosØ + isinØ] where Ø is such that tanØ = b/a e.g. change 3 + 4i to trig form = √(3^2+4^2) (cosØ + isin&...
*July 30, 2014*

**Math**

2nd: let z = 0 + 8i = 8( 0 + i) we need 0+i in the form cosØ + isinØ we need Ø, so that cosØ = 0 and sinØ = 1 mmmmhhh, Ø = 90 comes to mind so z = 8(cos90° + isin90°) so the cube root, and using De Moivre's z^(1/3) = 8^(1/3...
*July 30, 2014*

**Math**

For the 2nd: are you familiar with D' Moivres Theorem? let me know, and I will go through with this one 3rd: make a sketch and use the cosine law 35.1^2 = 32.7^2 + 20.2^2 - 2(20.2)(32.7)cosØ ( see if you get Ø = 100.7° )
*July 30, 2014*

**Math**

I assume <2,1> and <-1,1) are vectors then -2A + 3B = <-4,-2) + <-3,3) = <-7,1> magnitude = √(49+1) = √50 or 5√2 direction: let the angle be Ø tanØ = -1/7 Ø = appr 171.9° with the x-axis
*July 30, 2014*

**Alegbra1**

You will have to use brackets to show where the square root ends I suspect it is f(x) = √(-x+2) - 1 , or else why not combine the +2-1 ? then the number under the square root must not be negative, that is ... -x + 2 ≥ 0 -x ≥ -2 x ≤ 2
*July 30, 2014*

**math**

job/rate = time --> rate = job/time let the fathers rate = job/x let the son's rate be job/2x combined rate =job/x + job/2x = 3job/(2x) combined time = job ÷(3job/2x) = job (2x/3job) = 2x/3 but 2x/3 = 6 2x = 18 x = 9 It would take 9 hrs for the father to work ...
*July 30, 2014*

**math**

Making the first 3 as small as possible, they would have to be 1, 2, and 3 let the 4th be x and the 5th be y then 1+2+3+x+y = 90 x+y = 84 remember, y has to be the largest we want x to be as large as possible but still be less than y x y .. .. .. .. 40 44 41 43 42 42 --->...
*July 30, 2014*

**maths**

2(x^2 - 4x + ... ) + 2(y^2 + (5/2)y + ... ) = -10 2(x^2 - 4x + 4 ) + 2(y^2 + (5/2)y + 25/16 ) = -10+ 8 + 25/8 2(x-2)^2 + 2(y+ 5/4)^2 = 9/8 (x-2)^2 + (y+5/4)^2 =9/4
*July 30, 2014*

**Algebra**

let's work on the bottom 6^(2n+1) = 3^(2n+1)* 2^(2n+1) = 3^n * 3^(n+1) * 2^n * 2^(n+1) = 3^n * 2^n * 6^(n+1) now the 3^n would cancel the 3^n on top, leaving you with 1/(2^n * 6^(n+1) )
*July 30, 2014*

**Math; Alegbra**

If r = 3 Volume of sphere = (4/3)π r^3 = 36π volume of a cone = (1/3)π r^2 h =3π h 3π h = 36π 3h = 36 h = 12
*July 30, 2014*

**mathematics**

H = (1/28)L L = 28H L + H = 116 28H + H = 116 29H = 116 H = 4 then L = 112 one number is 16 let the other number be 4x then : 16 = 4*4 4x = 4*x 16x = 112 x = 7 and 4x= 28 The other number is 28 check: 16 = 2*2*2*2 28=2*2*7 LCF = 2*2 = 4 HCM = 2*2*2*2*7 = 112 is 4 equal to 1/28...
*July 30, 2014*

**early morning oops - Math**

But .... if the second derivative is linear, the original function must be a cubic. y'' = 6x y' = 3x^2 + a at x = 1 we have y = 5 - 3x is a tangent, so y' = -3 when x=1 -3 = 3(1) + a a = -6 y' = 3x^2 - 6 then y = x^3 - 6x + b at (1,2) 2 = (1)^3 - 6(1) + b b...
*July 29, 2014*

**Math**

ARrgghhh, really? Matrices for such a simple system? ok .... we need the inverse of 4 -2 7 1 I will assume you know how to find the inverse of a 2by2 I get 1/18 2/18 -7/18 4/18 now if we multiply that by 4 -2 7 1 we get 1 0 0 1 on left and the column matrix 33/18 3/18 on the ...
*July 29, 2014*

**Algebra**

from 3x = 4y ---> x = 4y/3 from 12y = 5z --> z = 12y/5 so z/x = (12y/5) / (4y/3) = (12y/5)(3/4y) = 9/5
*July 29, 2014*

