Friday
April 17, 2015

Posts by Reiny


Total # Posts: 29,591

Maths
Rather tedious to find the inverse of a 4by4 matrix, and out of the question to type it all out. Surely you can find an inverse calculator on the web. Just google and pick one then multiply that inverse by 5 8 12 7
February 10, 2015

Math
I just did this before you decided to repost under a different name
February 10, 2015

maths
sin30° = height/10 height = 10sin30 = ...
February 10, 2015

Trigonometry
I made a sketch and marked all the angles Let r be the distance between start and ending point. the angle between the two trips is 90+28°20'+28°20' = 146° 40' by the cosine law: r^2 = 86^2 + 124^2 - 2(86)(124)cos146°40' = 40591.28405 r = √...
February 10, 2015

math
if the base is a proper fraction (less than one) and you are raising it to positive exponents > 1, the answer is less than the base if the base is a improper fraction (greater than one) and you are raising it to positive exponents > 1, the answer is greater than the base...
February 10, 2015

Calculus
I will answer no more of these types until you show me some of your efforts and work
February 9, 2015

Calculus
these questions you are posting all basically all the same. a = 72 v = 72t+c when t = 0 , v = 17 17 = 0 + c, v = 72t + 17 s = 36t^2 + 17t + k when t = 0 , s = 10 so k = 10 s = 36t^2 + 17t + 10
February 9, 2015

Calculus
see http://www.jiskha.com/display.cgi?id=1423541938 and make the necessary adjustments
February 9, 2015

Calculus
height = -16t^2 + 96t v = -32t + 96 = 0 at the top 32t=96 t = 3 it will take 3 seconds to reach the max, and that max is -16(9) + 96(3) = 144 ft
February 9, 2015

MATH - exponent laws
-(11/17^-10/(9/5)^(1/10) use the y^x key, the most powerful key on your calculator (-11/-17)^-10 = 1/(11/17)^10 = 77.725... (I stored that in A on my calculator) (9/5)^(1/10) = 1.0605.. so -(11/17^-10/(9/5)^(1/10) = -77.725... /1.0605... = -73.28837824 I use the memories on my...
February 9, 2015

Math
What is 360 ÷ 18 what is 5 times that ?
February 9, 2015

Math
Not necessarily. The angles could be different, thus not similar Imagine the second figure having hinges at the vertices and you "squish" the figure.
February 9, 2015

Math
I am guilty of that more often than you are
February 9, 2015

Math
prob of making the free throw = 32/60 = 8/15 so the prob of NOT making it = 1 - 8/15 = 7/15
February 9, 2015

Math 110
can't make out a) if x5/3 is supposed to mean x^(5/3) use the notation I just used.
February 9, 2015

Math
a peek at the graph might guide you along http://www.wolframalpha.com/input/?i=plot+y+%3D++2x+%2B+1+%E2%88%92+sin%28x%29
February 9, 2015

Mat104
i = .055/3 = .018333... what is 955(1.018333..)^12 ?
February 9, 2015

Calculus
sketching should have been no problem both have axes on the x-axis, one has vertex (-49,0) and opens to the right the other has vertex (49,0) and opens to the left There is perfect symmetry and they meet at (0,7) and (0,-7) I would take horizontal slices, thus integrate with ...
February 9, 2015

math
gradient = slope = dy/dx dy/dx = 3ax^2 - 6x - 2 using the given: 7 = 3a(1) -6(1) - 2 7 = 3a - 8 3a = 15 a = 5
February 9, 2015

Calculus
well, finding y' and y'' is really the main part of the meal, the rest is just cleaning the dishes. you should know the derivatives of the 6 basic trig functions by heart. y' = secx(sec^2 x) + tanx(secxtanx) , by the product rule = sec^3 x + tan^2 x secx y'...
February 9, 2015

Math
a = -32 v = -32t + c since it was 'dropped' , when t=0 , v =0 so c = 0 v = -32t 120 = -32t t= 120/-32 = -15/4 s = -16t^2 + k when it hit the ground, t = 15/4 , s = 0 0 = -16(225/16) = k k = 225 s = -16t^2 + 225 So the height of the cliff is 225 ft
February 9, 2015

Differentiation
y' = (e^tanx )(sec^2 x)
February 9, 2015

Vector Cross & Dot Product
1. I got (-1,2,6) Your error is in the last calculation, I had 4(1) - (2(-1) = 6 and then (-1,2,6)dot((-1,0,3) = 1 + 0 + 18 = 19 2. since this problem depends on your answer from #1, check your calculations with the correct answer from #1, I did get (6,-3,2)
February 9, 2015

