Posts by Reiny

Total # Posts: 38,649

math
Why not take the easier equation? x+2y=6 ---> x = 6-2y now plug that into the other, 5x+3y=2 5(6-2y) + 3y = 2 30 - 10y + 3y = 2 -7y = -28 y = 4 then x = 6 -2(4) = -2 see how easy it is ?

Math
no 45000(.98)^15 = appr 33236

math
daily wage/man = 34000/( (12)(17) ) = 500/3 so for 16 men for 18 days wages = (500/3)(16)(18) = 48000

Math
Smaller --- x larger ----- x+4 1/x + 1/(x+4) = 14(1/x)(1/(x+4) multiply by x(x+4) x+4 + x = 14 2x = 10 x = 5 the two integers are 5 and 9 check: 1/5 +1/9 = 14/45 14 times product = 14(1/5)(1/9) = 14/45 my answers are correct

math
Let arcsin(x) = A let arctan(x) = B then cos(arcsin(x) + arctan(x)) = cos(A+B) = cosAcosB - sinAsinB ** from arcsin(x) = A sinA = x/1 cosA = ?(1-x^2) , using Pythagoras from arctan(x) = B tanB = x/1 , then sinB = x/?(x^2 + 1) cosB = 1/?(x^2 + 1) back into ** cosAcosB - ...

1000(1+.0155/4)^20-1/(.0155) careful with brackets, secondly you already did .062/4 , so why are you dividing .0155 by 4 ?? amount = 1000 ( 1.0155^20 - 1)/.0155 = 1000( 23.237857...) = \$ 23237.86

Calculus
given : dl/dt = 3 cm/s, dw/dt 3 cm/s P = 2l + 2w dP/dt = 2 dl/dt + 2 dw/dt plug in the values d^2 = l^2 + w^2 I assume you want the rate of change of the perimeter, not just its length. Your wording is confusing. 2d dd/dt = 2l dl/dt + 2w dw/dt you are given l and w, so you can...

Maths
M+T+W = 3(39) =117 W+TH+F+SA = 4(39.5) = 158 Add them M + T + 2W + TH + F + SA = 275 Finally: M+T+W+TH+F+SA = 240 Let's subtract those last two equations: ahhh, W = 35

Maths
I picked M as the midpoint of AB, and N as the midpoint of DC let P be the intersection of AN and DM in triangle ADM but not in triangle ADN --> triangle AMP by simple ratio calculations, the area of triangle AMP = (1/8)the square. so prob(of your event) = 1/8

maths
from x+y=-1, y = -1-x plug that into the first to find x, then back into x+y=-1

Math
distance for first leg = 240 km distance for 2nd leg = 180 km Interpretation 1: total distance traveled is the hypotenuse d^2 = 240^2 + 180^2 etc average speed = d/6 = ... interpretation 2: total distance = 240+180 = 420 total time = 6 avg speed = 420/6 = 70

Calculus Reposted
the rate at which x changes is given as 2 cm/sec which is dx/t. so you have to find the derivative with respect to time (t), you found the rate of change of y with respect to x xy = 12 x dy/dt + y dx/dt = 0 now plug in our given stuff. 4 dy/dt + 3(2) = 0 4dy/dt = -6 dy/dt = -6...

Maths B
Look at it as being given 2 ordered pairs (25,20000) and (50,30000), and being asked to find the equation of the straight line. Your general point will be (n,C) slope = (30000-20000)/(50-25) = 400 now you have the slope and using one of the given points, find the equation ...

Calculus
The rate of \$200 per year is dp/dt, so we need to differentiate with respect to t 5p+4x+px=100 5 dp/dt + 4 dx/dt + p dx/dt + x dp/dt = 0 we need x when p = 1.5 in the original: 5(1.5) + 4x + 1.5x = 100 5.5x = 92.5 x = 185/11 so we have: p = 1.5, x = 185/11 , dx/dt = .2, and dp...

