# Posts by Reiny

Total # Posts: 39,921

Math
In my diagram, then angle between their path is 55°, and at 3:00 the first ship has gone 56 mi and the second ship has gone 27 miles. Looks like a basic cosine law problem ... x^2= 56^2 + 27^2 - 2(56)(27)cos55° ..... x is not 62 miles, what did you get this time?

algebra
Everything you need for the formula is given. A = 1000 r = .035 t = 5 n = 4 A=P(1+r/n)^nt = 1000(1 + .035/4)^20 = .... you do the button-pushing

Math
Looks like mine was overkill

Math
Hope you accept the fact that the max of cosx + sinx is ?2 and its minimum is -?2 These occur at x = 45° and x = 225° (?/4 and 5?/4) see: http://www.wolframalpha.com/input/?i=y+%3D+sinx%2Bcosx we can write it as y = (cosx + sinx + sinx + 1)/(cosx + sinx) = 1 + (sinx + ...

Math
current area = 16(24) m^2 = 384 m^2 new plot is 16+2x by 24+2x new area = (16+2x)(24+2x) = 2(384) expand, simplify to a quadratic equation. Solve this quadratic using the method you learned. hint: it factors and has a nice integer solution

math
amount for X ---- 10x amount for Y ---- 7x amount for Z ---- 5x 7x - 5x = 140 carry on

Math
You are missing the main point, I did not say that 5 was the answer. First of all, you have to agree that 2^3 * 3^2 * 5^1 = 360 now match (a^m)(b^n)(c^r) with 2^3 * 3^2 * 5^1 clearly: a = 2 b = 3 c = 5 m = 3 n = 2 r = 1 then a+b+c-mnr = 2+3+5 - 3(2)(1) = 10 - 6 = 4

Math
go ahead, express 360 in that form. 360 = 2* 180 = 2*2*90 = 2*2*2*45 = 2*2*2*3*3*5 = 2^3 * 3^2 * 5^1 so , what do you think ?

Math- Just want to check
the LCM of 2,3, and 8 is 3*8 = 24 now we go higher until we reach a 3 digit number 24*2 = 48 24*4 = 96 24*5 = 120 ----- ahh, reached 3 digits check: is 120 divisible by your 3 choices ?

Math- Just want to check
I think I just said so.

Math- Just want to check
4(x + y) -2 = 2( 2(x+y) - 1) any integer multiplied by 2 is clearly even, so .....

Math
What is (8*30 + 9.5*31)/61 ??

Math
Does you answer really make sense to you ???

algebra
i = .08/4 = .02 n = 4(2) = 8 quarters amount = 500(1.02)^8 = .....

algebra
From your title, I will assume you meant 3^x = 15 take logs of both sides and use the rules of logs log (3^x) = log 15 x log3 = log 15 x = log15/log3 = .... (use your calculator)

algebra
This one is easy .... 5^x=125 5^x = 5^3 , so x = 3 fortunately 125 was a power of 5, unfortunately this will be the case rarely.

Math
let the number of ounces of raisins, peanuts, and chocolates be x , 2x, and 5x x+2x+5x = 112 continue

math
Clearly, the first two points lie in a horizontal line, so the distance between them is 8 Review how to find the distance between two points given the coordinates, then find the remaining two distances. Add up the 3 sides. Show your work so I can check it.

math
Did you get the other two ?

math
Make an attempt to translate the English into Math. I will do #2 for you, then you show me how you did the other two, and I will check it for you #2 "There were 18 more buttons in Bag B than in Bag A" ----> B = A+18 "There were 3 times as many buttons in Bag ...

math
let number of beads used by each be x after use: Natasha had 2356-x Lydia had 1176-x 2356-x = 3(1176-x) solve for x

Math
out of the 36 possible outcomes, the number of cases greater than 9 are: 4-6, 6-4, 5-5 , 6-5, 5-6, 6-6 prob(your event) = 6/36 = 1/6

Math
Clearly, the number must look like this: 6X,XX5 Also 3X + 11 = 23 continue ....

