Monday

March 30, 2015

March 30, 2015

Total # Posts: 29,332

**math**

A lot of wording just to confuse you. The fact that 2 people draw the apples has nothing to do with it, might just as well have Michael draw 2 apples, assuming the first apple is not returned to the bag. What is the prob they are both red or green ? prob(both red) = (5/9)(4/8...
*February 8, 2015*

**maths**

set up the 4by4 matrix of the coefficients. find the inverse of that matrix multiply that inverse matrix by 5 8 12 7 This will take several sheets of paper and lots of patience - not really suitable to write up in this format, matrices are horrible to type in jiskha. There are...
*February 8, 2015*

**math**

8 is not evenly divisible by 3 , so I guess we might have to cut some of those tiles.
*February 8, 2015*

**maths**

one rotation = 1π = π m 78.5 km = 78500 m number of revs = 78500/π = appr 24987
*February 8, 2015*

**math**

let the smaller of the unknown angles be 5x and the larger of the two be 16x so 130+20+5x+16x = 360 21x = 210 x = 10 so the two missing angles are 50° and 160° check: 50+160+130+20 = 360 50:160 = 5 : 16
*February 8, 2015*

**math**

number without a 1 = 9^7 = 4,782,969 so number where no 1 occurs = 4,782,969 number where a 1 does occur = 10,000,000-4,782,969 = 5,217,031
*February 8, 2015*

**precalculus**

let a = -33 , (the last one) let d = -33 , going backwards a+(n-1)d = appr -500 -33 + (n-1)(-33) = -500 -33 -33n + 33 = -500 -33n = -500 n = 15.15.. So there are 15 terms, and term(15) = -33 + 14(-33) = -495 so we have -495 , -462, -429, ... -66, -33 sum(15) = (15/2)(first + ...
*February 8, 2015*

**problem**

number of miles ---- m .5m + 42.15 ≤ 130 .5m ≤ 87.85 m ≤ 175.7 He can go 175 miles
*February 8, 2015*

**math**

I am not even going to guess what that means.
*February 8, 2015*

**maths please help and explain**

Did you not look at my reply to this from yesterday morning ? http://www.jiskha.com/display.cgi?id=1423307265 You have typed it exactly the same way, the same lack of brackets in the numerators, and the same ambiguity in B.
*February 8, 2015*

**trigo**

your equations all fit the pattern y = a (sin or cos)(kx) where |a| is the amplitude and the period is 2π/k I will do one of them , you do the others in the same way. 2. y = 4sin(5x) amplitude is 4 period = 2π/5 radians dy/dx = 4cos(5x) (5) = 20 cos(5x) = 0 for any ...
*February 8, 2015*

**math**

calls received after one session of calls = 4 calls received after two sessions of calls = 4^2 = 16 calls received after three sessions of calls = 4^3 = 64 ....... calls received after n sessions of calls = 4^n Please finish the question
*February 8, 2015*

**math:order of operation**

Pattern: at start: 3 butterflies after one minute: 3(2) = 6 butterflies after two minutes: 3(2)(2) = 3(2^2) butterflies after three minutes : 3(2^3) butterflies after four minutes : 3(2^4) butterflies but at that point she captured 7 of them after 4 min, number on screen = 3(2...
*February 8, 2015*

**PreCalculus**

I will assume the chips are not returned after being selected. a) You want the situation GGGGN and its other 4 variations, where N stands for non-green Prob(GGGGN) = (30/60)(29/59)(28/58)(27/57)(30/56) = 135/4484 But there are C(5,4) of these Prob(exactly 4 green) = 5(135/4484...
*February 7, 2015*

**dot product of vecotrs**

Sure looks like you corrected the typo, but made no effort to adjust the corresponding arithmetic. http://www.jiskha.com/display.cgi?id=1423332996 The unnecessary duplication of work could have been avoided.
*February 7, 2015*

**Math Help**

You need brackets: (1+ sec u)/tan u - tan u/(1+sec u) I am going to guess that you have just learned: sin^2 x + cos^2 x = 1 and its variations ... tan^2 x + 1 = sec^2 x cot^2 x + 1 = csc^2 x So (1+ sec u)/tan u - tan u/(1+sec u) = ( (1+secu)^2 - tan^2 u)/(tanu(1+secu)) = (1 + ...
*February 7, 2015*