Cross Product of Vectors
your initial vector is correct magnitude of (0,6,18) = √(0+36+324) = √360 = 6√10 so I see that your unit vector is also correct Perhaps you are looking at some answer key and the answer there looks different. They might have rationalized the denominator 1/&#...
February 9, 2015

math
Ms Sue correctly assumed that the largest rectangle one can have for a given perimeter is a square, and gave you a correct solution based on that assumption. Were you supposed to find the answer without making that assumption? Let me know and I will show you how.
February 9, 2015

math
What is the USE format ?
February 9, 2015

Math
yes, but that would give you how many brought skates, which is not the question. First, how many came ? (3/4) of 400 = 300 of those 1/5 brought skates number who brought skates = (1/5)(300) = 60 Assuming the rest rented skates, so 300-60 or 240 rented skates or if 1/5 brought ...
February 9, 2015

Trigonometry
since 1+cot^2theta=csc^2theta cot^2 Ø = csc^2 - 1 = (-3.589142)^2 - 1 = 11.8819403 cotØ = ± √11.8819403 = ± 3.447... but since Ø in in III, cotØ must be positive, so cotØ = 3.447.. Why were you doing 1/sin(-3.58914...
February 9, 2015

Algebra 2
(1 - √(3x)/√(6x) = (1 - √(3x)/√(6x) * √(6x)/√(6x) = (√(6x) - (√18)x)/(6x) = ( √(6x) - 3√2 x)/(6x)
February 9, 2015

Algebra 2
Follow the same steps suggested by Steve in your previous post or take the negative term to the right side, then square collect all like terms, isolate the square root term and square again.
February 9, 2015

Math - not PSC
y1/x1 = y2/x2 65/33 = y2/44 y2 = 44(65/33) = 260/3 or 86 2/3 = appr 86.67 or "If y is directly proportional to x" means y = kx if y = 65, x = 33 65 = 33k k = 65/33 y = (65/33)x when x = 44 y = (65/33)(44) = appr 86.67
February 9, 2015

math
If the base is a square of area 49, then each side is 7 cm so look at the block, you have 2 squares + 4 equal surfaces on the sides Surface area = 2(49) + 4(7)(10) = 378 cm^2 btw, I don't understand your previous post, it looks incomplete
February 9, 2015

linear algebra
I will give you 2 nice youtubes to show how this is done https://www.youtube.com/watch?v=taBHTo8sviM She sets it up nicely, but does not actually show how to find the determinant of a 3by3. This one shows a nice short-cut method to find the determinant, but I must point out ...
February 9, 2015

Math- Calculus
1. done by just getting a "feel" for the numbers e^(-2x) = 1/e^(2x) so as x ---> infinitity, the denominator gets huge and the result approaches zero as for the sinx it simply runs up and down between -1 and 1 no matter what x is or how large x is So the lim(e^(-...
February 9, 2015

Calc
1. lim tanx/x , as x ---> 0 (after each line below) = lim (sinx/cosx)/x = lim (sinx/x)(1/cox = lim sinx/x * lim 1/cosx , you should know these = (1)(1) = 1 2. y = x^2 dy/dx = 2x Let the point of contact be (a,b) we know b = a^2 and the slope of the tangent is 2a but using ...
February 9, 2015

math
Same as the standard "hand-shake" problem number of games = 10 choose 2 = C(10,2) = 45 In the hand-shake problem, we have 10 people and they all shake hands on meeting. so each of the 10 people can shake hands with 9 others for 90 shakes but that would include A ...
February 9, 2015

Algebra 1
#1, your middle term is -x , thus A #2 D #3 B How are you doing these, so far they are all wrong (4p-2)(p-4) = 4p^2 - 16p - 2p + 8 = 4p^2 - 18p + 8 #4 A = 2πr^2 + 2πrh = 2π(3x-2)^2 + 2π(3x-2)(x+3) = 2π[ 9x^2 - 6x - 6x + 4 + 3x^2 + 9x - 2x - 6] = 2π...
February 9, 2015

math algebra
In the golden rectangle the ratio of length : width = (1+√5) : 2 or appr 1.618 5/w = (1+√5)/2 w = 10/(1+√5) = appr 3.09 check: 5/3.09 = appr 1.6181.. good enough
February 9, 2015

Maths
8m, 9 cm = 809 cm number of pieces which are 9 cm long = 809/9 = 89.88.. or appr 90 cm each btw, in the true usage of the metric system, one would not say 8m, 9cm it would be either 809 cm or 8.09 m the beauty of the metric system is that you don't have to mix units like ...
February 9, 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 Your conclusion ?
February 9, 2015

Geometry
Use the information from my previous post to answer this one. Let me know what your answer is
February 9, 2015

