Sunday
December 21, 2014

Posts by Reiny


Total # Posts: 28,261

Math help
Since the angle of incidence is equal to the angle of reflection in the mirror you have tow similar right-angled triangles. Thus we can use our good ol' fashioned ratios x/7.5 = 5.5/3 3x = 41.25 x = 13.75 or 13.8 ft to the nearest tenth of a foot
December 6, 2014

Algebra
I don't think you are using the concept of the "inverse of a function" in the proper way, you are just solving the equation for c d = .15c - 1.5 .15c = d + 1.5 c = (d+1.5)/.15 now plug in d = 18 c = (18+1.5)/.15 = 130 We could have just plugged in d = 18 in the ...
December 6, 2014

calculus
you had ∫ e^(8x) (e^(8x) + e^(-8x) )/2 dx which is = ∫ ( e^(16x) + e^0 )/2 dx = (1/2)(1/16)e^(16x) + (1/2)x | from 0 to 1/16 = (1/2)(1/16) e^1 + 1/32 - (1/2)(1/16)e^0 - 0 = (1/32)e or = e/32
December 6, 2014

capacity problems
ummmh, what is 2 x 80 ??
December 6, 2014

7th grade math
#4 There are only 6 students, so just take (5/6)(120) = 100 so 100 prefer pepperoni #6. Taylor/Kate = 3/2 Taylor/120 = 3/2 2 Taylor = 360 Taylor = 180 #9 d) (-2/5) / (-1/5) = (-2/5)(-5/1) = 10/5 = 2 The others are correct
December 6, 2014

algebra
let the speed of the plane in still air be x mph let the speed of the wind be y mph then 570/(x+y) = 3 --->3x + 3y = 570 x + y = 190 570/(x-y) = 5 ---> 5x - 5y = 570 x - y = 114 add them 2x = 304 x = 152 back in the first: 152 + y = 190 y = 38
December 6, 2014

algebra
If you are taking Calculus .... E ' (v) = -.032v + 1.408 = 0 for max of E .032v = 1.408 v = 44 E(44) = ....just sub in
December 6, 2014

maths
Please proof-read your post before sending it route = root squre = square i/3 = 1/3 ?? So if 1/3 of the diagonal is 3√2, then the diagonal is 9√2 let the side of the square be x x^2 + x^2 = (9√2)^2 2x^2 = 162 x^2 = 81 x = √81 = 9
December 6, 2014

Algebra
notice you can take out r^2 as a common factor r^2(15.64 + 4.16) = 235.619 19.8 r^2 = 235.619 r^2 = 11.899945... r = appr 3.45 to the nearest hundredth
December 6, 2014

Math Trig
sec Ø = -13/5 in quad II so cosØ = -5/13 x = -5, r = 13 and y = +12 sinØ = 12/13 cotØ = -5/12
December 5, 2014

math
let the number of days be x let the rate per mile be $ y 4x + 450y = 244.5 3x + 200y = 149 1st times 3 ---> 12x + 1350y = 733.5 2nd times 4 --> 12x + 800y = 596 subtract them: 550y = 137.5 y = .25 sub back into 2nd 3x+200(.25) = 149 3x + 50=149 3x = 99 x = 33 The daily ...
December 5, 2014

math help
just replace you x with -7 and evaluate. you appear to have a typo
December 5, 2014

Calculous Finding K, using zeros
since as x ---> ± infinity, y --> + infinitey, the function must be of even exponent, so one of the roots must be a double root, as you have f(x) = k(x-3)(x+3)(x-5) but we are also told that the y-intercept is 17, so we have the point (0,17) on our polynomial. 17...
December 5, 2014

Math Calculous
so we have x-intercepts of 0 and 3 thus f(x) = kx(x-3) but (5,30) also lies on f(x), so ... 30 = k(5)(2) 10k = 30 k = 3 f(x) = 3x(x-3) or f(x) = 3x^2 - 9x
December 5, 2014

Calculous (Finding Zeros!)
Oh no, don't expand, then we would be in a real mess y = (x^2 + 2x - 5) (x^3 + 3x^2 - 40x) the first factor does not factor any more, so we use the quadratic equation to find two roots from there. x^2 + 2x - 5 = 0 x = (-2 ± √24)/2 = (-2 ± 2√6)/2...
December 5, 2014

