Monday
January 26, 2015

Posts by Reiny


Total # Posts: 28,733

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

Algebra
N + D = 45 5N + 10D = 360 ---> N + 2D = 72 Subtract them ---> D = 27 then in your head from the first equation, N = 18 So he has 27 dimes and 18 nickels check: 27+18 = 45 , check! 27 dimes = $2.70 18 nickels = $0.90 total = $3.60 check!
November 26, 2014

math
1/2 % = .5 % = .005 so you are correct. (your mom's 50% would be .5 )
November 26, 2014

CaLC AB
#2 tan(x+y) = x then sec^2 (x+y) * (1+dy/dx) = 1 sec^2 (x+y) + dy/dx sec^2 (x+y) = 1 dy/dx = (1 - sec^2 (x+y) )/(sec^2 (x+y) ) or = 1/sec^2 (x+y) - sec^2 (x+y)/sec^2 (x+y) = cos^2 (x+y) - 1 looks like e) is it.
November 26, 2014

CaLC AB
f(x) = sin^2 x or (sinx)^2 f ' (x) = 2sinxcosx or sin (2x) g ' (x) = x so is sin (2x) > x for x = 0, no x = 1.2 , sin(2.4) = .67.. , so no x = .9 , sin (1.8) = .97.. which is > .9 , so YES x = .8 , sin(1.6) = .99957.. which is > .8 , so YES x = 1.3 , sin 3 = ....
November 26, 2014

AP CALC. AB
f(x) = x^2 + 4x - 8 dy/dx = 2x+4 at x=2 , dy/dx = 8 f(2) = 4 + 8-8 = 4 tangent equation at x = 2 y-4 = 8(x-2) y-4 = 8x-16 y = 8x -12 8x-12 = 2(x^2 + 4x-8) 8x - 12 = 2x^2 + 8x - 16 2x^2 = 4 x^2 = 2 x = ± √2 so what do you think?
November 26, 2014

Math
so the TV was originally selling for 2999.99 ($3,000) the markdown was 1500 so the markdown was 1500/3000 = 1/2 or 50%
November 26, 2014

geometry
Go with MathMate, I misread the question
November 26, 2014

geometry
All angles in the equilateral triangle are 60° In the isosceles triangle the two base angles are 73 ° each ......... ( (180-34)/2 ) so angle ABD = 60+73 or 133°
November 26, 2014

Trig
1. can't see your diagram but will assume that the angle of 35° is between the two given sides, so ... R^2 = 98^2 + 55^2 - 2(55)(98)cos 145° 2. "each" vector ? , what vector 3. a = <9,8> b = <-8,7) a dot b = |a| |b| cosØ -72 + 56 = √...
November 26, 2014

analytic
duplicate post, see your other post
November 26, 2014

analytic
slope of first line = m1 = (6-9)/(2-1) = -3 slope m2 = (5-3)/(3+1) = 1/2 if Ø is the angle between them: tanØ = (m2-m1)/(1 + m2m1) = (1/2 - 3)/(1 + (1/2)(-3)) = (-5/2) / (-1/2) = 5 Ø = 78.7° to the nearest tenth
November 26, 2014

Statistics
z score = (your data value - mean)/sd I will do the first and fourth, follow the same procedure for the others 68, ? z = (68-70)/8 = -2/8 = -.25 ? 1.8 1.8 = (x - 70)/8 multiply by 8 14.4 = x-70 add 70 84.4 = x notice the z value may be ± but your data value must be ...
November 26, 2014

Math
10/12 = 50/60 = 25/30 = ... just multiply the numerator and denominator by the same non-zero constant e.g (5/6)*(2/2) = 10/12 etc
November 26, 2014

Trig
2csc^2x-8=0 csc^2 x = 4/2 = 4 then sin^2 x = 1/4 sinx = ±1/2 ---> so x can be in any of the 4 quads we know sinπ/6 = 1/2 so x = π/6 x = π - π/6 = 5π/6 x = π + π/6 = 7π/6 x = 2π - π/6 = 11π/6
November 25, 2014