Calculus- Related rates
dV/dt = 4? r^2 dr/dt 1 = 4?(2.25) dr/dt dr/dt = 1/(9?) <----- nice, you had that dA = 8?r dr/dt = 8?(1/(9?) = 8/9 you had 4/3, looks like a "sloppy" error.

Calculus- Related rates
V = (4/3)? r^3 dV/dt = 4? r^2 dr/dt given : when r = 1.5 , dV/dt = 1 find dr/dt for b), A = 4?r^2 dA = 8?r dr/dt , you have dr/dt from a) just plug in the given stuff

Maths
ok so far. Now use the last piece of information: "In 4 years Harry will be twice as old as Ben" B + 37 = 2(B+4) B + 37 = 2B + 8 29 = B <---- Ben's present age check: Ben is now 29 Harry is now 62 in 4 years: Ben is 33 Harry is 66 Is Harry twice as old as Ben...

Math
2l + 2w = p 2l + 600 = 800 ... l = ...

Related Rates
V=(?/3)(r^2)h but we are told that h = 2r or r = h/2 V = (1/3)? (h/2)^2 (h) = (1/3)? h^3/4 =(1/12)? h^3 dV/dt = (1/4)? h^2 dh/dt 10 = (1/4)?(625) dh/dt dh/dt = .... you finish it.

Maths
What is (26/52)(26/52) ???

Maths

Maths
both are binomial distribution problems prob(boy) = 1/2 prob(girl) a) in 4 children, we want 3 boys and 1 girl = C(4,3)(1/2)^3 (1/2)^1 = 4(1/16) = 1/4 b)2 boys, 2 girls = C(4,2)(1/2)^2 (1/2)^2 = 6(1/16) = 3/8

Maths
prob(all women) = C(4,3)/C(10,3) = ... prob(two men, 1 woman) = C(6,2)*C(4,1)/C(10,3) = ....

math
umhh, how about y = 15,000 + 75x

math
Your question makes little sense. The sum on the two dice is between 2 and 12 What's with all the weird numbers? ok, a) the prob of rolling a sum not more than 1010 = 1 b) prob of sum less than 77 = 1 so prob of sum not less than 77 = 0 c) prob of sum between 33 and 77 ?? ...

math
case 1 : Pay = .06s, where s is the total sales case 2: Pay = 1500 + .04s so you want to solve: .06s = 1500 + .04s go for it.

Math
A reflection of "what" over the x axis? what does log1/a(x) mean - is the base 1/a ?? like in log 1/a x ??

Maths
girls : boys = 3:6 = 1:2 let the number of girls be x let the number of boys be 2x 2x - x = 15 x = 15 we have 15 girls and 30 girls for a total of 45 pupils

Math - Linear Approximation
using: f(x)?f(xo)+f?(xo)(x?xo) <-- should be in your text 27.07 = 27 + .07 let f(x) = x^(2/3) f'(x) = (2/3)x^(-1/3) let xo = 27, x = 27.07 f(27.07) ? f(27) + f'(27)(27.07 - 27) = 27^(2/3) + (2/3)(27)^(-1/3) (.07) = 9 + (2/3)((1/3)(.07) = 9 + .01555.. = 9.01555.. by ...

Calculus
x^2 + xy + y^2 = 9 2x + x dy/dx + y + 2y dy/dx = 0 dy/dx(x + 2y)= -2x - y) dy/dx = (-2x-y)/(x+2y) <---- you had that, good! to have a vertical tangent, the denominator of the above has to be zero, that is, dy/dx must be undefined. x+2y = 0 x = -2y sub into the original: (-...

Math
look for factors so that at least one of the factors is a perfect square. e.g. 162 = 9 * 18 = 9 * 9 * 2 so ?162 = ?9 * ?9 * ?2 = 3*3*?2 = 9?2 You can always check your answer using a calculator.

math
?xe^x dx = xe^x - e^x + c, where c is a constant This one should be part of your repertoire of memorized standard integrals.

math
so SD = ?400 = 20 mean = 600 use http://davidmlane.com/normal.html and plug in your values

algebra
I will interpret that as: a(1) = -15 a(n+1) = a(n) - 8 so each successive term decreases by 8 y = -8x + b when x=1, y=-15 -15 = -8+b b = -7 y = -8x - 7 or in your variables a(n) = -8n - 7 "your best answer" was C, correct There is no "best answer", the ...

