Wednesday
September 17, 2014

Posts by Reiny


Total # Posts: 27,114

math
given function: y = x+1 Two step process inverse function: (interchange x and y variables) 1. x = y+1 2. solve new equation for y y = x-1 so f^-1 (x) = x-1 Use the above two step method for finding any inverse if it exists.
April 23, 2014

Math Help? Check my answers.
#1 Aren't the terms decreasing by 8 ? So after 6 , you would have -2, -10, -18 #2 aren't the terms increasing by 3 each time ??? So how can you possibly get 14 as the next number after 12 ??? #3 I am puzzled by your choices you started with -1, 9, 19, 29, adding 10 ...
April 23, 2014

math
Draw a "side view" of the cut sphere. draw a line from centre of the circular cut to the centre of the sphere. You will have a right-angled triangle with base 10 (half the diameter of the circle) and a hypotenuse of 15. let the third side be h h^2 + 10^2 = 15^2 h...
April 23, 2014

Math
Your given example illustrates a case where there is a definite number of ways for things to happen, thus it is a theoretical probability situation, you had that one. But you said: You draw five cards from a standard deck of 52 cards. P(heart) = 4/5 (fraction) Did you mean ...
April 23, 2014

ALGEBRA
For any centre (a,b) and radius r, the equation of the circle is (x-a)^2 + (y-b)^2 = r^2 look at your second equation, (x+6)^2 + (y-4)^2 = 16 or 4^2 doesn't it fit that pattern perfectly ? for a centre of (-6,4) and radius of 4 Now you can sketch it. Do the same for the ...
April 23, 2014

math
think of money $.700 = 70 cents $.007 = .7 cents which would you rather have ? or .700 contains 7 tenths .007 contains zero tenths, none, nada, nichts, nil. ...
April 23, 2014

math
No, the area of similar shapes is proportional to the square of the corresponding sides So 2:1 ----> 2^2 : 1^2 = 4 : 1 The area would be 4 times as large, or quadrupled. Proof: area of original = 5*3 = 15 new sides are 10 and 6 new area = 10*6 = 60 and 60 = 4 times 15
April 23, 2014

triangle measurements
Are you sure that there was no angle given, or perhaps the area was given? With only 2 pieces of information, we can't go further.
April 22, 2014

triangle measurements
Trying very hard to visualize a triangle that has a "top length" and a "lower length". You appear to give the length of 2 sides, which is not enough information to find anything else.
April 22, 2014

angle measurements HELP ME PLZ QUICKLY!!!
Yes, it is right-angled triangle. I thought you had answered A) and used "a" as your answer. Since you don't use any capitals in your sentence, and use "no" instead of "know" etc, it was easy to mis-interpret your answer. Your statement : I ...
April 22, 2014

angle measurements HELP ME PLZ QUICKLY!!!
yes, you are wrong I don't know how much more of a hint I could have given you. 1. I ruled out your choice with a reason for doing so 2. I gave you a very blatant hint !
April 22, 2014

angle measurements HELP ME PLZ QUICKLY!!!
An acute angle is an angle less than 90° your triangle has a 90° angle, often called a "right angle" Do you wish to rethink your choice? Aghast at : I no what this triangle would look like thought u should no!
April 22, 2014

Math
monthly rate = .0575/12 = .004791666.. n = 12(12) = 180 P ( 1 - 1.00479166..^-180)/.00479166.. = 250000 I get P = $ 2076.03
April 22, 2014

math
using the formula x = (-2 ± √(4 - 4(3)(2) )/6 = (-2 ± √ -20)/6 = (-2 ± 2√5 i )/6 = (-1 ± √5 i )/3
April 22, 2014

bearings
for intersection , use substitution in the 2nd equation 2x + 3y - 21 = 0 2x + 3(4x-7) = 21 2x + 12x - 21 = 21 14x = 42 x = 3 y = 4(3) -7 = 5 so we have the line going through (3,5) and (-2,8) slope of line = (8-5)/(-2-3) = -3/5 using (3,5) y-5 = (-3/5)(x-3) times 5 5y - 25 = -...
April 22, 2014

