Saturday
April 19, 2014

Posts by Reiny


Total # Posts: 26,017

math
Yup, found it. Rats! Hope Frank finds it.

math
3a+3(b+1)=c 3(b+1) = c - 3a b+1 = (c-3a)/3 or c/3 - 3

Math grade 9
not sure about grade 9, but I just checked an old grade 10 text from Ontario, and I used to teach it in 10 The proof followed your method using a general case.

Math grade 9
If (a,b) is a point not on the line Ax + By + C = 0 then the shortest distance from the point to the line is |aA + bB + C|/√(A^2+b^2) shortest distance = |5(1) + 6(1) -3|/√(1^2+1^2) = 8/√2 which rationalizes to 4√2

Math
Wouln't it automatically be a right-angled triangle if the x-axis and the y-axis form sides? So let's find the equation of the hypptenuse. m = -3, point is (1,3) y = -3x + b 3 = -3(1) + b b = 6 y = -3x + 6 base of triangle = x-intercept = 2 height of triangle = y-inter...

Math
did you sketch it? did you get something like http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%7C%2B1+%2C+y+%3D+5 notice that they intersect at (4,5) and (-4,5) ? and the altitude is 4, and the base is 8 Area = (1/2)(8)(4) = 16

Advanced Functions/ Precalculus Log
remember if the base of the log is 10, we don't have to write the base. so you have y= logx and y = 2log(x-4)+3 intersection: 2log(x-4) + 3 = logx log(x-4)^2 - logx = -3 log ( (x-4)^2 /x ) = -3 (x-4)^2 /x = 10^-3 x^2 - 8x + 16 = (1/1000)x 1000x^2 - 8001x + 16000=0 using t...

Math. Urgent please help
draw the altitude from A to form a right-angled triangle. Cos C = 4/16 = 1/4 In triangle BCD, by the cosine law ... BD^2 =8^2 + 8^2 - 2(8)(8)cosC = 64 +64 - 128(1/4) = 160 BD = √160 = 4√10 Where does the centroid G enter the picture?

Last two CALC questions. :)
8. f'(x) = -5cos(7-5x) f'(π) = -5cos(7-5π) = 3.769 or your last choice of 3.770

Calc help - check rest of answers, please?
I did #4 and #5 for you in your previous post #6 let the width of the base be x let the length of the base be 2x let the height be y given: Volume = 10 2x^2y = 10 y = 5/x^2 which was the last choice. cost = 10(2x^2) + 6( 2 ends + front + back) = 20x^2 + 6(2xy + 2xy + 2xy) = 20...

CALCULUS - Check my answers :)
#5 At a time of t seconds after the boy passed under the balloon, distance covered by boy = 15t height of balloon = 5 + 5t let the distance between them be d ft d^2 = (5t+5)^2 + (15t)^2 2d dd/dt = 2(5t+5)(5) + 2(15t)(15) dd/dt =( 5(5t+5) + 15(15t) )/d when t = 3, d^2 = 20^2 + ...

CALCULUS - Check my answers :)
#4, the way you typed it, ... y' = 2x/3 when x = 8, y' = 16/3, which is not found in any of your choices as the slope if you meant , f(x) = x^(2/3) then y' = (2/3)x^(-1/3) = (2/3)(1/x^(1/3)) when x = 8 y' = (2/3)(1/2) = 1/3 the only one that has a slope of 1/2 ...

math
yes, but be more confident in your choice

math
Treat these as if they were equations but keeping the in-equality sign instead of the equal sign, EXCEPT when you multiply or divide the in-equation by a negative, you must reverse the inequality sign. e.g. last one: -8x > -64 I would have to divide by -8 to get +x , so x &...

math
No, you did not follow the instructions, it says ... take the square root of each number , THEN add them up, so √a + √36 + √ 16 + √9 = 15 √a + 6 + 4 + 3 = 15 √a = 2 a = 4

math
How about you giving this one a try ? Just follow the steps they told you to take, let me know what you get, and how you got it.

math
Then 8^z + 10^z + 11^z = 3 by the "just look at it" theorem, z = 0 since (anything)^0 = 1

math
so just follow the instructions, ((1)(2)(3)z)^2 = 144 (6z)^2 = 144 36z^2 = 144 z^2 = 4 z = 2 Actually the wording of the question is flawed. Terms are separated by addition and subraction, there is only one term here. The correct wording should be : If #(w,x,y,z)means you squa...