Maths
i = .12/12 = .01 payment: p(1.01^48 - 1)/.01 = 2000 p = 32.67 outstanding balance after 35 payments = 2000(1.01)^35 - 32.67(1.01^35 - 1)/.01 = .... you do the button pushing

Math
Notice the y values decrease by 5 while the x values increase by 1, so the slope is a constant -5 thus the equation is y = -5x + b notice that the pair (0,-1) is the y-intercept which is what the b stands for , so ... y = -5x - 1 check it with some of the other given values, ...

math
I would just use a simple ratio ... x/9 = .8/16 x = 7.2/16 = \$.45 check: 9 ounces = 9/16 of a pound (9/16)(.8) = .45 (cheese at 80 cents per pound?? where? )

optional math
You MUST know the definitions. Seventh term of geometric series is 64 ---> ar^6 = 64 ** sum of its 10 terms is 1023 ---> a(r^10 - 1)/(r-1) = 1023 *** divide *** by ** , the a will cancel (r^10 - 1)/(r^6(r-1)) = 1023/64 64r^10 - 64 = 1023r^7 - 1023r^6 = 1023r^6(r-1) took ...

Algebra 1
Just factor 2y^2+5y-42 2y^2+5y-42 = (2y - 7)(y + 6) expand it, to show it is correct

DISTANCE TIME AND SPEED
let the distance be d km time at 90 km/h ---- d/90 time at 120 km/h --- d/120 d/90 - d/120 = 1 solve for d hint: multiply each term by 360 to clear fractions

math
Choosing 2 girls from the 4 --- C(4,2) Choosing 2 boys from the 6 --- C(6,2) choosing any 4 of the 10 --- C(10,4) make use of that

maths
part at 9% -- x part at 8% -- 200,000 -x .09x + .08(200000-x) = 17200 take over

pre calculus
height = -16t^2 + 320t + 0 at ground level, height = 0 16t^2 - 320t = 0 16t(t - 20) = 0 t = 0 , at the start or t = 20 b) you want -16t^2 + 320t > 1584 16t^2 - 320t + 1584 < 0 t^2 - 20t + 99 < 0 (t-11)(t-9) < 0 9 < t < 11 , where t is in seconds

Calculus
Go with Steve's answer. Mine gives the rate at which the shadow is lengthening, I missed the part where they want the rate at which the shadow is moving. so dy/dt + dx/dt = 5.5 + 3.2 etc

Calculus
I trust you made a sketch. On mine I let the distance between the man and the post be y ft, and the length of his shadow be x ft By similar triangles: 5.3/x = 14.5/(x+y) 5.3x + 5.3y = 14.5x 9.2x = 5.3y 92x = 53y 92 dx/dt = 53 dy/dt but we know dy/dt = 5.5 so dx/dt = 53(5.5)/92...

Algebra1
term(5) = a r^4 plug in your given values

Math,science
Just use your definitions: "5th term of an arithmetic progression is 23" ---> a + 4d =23 "the 12th term is 37" --> a + 11d = 37 You have two equations in two unknows. Solve them. Hint: I would subtract one from the other. Let me know what you get.

Algebra
length of side parallel to river --- y length of the other two equal sides --- x 2x + y = 600 ---> y = 600-2x area = xy = x(600-2x) = -2x^2 + 600x this is a downwards opening parabola. Find the vertex by whatever means you were taught to find the vertex, and extract your ...

Algebra
let the number of lower tickets be x let the number of upper tickets be y x+y ?10 ---> y ? -x + 10 8x + 5y ? 200 ---> y ? - (8/5)x + 40 sketch both inequalities then pick any two points in their intersection.