**Math**

since sinx = -12/13, and tanx is positive, x must be in quad III in your triangle: sinx = -12/13 ----> the given cosx = -5/13 tanx = -12/-5 = 2.4
*February 7, 2015*

**geometry**

one circumference = 8π ft 3 miles = 3(5280) ft or 15840 ft number of rotations = 15840/8π) = appr 630 times
*February 7, 2015*

**Math**

NOT to be a trig identity requires a single exception so take an angle for which you know the trig rations and test the equations e.g. let x = 45° you know sin^2 45 = cos^2 45 = 1/2 tan^2 45 = 1 and cot^2 45= 1 also sec^2 45 = 2, and csc^2 45 = 2 What do you think?
*February 7, 2015*

**^Math.^ Pls,I need help**

LS = (a-b)^2 = a^2 - 2ab + b^2 RS = (a+b)^2 - 4ab = a^2 + 2ab + b^2 - 4ab = a^2 - 2ab + b^2 = LS Q.E.D. or (quid est demonstrata) (Thus it has been proven)
*February 7, 2015*

**Vectors and Math**

I will use the notation: a = -i-3j+k = <-1,-3,1> b = 2i+4j-5k = <2,4,-5> and (3a+4b)(2b+4a) is the dot product = ( <-3,-9,3> + <8,16,-20>) dot (<4,8,-10> + <-4,-12,4>) = <5,7,-17> dot <0,-4,-6> = 0 -28 + 102 = 74 check my ...
*February 7, 2015*

**maths please help**

You will need brackets in the numerator as well in A B appears to have a typo C) notice the middle term denominator factors and it becomes the LCD 3/(x-3) - x^2/((3-x)(2+x)) - 2/(x+2) Do the others in the same way hint for D after you insert the brackets in the top you get (x+...
*February 7, 2015*

**Math**

I will assume you meant the numerator to be ( √(x^2+25) - 13 ) , so lim ( √(x^2+25) - 13 )/(x+12) , as x-->-12 = lim ( √(x^2+25) - 13 )/(x+12) * ( √(x^2+25) + 13 )/( √(x^2+25) + 13 ) = lim( x^2 + 25 - 169)/( ( √(x^2+25) + 13 )(x-12) ) = ...
*February 7, 2015*

**math**

volume of cone= (1/3)π(49)(18) = 294π cm^3 Height needed in the cylinder to hold that volume π(14^2)(h) = 294π h = 276/196 = 3/2 or 1.5 cm
*February 7, 2015*

**math**

ignore my reply above,
*February 7, 2015*

**math**

Adjust this solution to fit your problems, they are the "same" http://www.jiskha.com/display.cgi?id=1423275251
*February 7, 2015*

**math**

15^10/15^9 = 15
*February 7, 2015*

**math**

factor pairs of 36: 1 36 2 18 3 12 4 9 ---- so I could draw 4 different rectangles of area 36 with whole number sides factor pairs of 15 1 15 3 5 ---> only 2 possible
*February 7, 2015*

**math**

number of large --- x number of medium -- y number of small --- 180-x-y 6x + 5y + 4(180-x-y) = 820 6x+5y+720-4x-4y=820 2x+y=100 or y = 100-2x 22x+14y+11(180-x-y) = 2380 11x + 3y = 400 sub in y = 100-2x 11x + 3(100-2x) = 400 5x = 100 x=20 then y = 60 So 20 large, 60 medium and ...
*February 7, 2015*

**pre cal**

y' is a common factor y' (6y^2 - x) = x+y y' = (x+y)/(6y^2 - x)
*February 6, 2015*

**Calc**

Thanks Steve, I see it now, used 2x^2 instead of 3x^2
*February 6, 2015*

**Calc**

how about let u = 2x-3 then 2x = u + 3 x = (u+3)/2 then y = 2(u+3)^2 /4 - 2 = (1/2)(u^2 + 6y + 9) - 2 dy/du = (1/2)(2u + 6) = u + 3 = (2x-3) + 3 = 2x dy/d(2x-3) = 2x
*February 6, 2015*

**Math**

Label the top of the pole as T and its base as O in triangle OTP, tan38 = 15/OP OP = 15/tan 38 in triangle TOP, cos 25 + 15/OQ OQ = 15/tan25 in the right-angled triangle POQ PQ^2 = OP^2 + OQ^2 I will let you finish it.
*February 6, 2015*