math
If the scale factor is 3, then A(2,0) ----> A' (6,0) B(3,-1) ---> B' (9,-3) C(-2,-5) --> C' (-6,-15) Can't get any simpler than that. Might be a good idea to graph the original triangle and the new triangle. What do you notice ?

geometry
I sketched your triangle and concluded that the right angle must be at N It is easy to show that triangle MPN ≈ triangle NPO then MP/PN = PN/PO 15/9 = 9/PO 15PO = 81 PO = 81/15 = 27/5

Coordinates in 3-D, Polar Coordinates, Precalculus
Have some fun here, changing the values of a and b I used a=4 and b=3 http://www.wolframalpha.com/input/?i=plot+r+%3D4cos%28Ø%2B3%29+%2C-6.28+%3C+Ø+%3C+6.28 Notice I also placed a domain on Ø from -2π to +2π things really get interesting if you p...

math
number of correct answers --- x number of incorrect answers --- 150-x 2x - .5(150-x) = 270 2x - 75 + .5x = 270 2.5x = 345 x = 138 He/she should answer at least 138 questions correctly to have score of at least 270 check: 138(2) - 12(.5) = 270

math
let the payment be P P (1.035^16 - 1)/.035 = 100000 solve for P on your calculator you should get around ($4770 , not the exact answer so you will still have to do the calculation yourself)

Vectors
The plane must pass through the midpoint of the given points which is (3,10,6) A direction vector through the 2 points is [2, 4, 6] or reduced to [1,2,3] This must be a normal to the plane, thus the equation of the plane would be x + 2y + 3z = c but (3,10,6) must lie on it, so...

college algebra
multiply 2nd by 8 8x - 288y = -2640 subtract that from the first 297y = 2673 y = 9 sub into 1st 8x + 81 = 33 8x = -48 x = -6

Math
let the first odd whole number be n-8 then the others are n-6, n-4 , n-2 , n , n+2, n+4, n+6, and n+8 their sum = 9n (now wasn't that a clever way to define my numbers?) 9n = 243 n = 27 first = 27-8 last = 27 + 8 and that sum = 27+27 = 54

Math
I will assume a typo, and "treaters" is "greater" let the unit digit of the number be x let the tens digit of the number by y so the number is 10y+x and the product of the digits is xy when is xy > 10y+x xy - 10y > x y(x-10) > x y > x/(x-10) but...

math
Are you counting 1 as a factor ? 12 has a lot of factors, let's look at it 12 has factors 1,2,3,4, 6, and 12 , six of them none other comes close. I would say 12 if we exclude 1 as a factor.

Math
then log2 ((3x-1)/x) = -2 2^-2 = (3x-1)/x 1/4 = (3x-1)/x 12x - 4 = x 11x = 4 x = 4/11

MATH-MS.SUE PLEASE HELP
Maria sells 3 cookies per day Stephen sells 6 cookies per day Aisha sells7 cookies per day together they sell 16 cookies per day number of cookies needed to make $320 = 320/2 = 160 number of days needed to sell 160 cookies at a rate of 16 cookies per day = 160/16 = 10 days

Math
Did you observe how the numbers change ? +1 , -2 , +4 , -8 , +16 , ...... Can you see the pattern? Can you state the next number in your sequence ? let me know what you get.

math
I think we must assume the race track is a circle. Let's work in feet, there are 5280 feet in a mile, since it takes 3 laps to make a mile each lap is 5280/3 or 1760 ft for one lap. So the circumference of the race track is 1760 feet.

AP CALC
Did you notice that your given point does not lie on your curve ? Is there a typo? Usually for this type of question, the given point lies on the given curve. If that is what you intended , please confirm this before I attempt what will be a very nasty question

Math
Let the points scored by Alan, Gil and Deb be 2x, 3x, and 4x , .......... (notice that is in the ratio of 2:3:4 ) so 4x = 114400 x = 28600 then 2x = 57200 and 3x = 85800 Alan scored 57200 Gil scored 85800 Deb scored 114400 Add them up to get the total score.

Math
1st one, in your head, a = 4 or a = -2 2. |2a+5| > 3 2a+5 > 3 OR -2a -5> 3 a > -2 OR a < -4 3. looks like a typo , I see neither an equation nor an in-equation. If it is one of those, first divide both sides by 3, then it is very easy.