Trig
ok up to 2sin2x=1 then: sin 2x = 1/2 so 2x = ?/6 or 2x = 5?/6 <--- you had that. good! x = ?/12 or x = 5?/12 <-- again, you had that, now.... the period of sin 2x = 2?/2 = ? so adding ? to any existing answer will yield a new answer, x=?/12+? = 13?/12 x = 5?/12 + ? = 13...

Math Word Problem
total number of employees --- x females = .67x = 603 x = 603/.67 = 900 so 900-603 or 297 are male

math
Use the formula for the distance between two points (x1, y1) and (x2, y2) distance = ?( (x2-x1)^2 + (y2-y1)^2 ) plug in your given values

Math
-6x^2+15x-6 = -(x^2 - 15x + 6) = -(2x-1)(x + __ ) The reason you don't understand is that their second line is incorrect. Perhaps you typed it wrong This is what I would do: -6x^2+15x-6 = -3(2x^2 - 5x + 2) = -3(2x - 1)(x - 2)

Math
They would be 7, 14, 21, ... , 896 this is an AP, where a = 7, d = 7, term(n) = 896 a+(n-1)d = term(n) 7 + (n-1)(7) = 896 7 + 7n - 7 = 896 n = 128 , so there are 128 terms

Math
Translating what you said into English .... When 8 is divided by a certain number and the result is then divided by 6 the answer is less than 1/4 let the certain number be x (8÷x)÷6 < 1/4 8/(6x) < 1/4 6x/8 > 4 6x > 32 x > 32/6 x > 16/3 test: ...

math
Ignoring the grouting gap needed , we can fit 20 tiles along each side, so we need 20x20 or 400 tiles

Maths
let the original cost price be c each 1.2(2c) - 2c = 630 .4c = 630 c = 1575 check: cost price of two suits = 2(1575) = 3150 selling price = 1.2(3150) = 3780 profit = 630

Math
for #2, go with Steve's answer. I should have called it GCD instead of LCM

Math
After subtracting the \$20 from the \$140 we would know how much we paid for the pizza. How many slices do we have if each slice costs \$4 ? 2. This is like finding the LCM of 24, 64, and 56 At this level of arithmetic, you must have learned how to find that. e.g. 24 = 2*2*2*3 64...

Problems in three dimensions
The net of a regular tetrahedron consists of 4 equilateral triangles. Look at one of them: If the side is s, then the area = (1/2)(s)(s)sin60° = (1/2)(?3/2)s^2 = ?3/4 s^2 all 4 of them ----> 4(?3/4)s^2 = ?3 s^2 , as required

Math
a) just plug in -2 for x b) set 8-4x = 8 and solve for x c) http://www.wolframalpha.com/input/?i=plot+y%3D+8-4x d) set of real numbers for both e) and f), use the graph I gave you

Math
cscØ cosØ = -1 (1/sinØ)(cosØ) = -1 cotØ = -1 tanØ = -1, I know tan45° = +1 so Ø is in quadrants II or IV Ø = 180-45 = 135° or Ø = 360-45 = 315° so the additional information would have to be: in which ...

Math
Are the tickets put back into the draw after they were picked? Set it up like I showed you in your previous problem.

MAth
13 rocks: 8 red, 3 blue, 2 white expected value of Red = (8/13)(0) = 0 expected value of Blue = (3/13)(\$40) = 9.23 expected value of white = (2/13)(\$100) = 15.38 expected payout = \$24.61 Cost of game = \$20 Frank should play this game all day long, each time he is expected to ...

Trigonometry
You should have been told about the CAST rule, that is, an acronym telling you in which quadrants trig ratios are positive. Since sinC is positive and cosC is negative then C must be in quadrant II since sinØ = opposite/hyptenuse sinC = 7/25 --> y=7, r=25 x^2 + y^2= ...

Math
Your original post mentioned trapezoids and parallograms. None of your last 3 posts indicated which lines are parallel. I also suggested using letters, you did none of that. I still cannot visualize your figure.