Geometry
Since perimeter is a linear relationship, the ratio of perimeters of two similar figures is proportional to the ratio of their sides, thus 48 : 54 or 8 : 9 Since area is a quadratic relationship , ..... the square of their sides, thus 48^2 : 54^2 = 2304 : 2916 = 64 : 81
February 9, 2015

math
I assume you want this in simple interest. let the amount needed now be A A + A(.0547)(8/12) = 1762 A + A(.0364666..) = 1762 A(1.0364666..) = 1762 A = 1762/1.0364666.. = $1700.00
February 8, 2015

Calculus
just tedious work .... I suggest you make a sketch, and plot the points (0,20) , (2,22), .... you will get trapezoids by joining all the y-values and drawing in all the verticals look at the first trapezoid, its base = 2 the left vertical is 20 and the right vertical is 22 ...
February 8, 2015

math1979
Wow, let me know what stock that is. profit = 96-17 + 3.57 = 82.57 I = PRT 82.57 = 17(R)(1) R = 82.57/17 = 4.857 = appr 486 %
February 8, 2015

math
In your last line you have a = 30, d = -2 but you had found d = -10, which is correct so a = 30, d = -10 sum(n) = (n/2)(2a + (n-1)d ) , you should know that formula sum(15) = (15/2)(60 + 14(-10)) = -600
February 8, 2015

Math
One of the basic identities you should have at your disposal is sec^2 x = 1 + tan^2 x so sec^2 x + tanx = 1 1 + tan^2 x + tanx = 1 tanx(tanx + 1) = 0 tanx = 0 or tanx = -1 if tanx = 0 then x = 0 or x = 180° if tanx = -1, then x = 135° or x = 315° x = 0 , π , 3...
February 8, 2015

Math
f ' (x) = ax^(a-1)(1-x)^b + b(1-x)^(b-1) x^a = 0 for a max of f(x) x^(a-1) (1-x)^(b-1)[a(1-x) + b(x)] = 0 then x^(a-1) = 0 , which is not possible or (1-x)^(b-1) = 0 , which is also not possible or a-ax+bx=0 a = ax+bx a = x(a+b) x = a/(a+b) f(a/(a+b))) = [a/(a+b)]^a [(1-a...
February 8, 2015

Vectors/Scalars?
The dot product is an operation between any two vectors and is always a scalar, your (u dot v)dot (a dot c) = (a scalar) dot (a scalar) which would be undefined, since there is no such thing as a dot product between two scalars.
February 8, 2015

Math 1105
18x^2+36x+18 = 18(x^2 + 2x + 1) = 18(x+1)^2 so one square is x+1 by x+1, the other is 3√2 by 3√2
February 8, 2015

Math
what I stated is true for any positive base > 1 thus it is true for 9^x
February 8, 2015

Math
consider y = 9^x and look at its graph http://www.wolframalpha.com/input/?i=plot+y+%3D+9%5Ex You might want to change the equation to y = 2^x in the input window of Wolfram to show the shape is basically the same for any positive base > 1. if x = 0 , 9^x = 1 if x is ...
February 8, 2015

finite math
I don't know what example 1 is, thus I don't know how you are taught to do these. Here is how I would do it Number of ways to choose 8 from 15 = C(15,8) = 6435 at least one green ---> exclude the case of no green number with no green = (10,8) = 45 so the number with...
February 8, 2015

geometry
x/55 = tan49° x = 55tan49° get out your calculator
February 8, 2015

Math (Pre-Calc)
5√3 tanx + 3 = 8√3 tanx 3√3tanx = 3 √3 tanx = 1 tanx = 1/√3 x = π/6 in quadrant I or x = π + π/6 or 7π/6 in quadrant III x = π/6 , 6π/6
February 8, 2015

Math
A little "trick" needed here cosx/(1+sinx) , (those brackets are essential) = cosx/(1+sinx) * (1-sinx)/(1-sinx) ---> I multiplied by a version of 1, thus changing the appearance but not the value of the expression = cosx(1-sinx)/(1 - sin^2 x) = cosx(1-sinx)/cos^2 ...
February 8, 2015

math
price of cup ---- x price of spoon --- y Samuel: 3x+4y=324 Daniel paid 5x for his cups Mary paid 2y for her spoons 5x - 2y = 228 double this last equation 10x-4y=456 , add to the first 3x+4y=324 13x = 780 x = 60 back in 1st: 3(60) +4y = 324 I will let you finish it , and state...
February 8, 2015

math algebra 8
amount of 12% powder --- x amount of 20% powder --- 30-x .12x + .20(30-x) = .18(30) times 100 12x + 20(30-x) = 18(30) solve for x
February 8, 2015

Math
Assuming you made a sketch, and the 34° angle is at the end of the shadow, then h/11 = tan34 h = 11tan34 = ...
February 8, 2015

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

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