Pre-Calc/Trig...
A poorly worded question, we would not use logs to expand this perhaps you meant: if y = [(x+3)^4(x-5)^7] then log y = log (x+3)^4 + log (x-5)^7 = 4log(x+3) + 7log(x-5) btw, here are the 12 simplified terms of the expansion. http://www.wolframalpha.com/input/?i=expand+%28x%2B3...
December 5, 2014

intermediate algebra
√(40x^3) = √4*√10*√x^2*√x = 2x√(10x)
December 5, 2014

math
36 cm : 9 dm = 36 cm : 90 cm = 36 : 90 = 2 : 5
December 5, 2014

Precalc/Trig
looks like a direct case of the cosine law d^2 = 434^2 + 525^2 - 2(434)(525)cos 60° = 188356 + 275625 - 227850 = 236131 d =√236131 = 485.933
December 4, 2014

Algebra
after subbing .... -5(16) / 8^-1 = -80 (8) = -640 8^-1 = 1/8^1 so 1/8^-1 = 8^1 = 8
December 4, 2014

Algebra
5/√20 - 2√45 = 5/(2√5) - 6√5 = 5/(2√5) *√5/√5 - 6√5 = 5√5/10 - 6√5 = √5/2 - 12√5/2 = -(11√5)/2 I have a strong feeling you meant 3/(y+2) + 2/y = (5y-4)/(y^2-4) do you know why we would multiply by y(...
December 4, 2014

algebra 1
Just noticed a typo in my conclusion statement, should have read: The chemist will need 80 L of the 30%, and 120 L of the 50% solution. notice I did use 120L in my check
December 4, 2014

algebra 1
amount of 30% solution needed ---- x L amount of 50% solution needed ---- 200-x L .3x + .5(200-x) = .42(200) .3x + 100 - .5x = 84 -.2x = -16 x = -16/-.2 = 80 The chemist will need 80 L of the 30%, and 20 L of the 50% solution. check: .3(80) + .5(120) = 84 or , using the 2 ...
December 4, 2014

calculus
sec x = -3 then cos x = -1/3, and x is in the 2nd quadrant the triangle with angle x is in quad II and has a hypotenuse of 3 and an adjacent of 1, so the opposite is √(9-1) = √8 or 2√2 cot x = adjacent/opposite = -1/√8 or -√8/8 = -2√2/8...
December 4, 2014

Help math
let the two pieces be 3x and 7x , then 3x + 7x = v+4 10x = v+4 x = (v+4)/10 The longer piece was 7x or 7(v+4)/10
December 4, 2014

Math
|x-4| ≤ 10 - |x+4| x-4 ≤ 10-|x+4| AND -x+4 ≤ 10 - |x+4) |x+4 ≤ 14-x AND |x+4| ≤ 6 + x x+4≤14-x AND -x-4 ≤ 14-x AND x+4 ≤ 6+x AND -x-4 ≤ 6+x 2x ≤ 10 AND -4 ≤ 14 AND 4 ≤ 6 AND -2x ≤ 10 x ≤ 5 AND ...
December 4, 2014

Math
cube both sides 4 - x^(2/3) = -8 -x^(2/3) = -12 (x^2)^(1/3) = 12 x^2 = 1728 x = ± √1728 = ±24√3 so the difference between the two roots is 48√3
December 4, 2014

math
didn't Steve do this for you on Tuesday ? http://www.jiskha.com/display.cgi?id=1417568391 Always check back before posting the same question again.
December 4, 2014

Math: Reiny
In that case we need the intersection of y = x and y = -x+3 x = -x+3 2x = 3 x = 1.5 so area = ∫(upper y - lowery) dx from 0 to 1.5 = ∫(-x+3 - x)dx from 0 to 1.5 = ∫ 3 dx from 0 to 1.5 = 3x | 0 to 1.5 = 3(1.5) - 3(0) = 4.5
December 3, 2014

math
https://www.youtube.com/watch?v=GDLZYp2U9g8
December 3, 2014

math
First of all, here is a graph of the curve http://www.wolframalpha.com/input/?i=plot+x+%3D+t%5E3+%2B+6t%2C++y+%3D+4t+-+t%5E2+ As you can see, when t = 0 , x = 0, y = 0 when t = 4, x = 88, y = 0 so our parameter will run form t = 0 to t = 4 in general the area would be integral...
December 3, 2014