Math
Describe the figure by using letters such as ABCD, naming them in a counter-clockwise order. More information is needed, such as AB || BC or angleC = 35°

Math
so the odds against the event = 59 : 41

Math
prob(event) = .41 prob(not event) = 1-.41 = .59 odds in favour of the event = .41 : .59 = 41 : 59

math
Let three of the adjacent sides by x, y, and z then the volume is xyz and xy=8 xz=18 yz=25 (xy)(xz)(yz) = 8(18)(25) x^2 y^2 z^2 = 3600 (xyz)^2 = 3600 xyz = 60

Math
Why not type in the regular way like you did here ? http://www.jiskha.com/display.cgi?id=1486616450 I can't read your post the way it was typed.

Math
expected to see an "=" sign in tn-tn-2(n-3)/(n-1) check your spelling and correct. Also use brackets, eg is it : tn = t(n-2)*(n-3)/(n-1) ??

High School Geometry
from 4/ an arc from B to D suggests that the arc passes through A If that is the case, BD is the diameter and your arc is a half-circle. (Any angle subtended by a diameter is 90° ) I am going to guess that half the square lies within the half-circle. If that is the case, ...

Math
Visualize slicing a nice round object such as an apple in the way you described. Try to sketch a 3-D diagram. Your slice will have a circular surface. Sketch a right-angled triangle with hypotenuse of 16 and height of 9 The third side will the the radius of you circular slice...

Math
I did part a) here http://www.jiskha.com/display.cgi?id=1487781971

Math
prob(a 2) = 1/6 prob(not a 2) = 5/6 assuming you want exactly 50 out the 240 to be a 2. prob(50 2's out of 240 throws) = C(240,50)(1/6)^50 (5/6)^190 (my calculator can do the two powers but not the C(240,50) )

No calculations needed. You are earning 12% p.a. vs paying 9% compounded monthly Take the loan e.g. Interest payable for the first month on the loan = 20000(.09/12) = 150 interest earned on fund in first month = 20000(.12)(1/12) = 200

math
From your sketch, join the end of the chord to the centre, drop a height from the centre to the chord. You have a right-angled triangle, with 2 sides known, base is 5, hypotenuse is 13. By Pythagoras, find the height Find the central angle using basic trig. find the ...

mathematics
This is an AS with a = 5, d = 3 and term(n) = 383 your formula for term(n) = a + (n-1)d 383 = 5 + (n-1)(3) solve for n

Math
let the base area of the tank be x cm^2 volume including balls = 15x volume without the balls = 6x volume of the 3 balls = 9x volume of each ball = 3x Unless we know the base dimension of the tank, that is as far as you can go. e.g. if the tank has a base of 40 by 50 and a ...

math
sum = 1/2 + (1/3+2/3) + (1/4+2/4+3/4) + (1/5+2/5+3/5+4/5) + ... (1/9+2/9+... +8/9) = 1/2 + 3/3 + 7/4 + 10/5 + ... 36/9 = 1/2 + 1 + 3/2 + 2 + ... + 4 looks like an arithmetic series with a = 1/2, d = 1/2, and n = 8 sum = (8/2)(2(1/2) + 7(1/2)) = 4( 1 + 7/2) = 4 + 14 = 18

Calculus
so you know: height = -16t^2 + 160t + 0 , zero, since we started at ground level This is a downwards opening parabola, so it has a maximum at its vertex. What method have you learned to find the vertex, there are several ways. simplest way in this case: find the x-intercepts, ...

Math
No equation to solve. you probably meant "evaluate" the expression. (2^8?5^?5?19^0)^?2?(5^-2/ 2^3)^4?2^28 = ( (2^8)(5^-5)(1) )^-2 * ( (5^-2)(2^-3) )^4 * 2^28 = 2^-16 * 5^10 * 5^-8 * 2^-12 * 2^28 = 2^0 * 5^2 = 25 check my arithmetic

math
secA = 12/5 then cosA = 5/12 = .41666... use your calculator, make sure you either have it set in degrees or radians, depending on what you want. let me know what you got.