Pre-Cal
what about it? here is a picture of it http://www.wolframalpha.com/input/?i=y%3D%281%2F2%29cos%284%28t-6%29%29%2B6
April 22, 2014

math
Wow, 17% interest from a savings account ? anyway .... P( 1 - 1.17^-20)/.17 = 250000 .. P = $57, 309.99 this might seem unreasonably high, but remember the interest rate is unreasonable, As a matter of fact his fund will earn .17(250,000) or $42,500 in interest the first year...
April 22, 2014

Math
This time you want future amount i = .065/52 = .00125 P( 1.00125^312 - 1)/.00125 = 15000 ... P = 39.34 weekly payment is $39.34
April 22, 2014

Math
see same question in first of "Related Questions" below
April 22, 2014

Math
Car payments are usually calculated using compound interest. monthly rate = .07/12 = .005833333.. let the payment be P P( 1 - 1.0058333^-60)/.0058333 = 14000 P = 14000/50.50199.. = $277.22
April 22, 2014

Math
P(1.02)^20 = 5500 P = 5500/1.02^20 = 3701.34
April 22, 2014

math
if he knows the side to be x f(x) = x^2
April 22, 2014

Math
d(t) = 250 - 100t when t = 0 , d(0) = 250 ---> (0 , 250) when d(t) = 0 250 - 100t = 0 -100t = -250 t = 2.5 ----------------> (2.5 , 0) the d(t) intercept is 250 (just like the y-intercept of y = mx + b) the t intercept is 2.5 meaning: at the beginning the plane was 250 ...
April 22, 2014

Algebra 2
looks like y = (1/3)x , so you might call 1/3 as the constant of variation.
April 22, 2014

Calculus
After t hours, ship A has traveled 20 t km ship B has traveled 25t I sketched a right-angled triangle with legs 120-25t and 20t let D be the distance between them , making D the hypotenuse D^2 = ((120- 25t)^2 + (20t)^2 at 8:30 , t = .5 D^2 = 11656.25 D = 107.964.. 2D dD/dt = 2...
April 22, 2014

Algebra1
given: a = 3 term(33) = a+32d = -253 32d = -256 d = -8 sum(33) = (33/2)(first + last) = (33/2)(3 -253) = -4125
April 22, 2014

maths
still can't read what you are typing.
April 22, 2014

calculus
x ' (t) = 9t^2 - 81t + 162 so objects are "speeding up" when x ' (t) > 0 and slowing down when x ' (t) < 0 Consider the zeros of the expression 9t^2 - 81t + 162 = 0 t^2 - 9t + 18 = 0 (t-3)(t-6) = 0 t = 3 or t = 6 so the t of the vertex would be half...
April 22, 2014

maths
check your typing, I can't make out what you are saying.
April 22, 2014

Math
Did you want Maximum profit ? find the vertex of your parabola the x of the vertex is -b/(2a) = -1.4/(2(-.02)) = 35 days p(35) = 1.4(35) - .02(35)^2 - 20 = 4.5 whatever units
April 22, 2014

math (SIMPLE INTEREST)
repeat steps I showed you in your previous post (5 and 1/4 years = 5.25 years , or use 21/4 years )
April 22, 2014

math (SIMPLE INTEREST)
I = PRT = 20000(.11)(4.5) = 9900 so amount = 20000+9900 = .... (4 years, and 6 months = 4.6 years)
April 22, 2014

algebra
let's take the first 3 points and find the equation of the plane containing them direction vector #1: (-3,2,2) direction vector #2: (1,2,1) normal to these , take the cross-product = (-2, 5, -8) or (2, -5, 8) in the opposite direction equation of plane is 2x - 5y + 8z = c ...
April 22, 2014

math
Their normals are (1,4,-1) and (5,-3,-7) respectively clearly they are not parallel, or one of the normals would be a multiple of the other nor are they coincident let's look at their dot product: (1,4,-1) . (5,-3,-7) = 5 - 12 + 7 = 0 So they are perpendicular or orthogonal.
April 22, 2014