Math
let log1/4 32^-18 = x (1/4)^x = 32^-18 (2^-2)^x = (2^5)^-18 2^(-2x) = 2^-90 -2x = -90 x = 45
December 3, 2014

Math
I will assume it is 64^(1/3) which would be 4 , so your problem is log4 4^x = 1 x logb4/sub>4 = 1 x(1) = 1 x = 1
December 3, 2014

Math
yes 10/3 < √x < 24/5 square it 100/9 ≤ x ≤ 576/25 11.111.. < x < 23.04 so with whole numbers ... { 12, 13, ... 22, 23} count them up (just realized I used x instead of h, no big deal, eh)
December 3, 2014

math
not linear in real life, but .... so you have two points (0,18) and (5,9) slope = (9-18)/(5-0) = -9/5 so y-18 = (-9/5)(x - 0) y = (-9/5)x + 18 so when x = 11 y = (-9/5)(11) + 18 = -1.8 Now do you see how silly it is to label this linear ? (after 10 years there would be nothing...
December 3, 2014

math
Is the decay exponential, is it linear ? It must be stated
December 3, 2014

Math
y ≥ x is the region above and including y = x y ≤ -x + 3 is the region below and including y = -x + 3 I see a region open at the left, so we can't find the area. We need to close it up on the left. Are we looking at the little triangle between the two lines and...
December 3, 2014

math
cost per photo --- x cost = 2x + 20 = 55 2x = 35 x = 17.5 I will let you determine what I did and what I found
December 3, 2014

Math 120
4logb(X)-1/3logb(y)+2logb(z) = logb (x^4) - logb (y(1/3)) + logb (z^2) = logb (x^4 z^2)/y^(1/3)
December 3, 2014

math - pls check!!!
29. 4k-1 ≥ -3 4k ≥ -2 k ≥ -1/2 30. 6(c-1) ≤ -18 6c - 6 ≤ -18 6c ≤ -12 c ≤ -2 31. 3t > 5t + 12 -2t > 12 t < -6 , yeahhh you got it right 32. -6/7y - 6 ≥ 42 multiply be 7 -6y - 42 ≥ 294 -6y ≥ 336 y ≤ -56...
December 3, 2014

Math
You should learn to do this until you can do it in one step, it is essential to know. (p+3)(p-7) = p^2 - 7p + 3p - 21 = p^2 - 4p - 21 with practice you can get to the last line in one step
December 3, 2014

Calculus
Let his position in the lake be b, let A be the point on shore closest to him, let S be the store so AS = 2, AB = 3 Let P be the point between A and S. So triangle ABP is right angled and BP^2 = x^2 + 9 BP = (x^2+9)^(1/2) recall that Time = Distance/Rate Total Time = T = ((1/5...
December 3, 2014

Math
Assume that none of the couples knew each other, but hopefully each of the married people would be acquainted with their spouse so Sir John's wife would shake hands with 8 other people (not with Sir John) (My question to you: How many different handshakes took place ? )
December 3, 2014

MAth
correct
December 3, 2014

maths
area = 2.1(.39) m^2 = .819 m^2
December 3, 2014

Math
There exists an infinite number of fractions between any two fractions
December 3, 2014

math
Since Taryn earns 122.50 to mow 7 lawns he charges 122.5/7 or $ 17.50 to mow a lawn. Since Alastair earns 112.50 to mow 9 lawns he charges 112.5/9 or $ 12.50 to mow a lawn. The number of hours he spends mowing does not enter this part of the question. Earning of Taryn per hour...
December 3, 2014