**aalgebra**

the solution will be a point of the form (x,y)
*February 6, 2015*

**math**

A^2 = 9 8 16 17 which is A+B so B = 8 6 12 14
*February 6, 2015*

**spinner**

think of it as A, B, C AB AC BC mathematically: 3 choose 2 = C(3,2) = 3!/(2!1!) = 3
*February 6, 2015*

**Math**

1/5(2x-10) + 4x = -3(1/5x + 4 I see no closing bracket on the Right Side so I will assume you meant 1/5(2x-10) + 4x = -3(1/5x + 4) (1/5)(2x-10) + 4x = (-3/5)x - 12 multiply each term by 5 2x-10 + 20x = -3x - 60 25x = -50 x = -2
*February 6, 2015*

**Math**

Steve did this for you http://www.jiskha.com/display.cgi?id=1423099260 always check back before reposting
*February 4, 2015*

**Math**

Most mathematical authorities define an exponential function as f(x) = a^x, where a is any positive number, a ≠ 1, and x is any real number so #1 is True #2, what about y = (1/2)^x as x increases, y decreases, so False
*February 4, 2015*

**Math**

since all 3 factors have an exponent of 1/4 you can say: ⁴√18× ⁴√9 ÷ ⁴√2 = (18x9÷2)^(1/4) = 81^(1/4) = 3 (one of the basic exponent rules: (a^n)(b^n) = (ab)^n
*February 4, 2015*

**Calculus 2**

equating coefficients = partial fractions ? let (x^3+5x^2+12)/((x^2)(x^2+4)) = A/x^2 + (Bx+C)/(x^2+) = (Ax^2 + 4A + Bx^3 + Cx^2)/(x^2(x^2+4)) = (Bx^3 + (A+C)x^2 + 4A)/(x^2(x^2+4)) so B=1 A+C=5 4A=12 ---> A = 3 in A+C=5 ---> C=2 so we can write: (x^3+5x^2+12)/((x^2)(x^2+4...
*February 4, 2015*

**7th grade math**

good job checking your answer: n is at most 6, so 6 + 7 ≤ 13 ??, YES
*February 4, 2015*

**geometry**

The surface area of the side of a cylinder is 2πrh, in effect, the circumference of the circle times the height. (Visualize taking a piece of paper and forming it into a cylinder.) So for yours, the radius is 7 cm surface area = 2π(7)(45) = appr 1979 cm^2
*February 4, 2015*

**Math**

Do you just want the inequation?, if so, then 4n - 6 < .5(-n) If you want a solution: each term multiplied by +2 8n - 12 < -n 9n < 12 n < 12/9 n < 4/3
*February 4, 2015*

**Math**

write it this way: (a-7)/10 = (a-2)/8 cross-multiply 10a - 20 = 8a - 56 2a = -36 a = -18
*February 4, 2015*

**math**

If you know your trig relations and formulas, then its clearly C otherwise, you could test them with some angles. Remember, if you find even one exception to a mathematical rule, then that rule is invalid A, let Ø = 20, then its complement is 70° sin20 = appr .342 ...
*February 4, 2015*

**math**

radius of each balloon = 7.2 inches Volume of each balloon = (4/3)πr^3 = (4/3)π(7.2)^3 = appr 1563 cubic inches
*February 4, 2015*

**Algebra**

number of nickels --- n number of dimes ---- d n+d = 40 5n + 10d = 285 divide by 5 n + 2d = 57 subtract the two equations: d= 17 then in n+d = 40 n+17 = 40 n = 23
*February 4, 2015*

**Math**

Your description is not clear. A square prism has two ends that are squares, basically a box. see: https://www.google.ca/search?q=square+prism&biw=1663&bih=929&tbm=isch&imgil=Rh18AWgVlirFIM%253A%253BaxhcbOt3GqfHpM%253Bhttp%25253A%25252F%25252Fwww.k6-geometric-shapes.com%...
*February 4, 2015*

**math**

adults -- x kids --- 300-x solve: 15x + 12(300-x) = 4140
*February 4, 2015*

**algebra 1**

divide the 2nd by 3 ---> y = -5x + 2 first equation: y = -5x + 15 Since the two lines are parallel, there will be no solution, since they will never intersect.
*February 4, 2015*