Physics waves- check answer please
in air , v = 331.4m/s + 0.606m/s/degree celsius times T = 331.4 + .606(30) = 349.58 m/s time to travel 1.2 km = 1200/349058 = 3.4327 seconds in water: time = 1200/1498 = .801 seconds time difference = 3.4327 - .801 or 2.63 seconds for yours, ok, so far, but you have not yet ...
April 22, 2014

math
Something is sightly off mathematically 7/10 + 1/5 + 1/6 > 1 some must have arrived by more than one method. (insufficient data or bogus question)
April 22, 2014

math
more by car than foot = 7/10 - 1/6 = "How many fewer came by foot? " = 1 - 7/10 - 1/5 = assuming they came by one of those 3 ways.
April 22, 2014

probability
at most 5 dots --> 2 , 3, 4, 5 dots 11, 12, 21, 22, 23, 32 ---> 6 ways showing odd number of dots: 3, 5, 7 , 9 , 11 {12, 21, 23, 32, 43, 34 , 54, 45 , 65 , 56} so we want {at most 5 dots} AND {showing odd sum} = {12, 21, 23, 32} or 4 ways prob(stated event) = 4/36 = 1/9
April 21, 2014

math
solve: 5000(1.07)^n = 10000 1.07^n = 2 log both sides log 1.07^n = log 2 n log1.07 = log2 n = log2/log1.07 = appr 10.24 It will take appr 10 years
April 21, 2014

Math (Number Theory)
... = (1+n)+(1+n)+(1+n)+... for a total of n/2 such binomials = (n/2)(n+1 or n(n+1)/2 or (1/2)(n)(n+1) or (n^2 + n)/2
April 21, 2014

Math
That's better. multiply each term by 12 , the LCD 6x - 4 = 3x 3x = 4 x = 4/3 you are correct.
April 21, 2014

math
Proof of my answer: now ----- 3250 end of 1st year: 3250(1.06) = 3445 end of 2nd year: 3445(1.06) = 3651.70 end of 3rd year: 3641.70(1.06) = 3870.80 >> as I had before suppose they did 3250(1.06)3.5 = 3985.23 which is one of the choices, BUT contradicts the concept of &...
April 21, 2014

math
Trick question? Since the compounding is annually, the amount at 3.5 years is the same as it was after 3 years amount = 3250(1.06)^3 = 3870.80
April 21, 2014

Math
you have a geometric series, where a = 6 , r = -4 I suspect you have a typo. S(1) to me means the sum of 1 term that would simply be 6
April 21, 2014

calc
y^3 = 16x^2 when x = 4 y^3 = 16(256) y = 16 3y^2 dy/dt = 32x dx/dt sub in our values 3(256) (-1) = 32(4) dx/dt dx/dt = -768/128 = -6
April 21, 2014

Math
You have no right side of an equation. There was no equation to solve. Retype your question please
April 21, 2014

Math
Write fractions this way: x/2 - 1/3 - x/4 LCD = 12 6x/12 - 4/12 - 3x/12 = (3x - 4)/12 Your answer makes no sense. (It doesn't even have an x term)
April 21, 2014

Math
2 = 1( 1.0275)^n log 2 = n log 1.0275 n = log2/log1.0275 = ....
April 21, 2014

Math question
Did you notice that each term is half of the previous one? Which type of sequence matches that property?
April 21, 2014

Inverse Trig
for both cases, since for any -π/2 < y < 0 the sine will be negative, we only have to concern ourself with angles in the first quadrant. so if y = arcsin (√3/2) then y = π/3 ( I know sin 60° = sin π/3 = √3/2 ) and for the second one y = &#...
April 21, 2014

Inverse Trig
look at the sine curve, it is zero, or crosses the horizontal axis at 0 , ±π , ±2π .. or in general kπ , where k is an integer.
April 21, 2014

Inverse Trig
since sin(?) and arcsin(? are inverses of each other, arcsin( sin (6π) ) = 6π , but that is beyond your stated boundary. so arcsin(sin 6π) = arcsin 0 = 0 , π , 2π
April 21, 2014