Algebra 1
usually we write your point in the form (12,9) direct variation ---> y = kx so 9 = 12k k = 9/12 = 3/4 constant of variation is 3/4
December 3, 2014

algebra
x^3 + 3x^2 - 9x - 27 = 0 looks like grouping will work x^2(x+3) - 9(x+3) = 0 (x+3)(x^2 - 9) = 0 (x+3)(x+3)(x-3) = 0 x = ± 3 (x = -3 is a double root)
December 3, 2014

Algebra 1
y = kx , where k is a constant for the given: 14 = k(-4) k = -7/2 or -3.5 y = -3.5x when x = -6 y = -3.5(-6) = 21
December 3, 2014

Maths
sin(2Ø+30°) = cos(3Ø + 40°) we know that sin x = cos (90-x) so sin(2Ø-30) = cos(90 - 2Ø + 30) = cos(120 - 2Ø) then cos(120-2Ø)=cos(3Ø+40) 3Ø+40 = 120-2Ø 5Ø = 80 Ø = 16° or cos(3Ø + ...
December 3, 2014

Pre-Calc/Trig...
t(1) = (1/4)4^1 - 1 = 1 - 1= 0 t(2) = (1/4)(4^2 - 1 = 4 - 1 = 3 t(3) = (1/4)4^3 - 1 = 4^2 - 1 = 15 t(4) = (1/4)4^4 - 1 = 4^3 - 1 = 63 t(5) = ........ = 255 however, if you meant (1/4)4^(n-1) .....? just sub in and evaluate
December 3, 2014

math
You want the vertex of this parabola. the x of the vertex is -b/2a = -36/-32 = 1.125 seconds plug that in h = - 16(1.125)^2 + 36(1.125) + 9 = ....
December 2, 2014

algebra
e^(.07t) = 2 .07t lne = ln2 t = ln2/.07 = appr 9.9 years
December 1, 2014

Math
let each side be x we have 6 sides of area x^2 6x^2 = 6534 x^2 = 1089 x = √1089 = 33 ft so volume = 33^3 ft^3 or 35937 ft^3
December 1, 2014

math
18 1/5 is the exact answer, so you did not "estimate" in estimation they expect something like this 7 4/5 is appr 8 2 1/3 is appr 2 and 8x2 = 16 so my estimated answer would have been 16
December 1, 2014

calculus
the inner-most brackets are not needed, so f(x)=3ln(x^2 + 2) - 2x you should know how to differentiate a log function, so f ' (x) = 3(2x)/(x^2 + 2) - 2 = 0 for max/min 6x/(x^2 + 2) = 2 3x = x^2 + 2 x^2 - 3x + 2 = 0 (x-2)(x-1) = 0 x = 2 or x = 1 when x = 2, f(2) = 3 ln(6...
December 1, 2014

mathematics
Re-type in English please.
December 1, 2014

Algebra
You want f(x) to be zero, so -x^2 + 7x + 8x = 0 I suspect a type, why would you not just add 7x and 8x ? waiting for your correction.....
December 1, 2014

algebra
since your divisor is a monomial, just divide it into each term of the numerator = (1/2)x^3 - 2x^2 - 7/2
December 1, 2014

Algebra
You have a typo, there is no exponent on the first term anyway ... max when E ' (v) = 0 E ' (v) = ..... then set that equal to zero and solve for v for b) sub in your v from a) into the original equation
December 1, 2014

math
arhghh, should have said: so the number is indeed 27/5 or 5.4
December 1, 2014

math
I interpreted that as 5(x-2) = 17 5x - 10 = 17 5x = 27 x = 27/5 check: 2 less than 27/5 = 27/5 - 2= 17/5 and 5(17/5) = 17 so the number is indeed 17/5 or 3.4
December 1, 2014

math
Since distance = rate x time the rate is in m/s but the time is in hours so 1.5 hr = 1.5(3600) seconds = 5400 seconds we have distance = 5.9(5400) m = 31860 m = 31.86 km
December 1, 2014

Math
let's first solve it .... 4 = -2(4.5p + 25) 4 = -9p - 50 9p = -54 p = -54/9 check: LS (for left side) = 4 RS = -2(4.5(-54/9) + 25) = -2(-27 + 25) = -2(-2) = 4 = LS since LS = RS, my solution is correct
December 1, 2014

algerbra
did you mean ... 4^y = 64 ? I will assume such 4^y = 64 <-----> log4 64 = y
November 30, 2014