Math
18 = 2*9 25 = 5*5 35 = 5*7 LCM = 2*9*5*5*7 = 3150 but you want the largest 4 digit number so ... 3150*2 =6300 3150*3 = 9450 3150*4 = 12600 What do you think?

diploma applied physics1
or complete the parallelogram r^2 = 3^2 + 2^2 - 2(3)(2)cos135° = 13 - 12(-1/?2) r = appr 4.6 N or direction vector = (3,0) + (2cos45, 2sin45) = (3,0) + (1.414, 1.414) = (4.414 , 1.414) magnitude = ?(4.414^2 + 1.414^2) = appr 4.6

Maths
total juice = 5(1500) ml = 7500 ml number of glasses = 7500 ml/250 ml = ....

rational expressions and equations
original deck : x by 4x original area = 4x^2 new deck: length = 4x+6 new width = x+2 new area = (x+2)(4x+6) (x+2)(4x+6) - 4x^2 = 68 expand the left side, simplify and solve for x comes out very nicely

algebra
First of all, your question appears to contain a typo did you mean: (6x^2+35x + 24)/(x+5) ?? try this page: http://calc101.com/webMathematica/long-divide.jsp#topdoit

Algebra/calc simplfy
I will assume your derivative answer is correct, but not simplified Your teacher wants you to simplify it by using a common factor Notice 3x^5 is a common factor, so is (3x-2)^4, so .... 15x^6(3x-2)^4+6x^5(3x-2)^5 = 3x^5(3x-2)^4 [ 5x + 2(3x-2) ] = 3x^5 (3x-2)^4 (11x - 4) your ...

Math
I used a common factor of 9^89 suppose I had x^90 - x^89 wouldn't x^89 be the highest common factor and we have x^89(x - 1) so at the top I had: 9^90 - 9^89 9^89(9^1 - 1) = 9^89 (8) at the bottom the 3^2 is 9 , so (3^2)^89 = 9^89 , which canceled the 9^89 at the top , ...

Math
I will assume you meant: (9^90-9^89) / (3^2)^89 then = 9^89(9 - 1)/(9^89) = 8

Math
Main concept: when they pass each other , each will have travelled the same time distance covered by train A --- x distance covered by train B --- 337.5 - x time for A = x/55 time for B = (337.5-x)/35 x/55 = (337.5-x)/35 cross-multiply, solve for x, then find x/55

Math
inventory ---- x after day 1, inventory left = 3x/4 after day 2, inventory left = 3x/8 after day 3, inventory left = (5/6)(3x/8) = 5x/16 fraction of original is 5/16 check: suppose we had 240 items in the inventory day 1, sold (1/4) of 240 , leaving 180 day 2, sold 1/2 of 180...

Math
original total = 8(24000) = 192000 after new increase: (192000+x)/14 = 32000 192000+x = 448000 x = 256000 so average of newcomers = 256000/6 = 42,666.67

Math
If I interpret the question correctly, you are adding 16 new cards to a complete deck of 52. So the new deck now contains 8 Jacks prob(Jack) = 8/68 = 2/17 prob(not a Jack) = 1 - 2/17 = 15/17 "is divided up evenly in a 52 card deck" : poor wording

Math
number of \$1 tickets --- x number of 50 cent tickets ---- 2x number of 25 cent tickets ---- 2x+30 value equation: 100x + 50(2x) + 25(2x+30) = 3250 solve for x, sub back into my definitions

Math
number of adult tickets --- x number of children tickets ---- 700-x 5x + 3(700-x) = 2900 carry on ....

Algebra math
If you meant: if a number is subtracted from twice its reciprocal , then 2(1/x) - x = -23/5 times x 2 - x^2 = -23/5 times 5 10 - 5x^2 = -23x 5x^2 - 23x - 10 = 0 (x - 5)(5x + 2) = 0 x = 5 or x = -2/5 check: if x = 5, then 2/5 - 5 = -23/5 , checks! if x = -2/5), then 2(-5/2...

Math-college
all irrational and complex zeros come in conjugal pairs, so if i is a zero , so is -i if 3i is a zero , so is -3i so we have f(x) = a(x-i)(x+i)(x-3i)(x+3i) f(x) = a(x^2 + 1)(x^2 + 9) also f(-2) = 65 a(4+1)((4+9) = 65 65a = 65 a = 1 f(x) = (x^2 + 1)(x^2 + 9) or f(x) = x^4 + 10x...