Math
Each hour is equal to 30° or π/6 radians So to go from 3:00 to 5:00 would take 2π/6 or π/3 the arclength = rØ = 6(π/3) or 2π inches = appr 6.28 inches or circumference = 2π(6) = 12π the time from 3:00 to 5:00 represents 1/6 of a ...
April 21, 2014

Math
add them: 17x = 16 x = 16/17 back in 1 9(16/17) + 2y = 8 2y = 8 - 144/17 y = -4/17 they intersect at the point (16/17 , -4/17)
April 21, 2014

algebra
centre would be the midpoint of the the two given points, which would be C(-3,3) so the equation is (x+3)^2 + (y-3)^2 = r^2 plug in one of the points given to find r^2
April 21, 2014

GRAPHING HELP
x = − 1/3^2+4 is a vertical line , (I don't see a y value) must be a typo
April 21, 2014

alg.
for y = ax^2 + bx + c the x of the vertex is given by -b/(2a) once you have that x, sub it back into the original equation to find the corresponding y of the vertex.
April 21, 2014

math
look below at the first of "Related Questions", Steve gave an answer to the same question.
April 21, 2014

trigonometry
3 sinØ = 1.5 , 0 ≤ Ø ≤ 4 sinØ = 1.5/3 = .5 the sine is positive in I or II Ø = π/6 or Ø = π - π/6 which is 5π/6 the period of sinØ is 2π, so adding another 2π to π/6 yields 13π/6 , ...
April 21, 2014

math
If you are first of all looking for the integral of v=25sin50πt it should be -1/(2π) cos(50πt) + c the rest is physics, about which I know very little . from there the mean is usually found by ... 1/(10-0) ( -1/(2π) cos (500π - (-1/2π cos(0) ) = 1...
April 21, 2014

math
If it is right-angled, then x^2 + x^2 = (x^2)^2 x^4 - 2x^2 = 0 x^2(x^2 - 2) = 0 x = 0 , which is no good or x^2 = 2 x = √2 then the area = (1/2)(x)(x) = 1/2 (√2)^2 = (1/2)(2) = 1 square unit
April 20, 2014

math
7% per month ???? in the middle ages , they would burn folks on the stake for rates like that. It was called usury. anyway .... interest on balance = .07(1734.50) = $121.42 actual repayment from loan = 165-121.42 = $43.59 Balance next month = 1734.50 - 43.59 = $ 1690.92
April 20, 2014

math
prob(red, then blue) = (4/10(5/9) = 20/90 = 2/9 you do the rest
April 20, 2014

math
actually it is much bigger than that 1st place --- 10 different runners 2nd place ---9 3rd place ---8 ... last place --- 1 runner number of ways = 10*9*8*7*...*2*1 = 3,628,800 What your 10*9*8 is is the ways 1st, 2nd and third place could happen
April 20, 2014

Math
you have an arithmetic series: 4 + 6 + 8 + ... Easy to see that after 3 days, you will have already spent 18 hours, so you need one extra day of only 2 more hours to have a total of 20 hrs.
April 20, 2014

math
and g(x) is .... ??
April 20, 2014

math
current number of rooms = 30 current price per room = 12 let the number of additional increases of $1 be n numbers of rooms rented = 30 - 2n number of rooms not rented = 30 - (30-2n) = 2n price per room = 12 + n Profit = (12+n)(30-2n) - 4(30-n) - 1(2n) = 360 + 6n -2n^2 - 120...
April 20, 2014

Trig Maths
or from Steve's 5√3 sinθ = 21 cosθ sinØ/cosØ = 21/5√3 tanØ = 21/5√3 , and the tangent is + in I and III Ø = 1.18 in I or Ø = π + 1.18 = 4.32 in III
April 20, 2014