Calculus
Use implicit differentiation x^2 + y^2 = 2xy 2x + 2y dy/dx = 2x dy/dx + 2y 2y dy/dx - 2x dy/dx = 2y - 2x dy/dx(2y - 2x) = 2y-2x dy/dx = (2y - 2x)/(2y - 2x) = 1 well, that was weird let's see why .... x^2+y^2=2xy x^2 - 2xy + y^2 = 0 (x - y)^2 = 0 x - y = 0 y = x ahhhh!, ...
November 30, 2014

Sixth Grade Math
good job
November 30, 2014

Math PLEASE HELP ME
invested at 12% ---- x invested at 8% ----- 2x invested at 10% -----210000- x - 2x = 210000-3x .12x + .08(2x) + .10(210000-3x) = 20100 times 100 12x + 16x + 10(210000-3x) = 2010000 -2x = -90000 x = 45000 so 45000 at 12% ---> 5400 90000 at 8% -------> 7200 75000 at 10...
November 30, 2014

Geometry
I painted the courthouse blue, but now my screen is all smudgy. How do I get the paint off my monitor?
November 30, 2014

algebra
1. I got 180.8 which would round to 181 2. yup 3. 172.3356 4. 87.5 Were you rounding off before you got to the last answers?
November 30, 2014

Algebra word problem
Robert's current age --- x Mary's current age ---- x+2 x + x+2 = 28 take it from there
November 30, 2014

AP Calculus
huh? they don't come any easier f(x) = -x^2 + x f ' (x) = -2x + 1
November 30, 2014

Calculus
Step 1 of any limit question for me is to sub in the approach value. I that turns out to be a real number, that is your answer, all done! so when x = -1 your expression = (1-2+3)/(1+1) = 2/2 = 1 looks like B to me
November 30, 2014

Calc
L(x) = f(a) + f ' (a) (x-a) , where x = a f(x) = cosx - sin 2x f ' (x) = -sinx - 2cos 2x L(x) = f(0) + f ' (0) (x-0) = 1-0 + (0-2)(x-0) = 1 - 2x
November 30, 2014

AP Calculus
f(x)=(x^2-3x)/x^2 you could use the quotient rule, but .... f(x)=(x^2-3x)/x^2 = 1 - 3/x = 1 - 3x^-1 f'(x) = 3x^-2 = 3/x^2
November 30, 2014

Algebra
(7.8*10 to the 12th power)*800 = 7.8*800* 10^12 = 62400 * 10^12 = 6.24 * 10^15 (7.8*10 to the 10th power)*80,000 = 624000 * 10^10 = 6.24 * 10^14 so what do you think ?
November 30, 2014

SIXTH GRADE MATH
correct Did you notice that your thinking was along the same lines as that in your previous problem?
November 30, 2014

SIXTH GRADE MATH
yes, you are correct (they signed up 6 volunteers in 3 weeks, so in 1 week they would sign up 1/3 of 6 , which is 2)
November 30, 2014

SIXTH GRADE MATH
You are welcome
November 30, 2014

SIXTH GRADE MATH
Your ratio is 2:3, which means that the total number of games must be a multiple of 5 the only number I see to fit that is 25 e.g. we can split 25 into 2 parts 10:15 = 2:3 but we could not do that with 26 games and still have whole numbers
November 30, 2014

math
17.4 L + 376 ml = 17.4 L + .376 L = 17.776 L (compare the simplicity of the metric system to the complication of the Imperial system in the 2 previous posts)
November 29, 2014

Math
let (5x^3 - x^2 + 20x - 8)/(x^2+4)^2 = (Ax + B)/(x^2 + 4) + C/(x^2+4)^2 or = ( (Ax+b)(x^2+4) + C )/(x^2=4)^2 = ( Ax^3 + 4Ax + Bx^2 + 4B+C)/(x^2+4)^2 matching up coefficients of the original numerator ... A = 5 B = -1 4A = 20 ---> confirms A=5 4B+C = -8 -4+C = -8 C = -4 so ...
November 28, 2014