Math
We want 80x+150/x ? 35x+600/x 45x ? 450/x times x , (since clearly x is positive, the inequality sign does not change) 45x^2 ? 450 x^2 ? 10 x ? ?10 or appr 3.162 thousand downloads, that is 3162 downloads

Math
man's age --- 3x non' age ---- x (note 3x : x = 3 : 1) so (3x + x)/2 = 28 4x = 56 x= 14 finish it up

Math
amount = 20 (2)^t plug in t = 10, then t = 11 or do it the long way: now -- 20 after 1 hour -- 40 after 2 hours -- 80 ....

Math
Triangle AOB is isosceles, with angle OAB = angle OBA which makes each of them 40°

Math
Your number should have at least one perfect square as a factor, or else there is no advantage in separating the radical into factors e.g. ?24 = ?4*?6 = 2?6 ?24 = ?2*?12 ----> not simplified ?24 = ?3*?8 = ?3*?4*?2 = 2*?3*?2 = 2?6 ----> long way to get my first answer ?72...

math
Bread - 3 Spreads - 5 Veggies - C(7,3)= 35 Multiply them

math
https://www.jiskha.com/display.cgi?id=1441287038

math
see first question in Related Questions below.

Maths
7056 = (2*2*2*2)*(3*3)*(7*7) = 16*9*49 so ?7056 = 4*3*7 = 84

math
in your sequence, a = 88, d = -3 so you want a + (n-1)d = -17 88 + (n-1)(-3) = -17 88 - 3n + 3 = -17 -3n = -108 n = 36 state your conclusion

Math
what method have you learned ? The last one is trivial. What two numbers have a sum of -10 and a product of 24 ? I would "guess" at -6 and -4 So x = -6 or x = -4 One foolproof method, but not necessarily the best, is decomposition. multiply the coefficients of the x^...

Math
18 = 2*3*3 25 = 5*5 35 = 5*7 LCM = 2*3*3*5*5*7 = 3150 how about 3150k < 9999 k < 3.1 so largest 4 digit with above properties is 3*3150 = 9450 test it with your calculator. 1008 = 2*2*2*2*3*3*7 = 16 * 9 * 7 the first two factors are perfect square, so to make the last ...

cont'd - Calculus 2
correction: for ln (1 + x) = x ? x^2/2 + x^3/3 - x^4/4 + x^5/5 ..... x is between -1 and +1 e.g. let x = .46 on my calculator: ln(1.46) = .378436... using the above formula: ln(1.46) = .46 - (.46)^2/2 + (.46)^3/3 - (.46)^4/4 .... = .37545... using 4 terms

Calculus 2
let's look at the last one: ln (1 + x) = x ? x^2/2 + x^3/3 - x^4/4 + x^5/5 ..... of course x ? -1 this should be in your text, in your class notes, or you can easily look it up For the other two, how about just looking at the general binomial expansion: 2/(1+x)^3 = 2(1+x...

Math
"How many miles does Ernie walk when he hikes on the trail" You just stated he walked 1/6 mile Did you mean, how many miles does Ernie walk per hour when he hikes on the trail? rate = distance / time = (1/6) / (1/12) = 2

Math
I didn't say that 24 was the only answer, there is no unique answer. It is the answer only if we let m = 1 and n = 5 Since, as Scott pointed out, you did not state a second equation 9m + 3n can only be expressed in terms of either m or n

Math
from 2m + n= 7 n = 7 - 2m now plug that into 9m+3n = 9n + 3(7-2m) = 9n +21 - 6m = 3m + 21 your way should have said: m = (7 - n)/2 then 9m + 3n = 9(7-n)/2 + 3n = (63 - 9n)/2 + 6n/2 = (63 - 3n)/2 checking: if we let n = 5, then from yours m = 1 and 9m + 3n = (63 - 15)/2 = 24...

Math
clearly, yes

Math
I interpret 5x and 9y =28 as 5x + 9y = 25 since x and y must be positive integers, 5x could only have values of 5, 10, 15, 20, 25 9y could only have values of 9, 18, 27 now what number from the first set added to a number of the second set yields a sum of 28 ?