Math
number of 50's ---- x number of 10's ---- 2x number of 5's ----- 2(2x) = 4x Now, consider the value of those notes to form your equation. 50x + 10(2x) + 5(4x) = 1080 50x + 20x + 20x = 1080 90x = 1080 x = 12 we defined 10's as 2x so she has 2(12) or 24 $10 bills...
April 20, 2014

math
x + x(.08)(3) = 15000 1.24x = 15000 x = 12096.77
April 20, 2014

math
8. amount invested at 12% -- x amount invested at 8% --- 3000-x .12x + .08(3000-x) = 3200 times 100 12x + 8(3000-x) = 320000 4x = 29600 x = ??? (more than she invested!!!!) I think you have a typo, should the interest be RM 320 ?? That way it works out nicely, change the 3200 ...
April 20, 2014

Math
|3x+1|-|2-x|<3 Formal Way: Case 1 |3x+1| < 3 + |2-x| 3x+1 < 3 + |2-x| AND -3x-1 < 3 + |2-x| |2-x| > 3x-2 AND |2-x| > -3x-4 which leads to a) 2-x > 3x-2 OR -2+x > 3x-2 -4x > -4 OR -2x > 0 x < 1 OR x < 0 ----> x < 1 b) 2-x > -3x - 4 ...
April 20, 2014

maths
3x = 6y looks trivial, just divide by 6 y = (3/6)x + 0 y = (1/2)x + 0 for equations that contain all 3 terms, there is a two-step process 1. move all terms except the y term to the right side of the equal sign ----> 2y = 6x - 2 2. divide each term by the coefficient of the ...
April 19, 2014

math
a = 3 , d = 6 term(n) = a + (n-1)d 123 = 3 + (n-1)(6) 120 = 6n - 6 126 = 6n n = 126/6 = 21 there are 21 terms
April 19, 2014

naths
midpoint is (4,5) y - 5 = 2(x-4) arrange it any way you have to
April 19, 2014

Math
log2+ 3log1 = log 2 + 3(0) = log2 you SHOULD know that log 1 = 0
April 19, 2014

maths
from the 2nd: y = 5-x plug into the 1st: 2(5-x) - 5x = 3 I am sure you can finish that
April 19, 2014

geometry
ratio of corresponding sides = 7 : 5 since perimeter is a linear measurement, the ratio of perimeter is also 7 : 5 ratio of volumes = 6^3 : 5^3 = 343 : 125
April 19, 2014

Math
p% = p/100 so (p/100) ( ? ) =12 since we only want the 12 to remain on the left side my ( ? ) must be 100(12)/p or 1200/p check: (p/100) * (1200/p) = 12
April 19, 2014

Math
A - Give yourself an example and see which way is correct e.g. start with 5/8 now add 1 to both top and botto ---> 6/9 Is the value the same ???? B. Again, test with an example C. start with 5 , 5^2 = 25 mmmhh? how about 1/3 , what is (1/3)^2 or 1/9 compared with 1/3 Hint: ...
April 19, 2014

geometry
You are obviously looking at some circle diagram that I can't see. In BE , which is the centre, B or E ? Where does DC come from? Where does BD come from ? All I know so far is that AC is a chord.
April 19, 2014

calculus help
ignore the very last "the acceleration is 9.33" pressed "post answer" too soon so the acceleration is a = 13.59 ft/s^2 and v = 13.59t + 32.2667 a = 13.59 ft/s^2
April 19, 2014

calculus help
If the acceleration is a then v = at + c , where c is a constant: when t=0 , v = 22 mi/h = 32.2666.. ft/s 32.266.. = a(0) + c c = 32.2666.. when t = 3s , v = 50 mi/h = 73.333.. ft/s 73.333.. = a(3) + 32.26666... 3a = 41.06666.. a = 13.58888.. the acceleration is 13.89 ft/s^2 ...
April 19, 2014

elem algebra
let speed of boat in still water be x mph 17/(x-10) + 17/(x+10) = 10 time (x-10)(x+10) 17(x+10) + 17(x-10) = 10(x^2 - 100) 34x = 10x^2-1000 10x^2 -34x - 1000 = 0 x = 11.84 or some negative speed x = 11.84
April 19, 2014

maths
number of lunchers ---- x number of non-lunchers --- 30-x 5x + 3(30-x) = 110 5x + 90 - 3x = 110 2x = 20 x = 10 10 took their own lunch, 20 bought their lunch check: 10(5) + 20(3) = 110
April 19, 2014