**Calculus**

direction of the given line is (1,1) so if Ø is the angle it makes with the x-axis, then tanØ = 1/1 Ø = 45° so a line which makes an angle of 60° with the given line would have an angle of (45°+60°) or 105° or -15° now tan 105°...
*July 29, 2014*

**Calculus**

A normal to r is (0,1,1) cross (-1,0 3) or (3, -1, 1) , (I assume you know how to find a cross-product) So the plane must look like, 3x - y + z = c , where c is a constant from the line (x-3)/2 = (y+1)/-3 , z=1 the point (3,-1 ,1) must lie on the line, so it must also lie in ...
*July 29, 2014*

**Math**

Ok, starting to make sense now So I will assume you are given: sin(alpha+beta)=(sin alpha)(cos beta)+(cos alpha)(sin beta) and cos(alpha+beta)=(sis alpha)(cos beta)+(sin alpha)(sin beta) I will use A and B for easier typing You must also know that 1. sin(-A) = -sinA 2. cos(-A...
*July 29, 2014*

**Math**

That's not what you said originally, look at your post. So which identity are we deriving ?
*July 29, 2014*

**Math**

so you want us to use the identity: sin(A - B) = sinAcosB - cosAsinB to prove sin(A - B) = sinAcosB - cosAsinB ? mmmhhh? did you mean sin(A+B) ??
*July 29, 2014*

**Math**

let the time taken since 10:00 am till they meet be t hrs at 10:00 am , train will have already gone 130 miles when they meet, they both will have traveled the same distance, so ... 90t = 130 + 65t 25t = 130 t = 5.2 hrs or 5 hrs and 12 minutes that would put the time at 10:00...
*July 29, 2014*

**Math**

1 ---> 4 = 2^2 2 ---> 8 = 2^3 3 ---> 16 = 2^4 4 ---> 32 = 2^5 mmmhhh, look at the exponent of 2 and compare it to your input value. isn't it always one greater ? so .....
*July 29, 2014*

**error - Algebra**

Whoahh there Sheenybeany if the inequality is y/6 > 10 then y > 60 Why did you reverse the inequality sign? It is reversed only if you multiply or divide by a negative. Since we simply multiplied by 6, it stays the same. Since y > 60 is not one of the choices, we ...
*July 29, 2014*

**geometry**

mmmh, I guess that explains why he is still a bachelor
*July 29, 2014*

**arggg! ... Geometry**

How did I possible see 4 of equal sides ? but... my algebra worked out sooo nice! Reminds me of the classic StarTrek episode where Cpt Picard is tortured by the Kardashians and sees 4 lights. https://www.youtube.com/watch?v=moX3z2RJAV8
*July 29, 2014*

**Geometry**

let the sides be a, b, and c We know: 4a +4b + 4c = 24 ----> a+b+c = 6 and 4ab + 4ac + 4bc = 22 2ab + 2ac + 2bc = 11 The length of the diagonal is √(a^2 + b^2 + c^2) by algebra, we know (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc subbing in 6^2 = a^2 + b^2 + c^2 +11...
*July 29, 2014*

**math**

The way it is written, I must agree with Steve
*July 29, 2014*

**Math**

start at (-3,-4) and mark it since slope = rise/run = 2/3 the rise is 2 and the run is 3 so from the point (-3,-4) go to the right 3 (run of 3), then go up 2 (rise of 2) mark this new point, join with a line and you are done Easy, eh ??
*July 28, 2014*

**Math**

you replaced the y with -8 , but not the x with -3 Why not? -8 = -2(-3) + b -8 = 6 + b -14 = b so y = -2x - 14
*July 28, 2014*

**Math**

done below
*July 28, 2014*

**math**

1. can you think of two numbers which when multiplies yields -36 and when added is 16 how about 18 and -2 ???? (x+18)(x-2) 2. can you think of two numbers which when multiplies yields 9 and when added is -10 how about -1 and -9 (x^2 - 1)(x^2 - 9) now we have the difference of ...
*July 28, 2014*

**Math**

Natalie, use the method I showed you in your previous post slope of lines parallel to 8x + 4y = 7 = -8/7 slope of perpendicular lines = + 7/8
*July 28, 2014*

**math**

profit = 12.50 - 8.00 = 4.5 percentage profit = 4.5/8 = .5625 or 56.25%
*July 28, 2014*