**math**

first line: slope = (7-1)/(7-1) = 1 y = 1x + b using either point, I will use the simpler (1,1) 1 = 1 + b b = 0 first equation: y = x 2nd line: follow my steps.... to solve, sub in y = x from the 1st into the 2nd
*February 4, 2015*

**Algebra**

amount of $9.00 nuts --- x lbs 9x + 5(50) = 6.5(50+x) 9x + 250 = 325 + 6x 3x = 75 x = 25 your conclusion is .... ?
*February 4, 2015*

**Algebra**

prob(of your event) = (4/52)(3/51) = ...
*February 4, 2015*

**Trigonometry**

done look at your post which you had 6 minutes before this one
*February 4, 2015*

**Trigonometry**

label the top of the building as P and its bottom as Q look at triangle PAB angle A = 21° angle ABP = 180-32 = 148° , then angle APB = 11° using the sine law you can find PB then in the right-angled triangle PBQ BQ/BP = cos32 BQ = BPcos32 = .... add 100 and BQ
*February 4, 2015*

**maths**

Well, here I am, thinking all my life that a quadrilateral had 4 sides.
*February 4, 2015*

**Algebra 1B**

This topic usually requires several days in a standard classroom situation, so it is not possible to answer in a single post of this kind. I just Googles, "factoring trinomias" and got oodles of websites. I have been a fan of Khan Academy for years and this one ...
*February 4, 2015*

**Algebra 1B**

I suggest grouping 3y^3-9y^2+4y-12 = 3y^2(y - 3) + 4(y - 3) = (y-3)(3y^2 + 4) For factoring questions like this, you can always check your answer by expanding it, to make sure the original comes back
*February 4, 2015*

**Algebra 1B**

For the coefficients, the GCF is 6 for the variable it is x^3 so 6x^3
*February 4, 2015*

**Algebra**

ages now: Amy --- x Rosa --- x+14 Three years ago: Amy --- x-3 rosa ---- x+11 x+11 = 3(x-3) x+11 = 3x - 9 2x = 20 x = 10 sub into my definitions
*February 4, 2015*

**algebra**

Jamar: w = 3m+ 14 Scott: w = 5m + 8 A rather silly question!
*February 4, 2015*

**calculus**

Make your diagram using an x-y grid at noon, place ship B at the origin, and A on the left side of the x-axis After some time of t hrs, let B's position on the y-axis be Q, mark BQ=25t draw a vertical line in the South direction and label A's position as P, marking AP=...
*February 4, 2015*

**Geometry**

simplest way, list the points counterclock-wise, repeating the first point you started with 5 5 3 4 8 3 5 5 area = (1/2)(sum of down-products - sum of up-products) = (1/2)(20+9+40 - (15+32+15)) = (1/2)(7) = 7/2 , just as Steve had btw, this method works for any convex polygon
*February 3, 2015*

**Geometry**

There are many ways to do this, you will have to tell me at what level of math this is. e.g. Have you heard of Heron's Formula? e.g. do you know the cosine law? What grade level is this ?
*February 3, 2015*

**algebra**

I assume you meant: √(6x^3) * √(18x^2) = √(108x^5) = √36*√3*√x^4*√x = 6*√3*x^2*√x = 6√(3x)x^2 = 6x^2√(3x) I don't know how you fudged that answer looking at your second line, which is totally wrong it should...
*February 3, 2015*

**algebra**

the way you typed it, it becomes 5/2176782336 * 2/9 I seriously doubt that you intended that. Are you sure you don't have a typo ?
*February 3, 2015*

**algebra**

You must know the first few perfect squares, such as 4, 9, 16, 25,... perhaps up to 144 so for √(any number) , attempt to split the number into factors containing one or more of those perfect squares. e.g. √18 = √9 √2 = 3√2 √35 = √5&#...
*February 3, 2015*

**Math (PreCalculus)**

write it this way: (sec^2 x - 1)/sinx = tanxsecx In your repertoire of basic trig formulas you should have sec^2 x = tan^2 + 1 LS= (tan^2 x + 1 - 1)/sinx = (sin^2 x/cos^2 x)(1/sinx) = sinx/cos^2 x = (sinx/cosx) (1/cosx) = tanx secx = RS
*February 3, 2015*