Trigonometry
sin^2 x = 3/4 sinx = ±√3/2 I know sin 60° = √3/2 or sin π/3 = √3/2 so x = π/3, 2π/3 , 4π/4 , 5π/3 2 tan^2 x = √12 = 2√3 tan^2 x = √3 now you should know the trig ratios of the 30-60-90 triangle. once you ...
November 25, 2014

Brief Calculus
look at the graph first. http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5Ex%2C+y+%3D+2x%2B1%2C+-2+to+1 I is obvious that y = e^x and y = 2x+1 intersect at the y-axis at (0,1). there is another intersection but it beyond x = 1, so of no concern to us So area = ∫ (e^x...
November 25, 2014

Geometry
In the actual case they had 18° So in the general case they now have x° So let's do exactly the same thing So if we have n sides and the exterior angle is x° then the interior angle is 180-x So (180-x)n = (180)(n-2) 180x - nx = 180n + 360 solving for n: 180x - ...
November 25, 2014

math show work please
Did you notice that x^2 + 8x + 15 = (x+3)(x+5) which happen to be the denominators on the left side So let's multiply everybody by (x+3)(x+5) (x+5) + 4(x+3) = 2 Now how easy is that from there ?
November 25, 2014

math show work please
1 - 11/x + 30/x^2 = 0 times x^2 x^2 - 11x + 30 = 0 (x-5)(x-6) = 0 x = 5 or x = 6
November 25, 2014

calculus
s = (3+6t)^(1/2) v = (1/2)(3+6t)^(-1/2) (6) = 3(3+6t)^(-1/2) a = (-3/2)(3+6t)^(-3/2) (6) = -9(3+6t)^(-3/2) when t = 1 a =-9(9)^(-3/2) = -9(1/27) = -1/3 you are correct!
November 24, 2014

trig
Oh my! I know that cos π/3 = 1/2 and cos π/6 = √3/2 (What is the matter with me ? )
November 24, 2014

trig
1. 4cosx = 2 cosx = 2/4 = 1/2 I know cos π/6 = 1/2 , so x = π/6 but the cosine is positive in quadrants I or IV so x is also 2π- π/6 = 11π/6 #2 sec^2 = 4/3 1/cos^2 x = 4/3 cos^2 x = 3/4 cos x = ± √3/2 so x could in any of the 4 quadrants ...
November 24, 2014

MATH
I got 12 Make a Venn diagram consisting of two intersecting circles, one called M, the other called L Put a rectangle around the circles. place 5 in the intersection of M and L since M contains 18 , but 5 are already written down, place 13 in the M only part of the circle. ...
November 24, 2014

Math
What is 10000(1.01)^72 ?
November 24, 2014

calculus
dy/dx = 2x - 6 = 0 for horizontal tangent 2x-6 = 0 2x=6 x = 3 , which is choice a)
November 24, 2014

algebra
ratio of x and y coefficient of first = 2 : 5 ratio of x and y coefficients of 2nd = 4 : 10 = 2:5 but the constants are not in that ratio, so you have two parallel lines
November 24, 2014

Math
This is my interpretation of the question: R-- right W -- wrong there are 8 ways for the selection to take place (or there are 2 ways to pick the first cheese, right or wrong, 2 ways to pick the 2nd, and 2 ways to pick the third: 2x2x2=8 ) WWW WWR ** WRW ** WRR RWW ** RWR RRW ...
November 24, 2014

math
let the acceleration be a , (I expect a to be negative) v = at + c when t = 0 , v = 8 8 = 0+c ---> c = 0 so v = at + 8 when t = .36, v = 0 0 = a(.36) + 8 a = -8/.36 = appr -22.2 m/s^2
November 24, 2014

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