Calculus
yes

Algebra
I will assume you mean: f(x) = (2-3x)/(5-2x) and you want to know the value of a so that f(a) = 36 so (2-3a)/(5-2a) = 36 2 - 3a = 180 - 72a 69a = 178 a = 178/69 check my answer on your calculator by evaluating f(178/69)

Calculus
Use implicit differentiation. e^y -y=x^2 -2 e^y (dy/dx) - dy/dx = 2x dy/dx( e^y - 1) = 2x dy/dx = 2x/(e^y -1) so for the point (2,0), dy/dx = 2(2) / (e^0 - 1) = 4/0 this tells me that at (2,0) the tangent slope is undefined, thus the tangent will be a vertical line The ...

Math
of 17 terms, the middle term is term 9 so a + 8d = 5 -----> a = 5-8d sum(17) = (17/2)(2a + 16d) = (17/2)(10-16d + 16d) = (17/2)(10) = 85

math
I will interpret this as: In the xy-plane, the center of a circle has coordinates ( 6,10) and the circle touches the y-axis at one point only. What is the radius of the circle. If you make a sketch of the circle that has a centre of (6,10) and touches the y-axis, you can see ...

math
In my diagram, I have PS as the longer of the parallel sides. From Q and R, draw perpendiculars to meet PS at M and N respectively. So I have two equal triangles and a rectangle. In triangle PQM, PM/6 = cosx ----> PM = 6cosx QM/6 = sinx -----> QM = 6sinx area = 2 ...

math
I think this is a binomial distribution question. prob(knows) = 12/26 = 6/13 prob(not know) = 7/13 prob(students knows at least 8 of 10) = prob(8of10) + prob(9of10) + prob(10of10) = C(10,8)(6/13)^8 (7/13)^2 + C(10,9) (6/13)^9 (7/13) + C(10,10) (6/10)^10 = (you do the button ...

math
3 negatives: -1/3, -1/4, - 789/25987 3 positives: 3/11, 3/5555, 187/500 test by finding the decimal equivalent for each one. Do they fall between -.5 and .375 ? (see, I can type "between" without any problems, why can't you?)

Math
prob(win) = .1 prob(not win) = .9 prob(at least 5 of 50) = 1 - (prob(none of 50) + prob(1 of 50) + prob(2 of 50) + prob(3of50) + prob(4of50) ) = 1 - (.9^50 + 50(.1) (.9)^49 + 1225(.1)^2 (.9)^48 + 19600(.1)^3 (.9)^47 + 230300(.1)^4 (.9)^46 ) = .5688 check my arithmetic, I did ...

math
re-arrange the first to say: y = 4x-6 Now sub that into the 2nd: 2x + 3(4x-6) = 5 solve for x, then sub into y = 4x-6 or write down the first: 4x - y = 6 double the second: 4x + 6y = 10 subtract them: -7y = -4 y = 4/7 sub back into the first you should of course get the same ...

math
e.g -5/7, -2/3, -12345/12355, etc a lot of them. What is the mathematical name for "a lot of them" ?

maths
re-type using mathematic symbols Make sure you use brackets if they matter e.g. 8ki^-1 ? (8ki)^-1

maths
We can divide by every rational number except ....

maths
area of rectangle ÷ one side = the other side, so .... (120/49) ÷ (10/7) = ....

Math
words spelled correctly by Elise --- x words spelled correctly by Chris --- x+5 solve for x: x + x+5 = 27

Math
I will do the first, then you show me how you did the second. x^2 + 7x = 4 x^2 + 7x - 4 = 0 a = 1, b = 7, c = -4 x = (-b ± ?(b^2 - 4ac) ) / (2a) = (-7 ± ?(49 - 4(1)(-4))/2 = (-7 ± ?65)/2

math
Zero is a real number.

math
prob(John wins) = 4/5 -----> prob(John loses) = 1/5 Since the events do not depend on each other, what do we do with the probabilities in Prob(Megan winds AND John loses) ??