**MATH**

a = 5 last term = 61 sum(n) = (n/2)(first + last) 957 = (n/2)(5 + 61) 1914 = 66n n =29
*February 3, 2015*

**Math**

correct so far You have only found the value of y, you still have to find x sub y = 2 into either of the original equations to find x
*February 3, 2015*

**Math**

both sinx and cosx are defined for every value of x the problem occurs with the reciprocal functions such as secx or 1/cosx and cscx also since tanx = sinx/cosx, tanx is undefined if cosx = 0, such as x=90° or π/2 similarly cotx runs into problems when sinx=0 ,such as...
*February 3, 2015*

**Math**

you were on the right track. look at these two columns n r , where r is the remainder after dividing by 5 1 3 2 4 3 2 4 1 5 3 6 4 7 2 8 1 9 3 10 4 11 2 12 1 So the remainders cycle as 3 4 2 1, so if n is evenly divisible by 4 , the remainder of 3^n divided by 5 will be 1 if n ...
*February 3, 2015*

**Algebra 2**

You have to know how to complete the square. f(x) = -x^2 - 3x = -(x^2 + 3x +9/4 - 9/4) = -( (x + 3/2)^2 - 9/4) = -(x + 3/2)^2 + 9/4 take it from there, all the information is just there in front of you for you 2nd problem, [f o g o h] (-2) means f(g(h(-2))) to me = f(g(-8)) = ...
*February 3, 2015*

**typo - Math**

that last line should say y = 3.5
*February 3, 2015*

**Math**

let the speed of the boat in still waters be x mph let the speed of the current be y mph So going downstream or with the current the speed is x+y going against the current the speed is x-y so 40/(x+y) = 4 4x + 4y = 40 x + y = 10 , #1 and 40/(x-y) = 5 5x - 5y = 40 x-y = 8 , #2 ...
*February 3, 2015*

**College Algebra**

Just realized that I did this same question back in 2007, (and got the same answer) http://www.jiskha.com/display.cgi?id=1195533760
*February 3, 2015*

**College Algebra**

time for 1st trip = 200/55 = 40/11 hrs time return trip = 200/40 = 5 hrs avg speed = 400/(5+40/11) = 880/19 mph or appr 46.3 mph
*February 3, 2015*

**Math**

so we have this pattern: 1 5 2 11 3 18 4 26 notice that on each consecutive day, the increase is one more than the previous day's increase, suggesting a quadratic expression let number = an^2 + bn + c , were n is the number of days if n = 1: a+b+c = 5 if n = 2: 4a + 2b + c...
*February 3, 2015*

**math**

ar = 16 ar^4 = 2 divide the 2nd equation by the first ar^4/ar = 2/16 r^3 = 1/8 r = 1/2 back in first: ar= 16 (1/2)a = 16 a = 32
*February 3, 2015*

**algebra**

y^2 - 12y + 31 = 0 clearly , it does not factor, so let's use the formula y = (12 ± √20)/2 = (12 ± 2√5)/2 = 6 ± √5 So what do you think?
*February 3, 2015*

**college algebra**

number of rows --- x number of seats per row --- x+8 x(x+8) = 1920 x^2 + 8x - 1920 = 0 (x-40)(x+48)=0 x = 40 or x = -48, which of course makes no sense there are 40 rows, and each row has 48 seats
*February 3, 2015*

**Math Homework**

you want to use these identities http://www.mathwords.com/s/sum_to_product_identities.htm especially this one sinx - siny = 2cos( (x+y)/2 )sin(( x-y)/2 ) sin 5π/4 - sin3π/4 = 2cos(π)sin(π/4) = 2(-1)(√2/2) = -√2
*February 3, 2015*

**Math - Answer Check**

http://www.jiskha.com/display.cgi?id=1422926711 How can I tell without seeing your calculations ?
*February 3, 2015*

**math**

(1/36)^(w+2) = (1/216)^(4w did you realize that 36 = 6^2 and 216= 6^3 (1/6^2)^(w+2) < (1/6^3)^(4w) 6^(-2(w+2)) < 6^(-3(4w)) 6^(-2w-4) < 6^(-12w) then -2w-4 < -12w 10w < 4 w < 4/10 or w < 2/5 or .4
*February 3, 2015*