**math**

I will assume from your poorly worded question that the sale price is $10.00 so if the original is $x .8x = 10 x = 10/8 = 12.50 Now, do you need the profit percentage before or after the sale? You decide
*July 28, 2014*

**Math**

use a two step process 1. take all terms except the y term to the right side 4x + 5y = 3 ----> 5y = -4x + 3 2. divide each term by the coefficient of the y term 5y = -4x + 3 y = (-4/5)x + 3/5 now you have it in the form y = mx + b, where m is the slope, so the slope is -4/5
*July 28, 2014*

**Calculus**

if F' (x) = -7x then F(x) = -(7/2)x^2 + c but F(0) = 1 1 = 0(-7/2) + c c = 1 F(x) = (-7/2)x^2 + 1
*July 28, 2014*

**math**

Johnny, looks like "homework dumping to me" How about showing us what steps you have taken in these problems or indicate where your difficulties lie.
*July 28, 2014*

**math**

I suppose we could do this .... 12V = 3W V = 3W/12 = W/4 then 2W - 8V = 2W - 8(W/4) = 2W - 2W = 0
*July 28, 2014*

**Geometry**

I agree with Bob My understanding of a trifoil has been this: http://www.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/9/9d/Trefoil-Architectural.png&imgrefurl=http://commons.wikimedia.org/wiki/File:Trefoil-Architectural.png&h=218&w=231&tbnid=...
*July 28, 2014*

**general math**

This is how I would have expected my students to write up the solution to this equation 5x − 2 = 2x + 7 5x - 2x = 7 + 2 3x = 9 x = 3
*July 28, 2014*

**Maths (differentiation)**

the way you typed it, Wolfram read it as http://www.wolframalpha.com/input/?i=+Y+%3D+1%2FSinX%5E2 and y = (sinx)^-2 dy/dx = -2(sinx)^-3 (cosx) = -2cotx /sin^2 x or = -2cotx csc^2 x if you meant: y = 1/ sin(x^2) then y = sin(x^2)^-1 dy/dx = -1sin(x^2)^-2 cos(x^2) (2x) = -2x cot...
*July 28, 2014*

**Math**

number of tests before the last one ---> x total marks at that point = 84x then (84x + 100)/(x+1) = 86 86x + 86 = 84x + 100 2x = 14 x = 7 So there were 8 tests, including his perfect test at the end.
*July 27, 2014*

**Maths**

Kelvin --- x Ken ----- x+6 average of Kelvin and Ken = (2x+6)/2 = x+3 David = (x+3) + 6 = x+9 (x + x+6 + x+9)/3 = 42 3x + 15 = 126 3x = 111 x = 111/3 = 37 David is 37+9 = =46 check: Kelvin --> 37 Ken----> 43 David ---> 46 average of Kelvin and Ken = (37+43)/2 = 40 Is ...
*July 27, 2014*

**math**

number of girls = 3x number of boys = 4x (check: total is 7x) total weight of all children = 7x(36) = 252x total weight of all the girls = 3x(32) = 96x so the weight of all the boys = 252x-96x = 156x average weight of boys = 156x/(4x) = 39 kg
*July 27, 2014*

**Maths**

Did you make a sketch? If so, you can see that cosØ = 2/6 = 1/3 Ø = cos^-1 (1/3) = appr 70.5°
*July 27, 2014*

**math**

Let the salaries of A, B, and C be 2x, 3x, and 5x respectively. then 3x + 5x = 8000 8x=8000 x = 1000 A's is 2000 C's is 5000 we don't really have to find their actual salaries amount that C has more than A is 5x-2x = 3x Percentage of that of A = 3x/2x = 3/2 = 1.5 ...
*July 27, 2014*

**math**

breadth --- x length ---- 1.2x 2(x+1.2x) = 88 x+1.2x = 44 2.2x = 44 x = 20 area = x(1.2)x = 1.2(20^2) = 480 m^2
*July 27, 2014*

**correction - calculus 2**

∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 should be ∆x = (6-1)/10 = 5/3 , so ∆x/3 = 5/30 = 1/6 and the 5/3 in front of the big brackets should be 5/30 or 1/6
*July 26, 2014*

**calculus 2**

I assume that you know the formula .... in case you don't, here is the method http://www.mathwords.com/s/simpsons_rule.htm ∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 interval = (6-1)/10 = 1/2 then we have (5/9)[ f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4...
*July 26, 2014*

**calculus 2**

fix your equation first
*July 26, 2014*

**math**

since the function is linear, the slope must be constant for any pair so (12-a)/(1-0) = (b-12)/(2-1) 12-a = b-12 24 = a+b
*July 26, 2014*

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