Math
Use your definitions and formulas a + 2d = -12 a + 6d = 8 subtract the two equations, and find d once you have d, go back into the first equation to find a then find a + 9d

math
Let the number be x (x+1)(x-4) = 36 x^2 - 3x - 4 = 36 x^2 - 3x - 40 = 0 (x-8)(x+5) = 0 x = 8 or x = -5 check: if the number is 8 then is 9 times 4 = 36 ? yes If the number id -5, is -4 times -9 = 36 ?, yes the number could be 8 or it could be -5

Maths
yes -3?/4 radians = -135° -135° is in quadrant III by the CAST rule. -135° is in the same position as 225° or (180° + 45°) . the equivalent angle in standard position is 45° so tan (-135°) = tan (-3?/4) = 1

Calculus
I made a diagram showing a diagonal WE I placed P along an arc called a so that the central angle is 2Ø I joined PW and let PW = x Recall that the central angle subtended by an arc is twice the angle subtended at the circle, so angle PWE = Ø recall arc = r x ...

Math
let the number of 50 cent increases be n Now: number sold = 60 price per mug = 4 after increase: number sold = 60 - 6n selling price = 400 + 50n Profit = Revenue - cost = (60-6n)(400+50n) - 250(60-6n) = (60-6n)(400+50n - 250) = (60-6n)(150 + 50n) = - 300n^2 + 2100n + 9000 if ...

Math
correct see my answer to the same question a few minutes ago

Math
1st prize = 100,000 2nd prize = (.6)(10,000) = 6,000 3rd prize = (.6)^2 (10000) = 3600 ... 6th prize = (.6)^5 (10,000) = .....

Maths
You are correct so far, r = ?2 all you need is Ø, and you almost got it tanØ = -1 we know that tan ?/4 = +1, (tan 45° = 1) and we also know that 1 - i would form an angle in quadrant IV so Ø must be 2? - ?/4 = 7?/4 so 1 - i = ?2cos 7?/4 + ?2sin 7?/4 or...

Precal12
Thanks Steve, good catch.

Precal12
(n+1)C(n-1) = 28 (n+1)! / ((n+1-n+1)! (n-1)! ) = 28 (n+1)! / (2! (n-1)! ) = 28 (n+1)(n)(n-1)!/(2! (n-1)! ) = 28 n(n+1)/2 = 28 n^2 + n = 56 n^2 + n- 56 = 0 (n-8)(n+7) = 0 n = 8 or n = -7 , but n ? 0 n = 8 another way would be to realize that n+1 and n-1 have a difference of 2. ...

Math/Pre-calculus
Did not see Damon's answer, I had the page open all this time.

Math/Pre-calculus
I think you have a typo or a flaw in your equation. P(t) = P0 e^(k/t) makes no sense at t = 0 and since you are asking for the initial value P0, that would assume we need t = 0 in our calculation. That would make our result undefined. Fix your problem.

Math
the concept of odds is not quite the same as probability odds in favour of some event = prob(the event) : prob(not the event) prob(rain for 3 days) = .3^3 = 27/1000 = .027 prob(no rain on any of the 3 days) = 1-.027 = .973 or 973/1000 so odds in favour of no rain at all = 973/...

Math
I will assume you want the measure of the angles of triangle ADC Well, the angles of a triangle must add up to 180° Just noticed your given data makes no sense. Where does angle B enter the picture? You said "triangle ADC"

Math
40 = 1 x 40 = 2 x 20 = .....

Math
The LCF of 14 and 35 is .... ?

Math
What is the HCF of 18 and 27 ?? (lucky that falls between 1 and 10)

math
Present age: Dana ----- x Michael ---- x - 63 7 years ago: Dana ---- x-7 Michael --- x-63-7 = x-70 x-7 = 4(x-70) x-7 = 4x - 280 -3x = -273 x = 91 So Dana is now 91 and Michael is 28 check: 7 years ago , Dana was 84 and Michael was 21 Was Dana 4 times as old as Michael ?? , YES

math
NO You have to use the formula for "amount of an annuity" i = .02/4 = .005 n = 10(4) = 40 amount = 1000( 1.005^40 - 1)/.005 = \$44,158.85 What are you doing with, Total = 1220.79 40,000 + 1220.79 = 41,220.79 ?????

MATHS
x(1.05)^2.5 - x = 416.2 solve for x

Maths
2 years, 8 months = 1 + 8/12 = 5/3 years interest = 6300(1.07)^(5/3) - 6300

Math
for loan A, i = .12/12 = .01, n = 12 for loan B, i = .125, n = 1 rate for A = 1.01^12 - 1 = .1268.. rate for B = 1.125 - 1 = .125 so what do you think?