Math
s^3 = 50653 s = 37 surface area = 6s^2 = 8214
November 28, 2014

math
3√7 is the best you can do
November 28, 2014

maths
area = x(x+12.8) , where x is the width more data needed to continue
November 28, 2014

MATH
√63 = √9 √7 = 3√7
November 28, 2014

math
i = .07/4 = .0175 n = 7(4) = 28 x(1.0175)^28 = 30000 x = 30000/1.0175^28 = $ 18456.85
November 28, 2014

Math
#2 , (without expanding) y - 1.5 = a(x+2)^2 a = (y-1)/(x+2)^2 to get x: (y-1.5)/a = (x+2)^2 x+2 = ± √( (y-1/5)/a ) x = -2 ± √( (y-1/5)/a ) follow the same steps for #1, which is easier
November 28, 2014

math
I think you have a typo Your statement is only true for n = 1 http://www.wolframalpha.com/input/?i=evaluate+3n+%2B+7n+-+2+for+n+%3D+1%2C2%2C3%2C4 Is there supposed to be a power somewhere?
November 28, 2014

calculus
a = -9.8 then v = -9.8t + c when t = 0 , v = 5 m/s 5 = 0 + c, ----> c = 5 v = -9.8t + 5 s = -4.9t^2 + 5t + k when t = 0, s =442 442 = 0 + 0 + k s = -4.8t^2 + 5t + 442 b) highest point when v = 0 0 = -9.8t + 5 t = 5/9.8 = appr .51 sec when t = .51 s = -4.9(.51)^2 + 5(.51) + ...
November 28, 2014

maths
Since the distance covered by the belt depends on the circumference of the circles , ... 150(2π(15)) = 300(2πr) 15π = 2πr r = 15/2 = 7.5 cm or the speed of the pulleys is inversely proportional to the their radii r/15 = 300/150 r/15 = 2 2r = 15 r = 7.5
November 28, 2014

Algebra
I assume you want her pay to be a function of the number of hourse worked let the number of hours worked be h Pay ≥ 10h + 7.5h pay ≥ 17.5 h
November 28, 2014

Math
I did a similar question last night just change the numbers http://www.jiskha.com/display.cgi?id=1417144323
November 28, 2014

math
number correct ---- x number incorrect ---- 200 - x number left unanswered--- 0 2x - (1/2)(200 - x) = 360 4x - 200 + x = 720 5x = 920 x = 184 so on his test he got 184 correct and 16 wrong. check: 184(2) - 16(1/2) = 368 - 8 = 360 with the new scoring system: score = 184/2 - 2(...
November 28, 2014

MATH 100
let the light be situated x ft from one light and 9-x from the other. Let the power be P, where P is a constant let I be the total illumination. I = P/x^2 + 10P/(9-x)^2 = Px^-2 + 10P(9-x)^-2 dI/dx = -2Px^-3 - 10P(9-x)^-3 (-1) = 0 for a min of I 10P/(9-x)^3 = P/x^2 divide by P...
November 27, 2014

math
happens to everybody
November 27, 2014

math
let the original fraction be x/y (x+1)/(y+1) = 2/3 3x + 3 = 2y + 2 ----> 3x - 2y = -1 , #1 (x-2)/(y-2) = 3/5 5x - 10 = 3y - 6 ----> 5x - 3y = 4 , #2 #1 times 3 ---> 9x - 6y = -3 #2 times 2 ---> 10x - 6y = 8 subtract them: x = 11 in #1: 33 - 2y = -1 -2y = -34 y = 17...
November 27, 2014

math
number of 20 paisa coins --- x number of 25 paisa coins --- 50-x 20x + 25(50-x) = 1150 20x + 1250 - 25x = 1150 -5x = -100 x = 20 so she has 20 of the 20paisa and 30 of the 25 paisa coins check: 20+30 = 50 , check! 20(20) + 25(30) = 1150 , check!
November 27, 2014

Algebra
n+d = 45 5n + 10d = 360 or n + 2d = 72 so... n+d = 45 n + 2d = 72 subtract them to eliminate the n , then solve for d sub d back into the first and all is easy.
November 27, 2014

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