Math
http://www.wolframalpha.com/input/?i=plot+y%3D-2x+,+-x%5E2

Math/Calculus
For this type of problem , the first thing you should do is to make sure that the given point actually lies on the curve, or else whatever we do would be just gibberish. I did this, and both points satisfy their matching equation. So, we take the derivative, plug in the point ...

Calculus
using: f(x)?f(xo)+f?(xo)(x?xo) <-- should be in your text 1° = 1° - 0° so let xo = 0, then x = 1 we have : f(x) = sinx f'(x) = cosx since we are using Calculus on trig, our x must be in radians 1° = ?/180 f(1°) = sin0 + cos(0)(?/180-0) = 0 + (1)(?/...

precalculus, complex numbers
can 't read it, don't use codes, they don't work here

Math Derivatives
product rule f'(x) = xcos(?/x)(-?/x^2) + sin(?/x) = (-?/x)cos(?/x) + sin((?/x) f''(x) = (-?/x)(-sin(?/x))(-?/x^2) - (?/x^2)(cos(?/x)) + cos(?/x)(-?/x^2) simplify if needed

Math - Related Rates
V = (4/3)? r^3 when V = 36? 36? = (4/3)? r^3 27 = r^3 r = 3 m dV/dt = 4? r^2 dr/dt 2 = 4? (9)dr/dt dr/dt = 2/(36?) m/min = appr .01768 m/min

Algebra I
I would do it this way: Amount of pure water needed --- x gal Amount of the 60% stuff ------ 6-x .6(6-x) + 0x= .5(6) 3.6 - .6x = 3 -.6x = -.6 x = 1 so use 5 gal of the 60% plus 1 gal of pure water your answer of 7.5 gal should have made no sense to you. You want to end up with...

Algebra
Don't use x as a multiplication sign, use * or use brackets, so I see your product as (a)(b)(a)(b) = (ab)^2 or = a^2 b^2 when you say ab^2, it is only the b that is squared.

Derivative-Optimization Problems
side parallel to river --- y m each of other two sides --- x 2x + y = 600 ---> y = 600-2x area = xy = x(600-2x) = -2x^2 + 600x d(area)/dx = -4x + 600 = 0 for a max of area -4x = -600 x = 150 then y = 600-2x = 300 largest area = 150(300) = 45000 m^2

Math
your equation: y = 80 + 10n your brother's equation: y = 275 - 15n b) when does 80+10n = 275-15n ? c) whatever you got for n in b) sub this into "your" equation

Algebra
.125 , .125r, .125r^2, .125r^3, .125r^4, .125r^5, 8 .125r/.125 = 8/.125r^5 r = 64/r^5 r^6 = 64 r = ± 2 set 1: .25, .5, 1, 2, 4 set 2: if r = -2 -.25, .5, -1, 2, -4

maths
make a sketch. draw poles AB and PQ with B and Q on the ground Draw the reflection of AB in the horizontal and call it BA'. Joint A' to P Label the intersection of A'P with BQ as M. let BM = x, then MQ = 20-x Of course the shortest distance between any two points ...

Math word problem
here is your problem: 1.50(x) + 4.00(y) = 712 1.50(x) + (y) = 712/4 you divided the 2 last terms by 4, but not the first one

Maths
Use the formula for the sum of terms (7/2)(2a + 6d) = (13/2)(2a + 12d) times 2, then expand 14a + 42d = 26a + 156d -12a = 114d a = -19/2 d sum(20) = 10(2a + 19d) = 20a + 190d = 20(-19/2 d) + 190d = 0

Algebra
I read your (f of g)(x) as f( g(x) ) By the "Just look at it" theorem, if g(x) = x+3 and f(x) = 1/x^3 then f(g(x)) = f(x+3) = 1/(x+3)^3 , which is h(x)

math
We don't do assignments for students. What part of this do you find difficult? Most are formula-based questions which you must have in your notes.

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