**Trigonometry**

I tried your #1 with x=10° and it did not work so it is not even an identity #2 and #3. you will have to remember that cos 2A = 1 - 2sin^2 A , and sin 2A = 2sinAcosA or cosx = 1 - 2sin^2 (x/2) , and sinx = 2sin(x/2)cos(x/2)
*February 3, 2015*

**correction - Math**

I should have read your question a bit more carefully It asked for the equation of the lines perpendicular to the line joining the points Now the question makes even less sense, since we don't know through which point our perpendicular will pass Your answers appear to find...
*February 3, 2015*

**Math**

Are those supposed to be your answers ? None make any sense, since it asked for the equation of the line I will do a) 2 points (1,4) and -1,1) slope = (1-4)/(-1-1) = -3/-2 = 3/2 , note that the brackets in the first calculation are essential using the point (1,4) y-4 = (3/2)(x...
*February 3, 2015*

**linear algebra**

My explanation of step 4 of my method is not as clear as I intended. The webpage I gave you states it better and shows the pattern Btw, if you had a 4 by 4 you better get several sheets of paper, since you have to bring it from a 4 by 4 to a 3 by 3, that alone would involve 16...
*February 3, 2015*

**linear algebra**

There are several ways to find the matrix, here is my method 1. find the determinant of A, I go det(A) = 1 2. flip the matrix along its top-left to bottom-right diagonal to get -5 -3 -9 2 1 3 2 1 4 3. replace each of the terms of this matrix by its cofactors e.g -5 is replaced...
*February 3, 2015*

**Math**

recall that cos (2x) = 1 - 2sin^2 x or cos x = 1 - 2sin^2 (x/2) then yours is ... sin (x/2) = 1 - (1 - 2sin^2 (x/2)) sin (x/2) = 2sin^2 (x/2) 2sin^2 (x/2) - sin (x/2) = 0 sin x/2(2sin x/2 - 1) = 0 sin (x/2) = 0 or sin(x/2) = 1/2 case 1: sin (x/2) = 0 x/2 = 0 , π, 2π ...
*February 3, 2015*

**Math Help**

Even though you got the correct answer you did not follow the required method. (That's like winning a 100 m backstroke race by using the butterfly stroke , you would be DQ'd) It said to use the Half-Angle formula There are two, sin (2A) = 2sinAcosA and cos(2A) = cos^2 ...
*February 3, 2015*

**maths surds please help and explain**

Ok, so you are saying a. 1/√a + 2 = (1/√a)(√a/√a) + 2 = (√a)/a + 2 b. still not clear if you meant √(18/25) or √18 /25 for first interpretation: = 3√2/5 for 2nd interpretation: = 3√2 /25 c). I will take the original as ...
*February 3, 2015*

**maths surds please help and explain**

e) is the only one not ambiguous, √5*(√72/√3) = √5*√24 = √120 = 2√30 Also your use of x is not consistent in c) you are using x as a multiplier, in d) you are using x as a variable if you have to show a multiplication signs, either use...
*February 3, 2015*

**maths surds please help and explain**

you really have to use brackets to establish the order of operations you want. e.g. in #1, the way you typed it it would be (1/√a) + 2 but I sense you meant 1/(√a + 2) in b) did you mean √(18/25) ? etc
*February 3, 2015*

**algebra**

You have 3 terms, two of which contain the common factor (2a-b) Is that -8 at the end supposed to be a multiplier ? The way you typed it, it does not factor.
*February 3, 2015*

**math**

speed = distance / time clearly the car went 123 miles in 2 hours so speed = ?????
*February 2, 2015*

**math**

width --- x length --- 4x x(4x) = 144 x^2 = 36 x=6 width = 6 ft, length = 24 ft check: area = 6x24 = 144
*February 2, 2015*

**MATH**

David Lane's webpage is perfect for this type of question and replaces the charts and tables found in the back of textbooks http://davidmlane.com/hyperstat/z_table.html Just fill in the data for c) remember that 96% would be shorter. You might want to use the second ...
*February 2, 2015*

**Calculus - Differentiation**

I would write it as y = 3(1 - 6x^4)^-1 , and use the chain rule dy/dx = -3(1 - 6x^4)^-2 (-24x^3 = 72x^3/(1 - 6x^4)^2
*February 2, 2015*

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