Math
Steve gave a good example to Taylor here for the same question: http://www.jiskha.com/display.cgi?id=1360645422
April 19, 2014

math
Your mean is correct to get a mean of 72, let the extra score be x and he now has 10 scores to average (633 + x)/10 = 72 633 + x = 720 x = 720-633 = 87 he needs an 87 or, think of it this way. to have an average of 72 on 10 tests, he needs a total score of 720 so far he has ...
April 19, 2014

maths
The question makes no sense to me. Are you saying that the angle has the same numerical value as the side BC ? Interesting mix of linear measurement and angle measurement. Are you using degrees or radians ? so you could use any 0 < x < 180 e.g. if x = 20 then angle ABC...
April 19, 2014

Calculus Help Please Urgent!!!
I stand by mine and Damon's answer for a minimum area. I even ran a simple 1980's style "BASIC" program to show it 10 a = 5000 20 for x = 0 to 14 step 1.000000E-05 30 y = (14-4*x)/3 40 na = x*x+sqr(3)/4*y*y 50 if na < a then a = na : side = x 60 next x 70 ...
April 18, 2014

Calculus Help Please Urgent!!!
I also got 6.09 (actually 6.0895..) I defined the side of the triangle slightly different from Damon to avoid as many fractions as I could. let each side of the square be x m let each side of the equilateral triangle be 2y m that way I can say that the height of the triangle ...
April 18, 2014

Algebra
Sandra, the placing of brackets is crucial here The way you placed them makes them insignificant, it is the same thing as 3/2a + 5/2a According to the rules of operations, this is the same as (3/2)a + (5/2)a = (8/2)a = 4a so you must have meant: 3/(2a) + 5/(2a) , the way both ...
April 18, 2014

Math
multiply each term by z z^2 + 1 = 2z z^2 - 2z + 1 = 0 (z-1)^2 = 0 z-1 = 0 z = 1 you had that, good job
April 18, 2014

math
Make a sketch of your triangle in quadrant II to see that x = -3, r = 4 and from Pythagoras that y = √7 in II so sinØ = √7/4 sin 2Ø = 2sinØcosØ = 2((√7/4)(-3/4) = -3√7/8
April 18, 2014

MATH
Each side of the base will be (24-2x) v(x) = x(24-x)^2 Wolfram's magic done here: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%2824-x%29%5E2
April 18, 2014

calculus
your equation came out looking rather jibberish on my computer, but I see it contans x's and y's I can give you the general method of doing this question .... Find the derivative with respect to t, then your result should contain dx/dt and dy/dt , as well as x and y ...
April 18, 2014

Math
from the 2nd: x = 5y+7 plut into the first: x + 2y = -7 5y+7 + 2y = -7 7y = -14 y = -2 back in x = 5y+7 = 5(-2)+7 = -3 x = -3 , y = -2
April 17, 2014

Math
I understand bi-monthly to mean every other month, or 6 times a year. The main problem here is that the payment period does not coincide with the interest period, so my normal formula does not work so we will convert the 6% compounded bi-monthly to one of i compounded semi-...
April 17, 2014

precal
|y-8.0|<=1.5 y-8 ≤ 1.5 and -y+8 ≤ 1.5 y ≤ 9.5 and -y ≤ -6.5 y ≤ 9.5 and y ≥ 6.5 which can be written as 6.5 ≤ y ≤ 9.5 (or in words, y is between 6.5 and 9.5 inclusive
April 17, 2014

Math
each individual question has a prob of 1/2 of being correct so you want (1/2)(1/2) .... (1/2) --- (8 times) = (1/2)^8 = 1/256
April 17, 2014

Math
red from 1st ---> 8/18 = 4/9 red from 2nd ---> 10/13 prob(2res) = (4/9)(10/13) = 40/117
April 17, 2014

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