Math
Nina, why do you keep reposting this question. I see from the Related Questions below, that it was successfully answered for you by Ms Sue.

Quick math help
Wow, I must say, if you cannot do those questions, then you are certainly not ready for your math exam 1. if the y-intercept is 0, doesn't that mean the line goes through the origin or (0,0) ???? so in y = mx + b form ... y = (-1/5)x multiply by 5 5y = -x standard form has...

Vectors
Your question doesn't make a lot of sense to me. "Determine a value of k that is 10 units away from the plane ..." ?? How can a number be 10 units away from a plane? A point can be, or a line could be if that line would be parallel to the plane. Let's check i...

math- can you please check my work
Since it asked for the height of the balloon , should you not have added the original 60 feet to each of your answers ? e.g. after 2 seconds = 60 feet + 30 new feet = 90 ft so I would give my equation as height = 60 + 15t Your answers describe the height of the balloon after i...

GEOMETRY TANGENTS
done, look at your previous post of this

math
mmmmmhh, how about 25 ?

GEOMETRY TANGENTS
Who knows ? You don't mention x in your description. You don't mention where B, D, and F are located, but I must have labeled mine the same way as Steve, since I got his answers as well. What still has to be found is AD In triangle ACE 9^2 = 16^2 + 15^2 - 2(15)(16)cosC...

Math
g(x) = f(x) + 6 = x^2+5 + 6 = x^2 + 11

Please help trig proof
LS = (cotx + cscx)/(sinx + tanx) = (cosx/sinx + 1/sinx)/(sinx + sinx/cosx) = ( (cox + 1)/sinx) / ( (sinxcosx + sinx)/cosx) = (cosx + 1)/sinx * cox/(sinx(cosx + 1) = cotx (cosx + 1)/(sinx(cosx + 1) ) = cotx (1/sinx) = cotx cscx = RS

Trignometry
LS = (1-cosx)/(1+cosx) = (1-cosx)/(1+cosx) * (1-cosx)/(1-cosx) = (1-cosx)^2 /(1 - cos^2 x) = (1-cosx)^2 /sin^2 x = ( (1-cosx)/sinx )^2 = (1/sinx - cosx/sinx)^2 = (cscx - cotx)^2 = RS

Calculus
What I can do is to lead you to some pages that explain the difference in dy and ∆y I thought this youtube did a good job http://www.youtube.com/watch?v=xoAnLgs6hiM There are also numerous other youtube links listed in the right column btw, I agree with your answers.

Vectors
Aren't we just finding the distance from the point (4,-2,k) to the plane 10x - 7y + z - 28 = 0 ? and we know that distance is 10 |10(4) - 7(-2) + 1(k) - 28|/√(100 + 49 + 1) = 10 |k + 26| = 10√150 = 50√6 k + 26 = 50√6 OR -k-26 = 50√6 k = 50W...

Calculus
Didn't we go through this with you yesterday ??? http://www.jiskha.com/display.cgi?id=1387091654

Simplifying trig expression
You could actually prove this for yourself by using one of the expansion formulas recall sin(A+B) = sinAcosB + cosAsinB so sin(x+90) = sinx cos90 + cosx sin 90 = sinx (0) + cosx (1) = cos x test it with some angles you should know let x = 30° sin (30+90) = sin 120 = √...

mathes
Let the point of contact be P(a,b) or P(a, √(a-3) ) If it is to be a normal at P, then the tangent at P must be perpendicular to 6x + 3y - 4 = 0 that is, the tangent must have a slope of +1/2 dy/dx = (1/2)(x-3)^(-1/2) = 1/( 2√(x-3) ) 1/(2√(x-3) ) = 1/2 2ͩ...

Pre-Calculus
After showing that both f(1) and f(-1) ≠ 0 try f(2) = 8 -36+48-20 = 0 so (x-2) is a factor Now use synthetic division and x^3 - 9x^2 + 24x - 20 = (x-2)(x^2 - 7x + 10) = (x-2)(x-2)(x-5) so x^3 - 9x^2 + 24x - 20 = (x-5)(x-2)^2 For a cubic, once you find one root, you can r...

MATH
Steve did this correctly for you here http://www.jiskha.com/display.cgi?id=1387129761 and Kuai did it again for you here http://www.jiskha.com/display.cgi?id=1385326928 You do you keep reposting it?

calculus hw
must be done in 2 parts total area = ∫ (x^3 - 2x - x^2) dx from -1 to 0 + ∫(x^2 - x^3 + 2x) dx from 0 to 2 = [x^4/4 - x^2 - x^3/3]from -1 to 0 + [ x^3/3 - x^4/4 + x^2] from 0 to 2 = (0 - (1/4 - 1 - 1/3) + (8/3 - 4 + 4 - 0) = 1 - 1/4 + 1/3 + 8/3 = 4 - 1/4 = 15/4 che...

math
probably did not get the correct graph because you skipped the brackets If you entered the equation as y = x/x-7 , you got a straight horizontal line at y = -6 because y = x/x - 7 = 1-7 = -6 You MUST include brackets, such as y = x/(x-7) http://www.wolframalpha.com/input/?i=pl...

math
I get height = 1.9 cm check: area = (1/2)(4.2)(1.9) = 3.99

math
area = (1/2) base x height 3.99 = (1/2)(4.2)(height) height = 2(3.99)/4.2 = ...

Math
Poor wording of the question, there is only one way to spell Mississippi, what you meant is "in how many ways can I arrange all the letters of the word Mississippi ? " 4 s's 2 p's 4 i's 1 m number of ways = 11!/(4!4!2!) = 34650

geometry
The two chords intersect to form 2 similar triangles, in this case 2 similar right-angled triangles so we can easily find that ED = 24 by Pythagoras: AC = √20 and BD = 6√20 Does that give you a start ?

Trigonometry
draw a horizontal line from the top of the tree to the building to create 2 right-angled triangle That line is common to both So, set up a trig equation for each triangle using that common side. You can then use substitution to get your answer.

math
height of pole --- h tan 60 = h/5 h = 5tan60 at 45° , tan45 = h/x , where x is the length of the new shadow x =h/sin45 = 5tan60°/tan45° = .... you push the buttons

Math
if even: f(-x) = f(x) if odd : f(-x) = -f(x) check for a given value: e.g. x = 5 f(-5) = 5/24 f(5) = -5/24 ---- > not even f(5) = -5/24 f(-5) = 5/24 = -f(5) should be obvious that the function is odd since f(-x) = -(-x)/(x^2-1) = x/(x^2-1) = - f(x)

Calculus
look at the solution I just gave catlyn in the previous post compare your graph with hers http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E4+%2C+y+%3D+x neat eh?

calc
intersection: x^4 = -x x^4 + x = 0 x(x^3 +1) = 0 x(x+1)(x^2 -x + 1)= 0 2 real solutions, x = 0 or x = -1 http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E4+%2C+y+%3D+-x area = ∫(-x - x^4) from -1 to 0 = [- x^2/2 - x^5/5] form -1 to 0 = (0 - (-1 -(-1)/5) = 1 - 1/5 = 4/5

business calc
I will assume that you meant: ∫ x/(2x^2 - 6) dx from 3 to 4 , (not 4 to 3) = (1/4) ln(2x^2 - 6) from 3 to 4 = (1/4) (ln 26 - ln 12) = (1/4) ln (26/12) = (1/4) ln(13/6) or (1/4)(ln 13 - ln6)

correction - Math
That is not correct the 42.00 represents .7 of the original price so .7x = 42 x = 42/.7 = $60 The original price was $60 check: 30% discount of $60 = .3(60) = 18 sale price = 60 - 18 = 42 your way: .3(42) = 12.60 your price = 42+12.60 = 54.6 now .3(54.6) = 16.38 your sale pri...

Math
done by Ms Sue http://www.jiskha.com/display.cgi?id=1386993323

algebra
You have now posted this same question about 5 times. Both Steve and I, and now Kuai, have answered this question for you with the same result. Do not repost a question unless you have checked on your previous posts. I suggest you mark the time of your postings, and find them ...

math
First of all, I am sure you meant f(x) = (x-2)/(x-3) , those brackets are essential! or y = (x-2)/(x-3) step1 in forming the inverse: switch the x and y variables ---> x = (y-2)/(y-3) step2: solve this new equation for y xy - 3x = y-2 xy - y = 3x - 2 y(x-1) = 3x-2 y = (3x-2...

math - inequalities
first one: x+7 ≥ 3x -2x ≥ -7 x ≤ 7/2 x ≤ 3.5 2nd one: 3x + 4 ≤ 5x -2x ≤ -4 x≥ 2 so "common" implies belonging to first AND the second, or 2 ≤ x ≤ 3.5 which for integers would be {2,3}

math
1/13 = .076923076923076923... notice the repeat is 076923 is 6 digits long 1st after decimal is 0 7th after the decimal is 0 13th after the decimal is 0 ... 37th after the decimal is 0 43rd after the decimal is 0 notice that the numbers 1,7,13, ... 37, 43 all leave a remainder...

Pre Calculus
secØ tanØ / sinØ = (1/cosØ)(sinØ/cosØ)(1/sinØ) = 1/cos^2 Ø or sec^2 Ø

Math 111
let rate of boat in still water be x mph let the rate of the current be y mph (4/3)(x+y) = 20 times 3 4x + 4y = 60 divide by 4 x + y = 15 (20/9)(x-y) = 20 times 9 20x - 20y = 180 divide by 20 x - y = 9 add them 2x = 24 x = 12 in x+y = 15 , if x = 12, then y = 3 speed of boat i...

Finite Math
I know some or even all of your answers must be wrong, since the sum of all the prob's has to add up to 1 The sum of your first 2 results is already over 1 first one is correct, I assume you did C(48,4) /C(52,4) = .718736.. Doing the 2nd the same way you want to chose 1 ac...

Calculus
Really a physics question. I know that Work = Force x distance.

math
volume of first jar = π(1.5)^2 (4) = 9π inches^3 volume of 2nd jar = π(3^2)(3) = 27π which is 3 times the volume of the first, so it should cost 3 times as much 3(0.60) = $1.80

Math
so the time from midnight to noon of next day = 36 hours ( from midnight to noon of the same day = 12 hours so to noon of next day = 12+24 = 36 hrs ) amount in bloodstream = 15 (1/2)^(36/48) = 8.92 mg

Math
population = 18691 (2)^(4/15) = 22485.7 or appr 22486

Trigonometry
1. let the width of the tent be 2x from my diagram, tan 50° = 6.25/x x = 6.25/tan50 = 5.24 So the tent is 2(5.24) appr 10.5 ft wide 2 make a diagram showing a side-view of the pool Draw a line parallel to the surface of the pool from the shallow end to the deep end, giving...

Math - Trig
a) after you make your sketch you should see that cos A = 120/d b) if d=1500 cosA = 120/1500 = .08 A = appr 5.4° ( here is what I did on my calculator ..... 120 ÷ 1500 = 2ndF cos = to get 85.4114... c) repeat the steps I showed you in b) let me know what you got

math
g(2) = 3(2) - 5 = 1 so f(g(2)) = f(1) = 2(1) + 1 = 3

Math
Saw this when you posted before, looks incomplete My first reaction is to say, "an infinite number of them" since you state no conditions for your square. e.g. Do the vertices of the square have to land on the sides of the rectangle? IF so, then there would be 3, whe...

math
Probably shouldn't tell you this, but there is "magic" fraction button on your calculator that does all your operations in fraction form look for a key labeled: a b/c to enter 57/18 57 a b/c 18 = see what you get ? now press 2ndF a b/c and 2ndF a b/c again, WOW n...

math
You should recognize √3/2 to be a ratio from the 30-60-90° right angled triangle. e.g. I know sin 60° = √3/2 and 60° = π/3 radians I also know that the sine is positive in quadrants I and II by the CAST rule, so Ø = π/3 and π - ...

Algebra
change in record sales = 4683 - 14000 = -9317 change in time = 11 years rate of change = -9317/12 = -776 records/year I included the years 1987 and 1998 .

math
I count 7 months, so rate of change per month = (800 - 1050)/7 = - $35.71 balance is declining at a rate of appr $36 per month

trig
let AP be the vector of magnitude 23 lbs and direction 18° and BP be the vector of magnitude 27 lbs and direction -15° Complete the parallogram APBQ , with AP=2 BP=27 angle P = 33° then angle B = 180-33 = 147° So PQ is the force pulling by the puppy to hold the...

Precalculus
sure, After sketching in all the angles, and doing some arithmetic, I have a triangle with sides 30 and 40 and the angle between them as 10° let the resultant be R R^2 = 30^2 + 40^2 - 2(30)(40)cos10° = 900+1600-2400cos10° = 136.46.. R = √136.46 = 11.68 , whic...

Quick math help
use the first 2 points to find the slope How is the slope of your new line related to this slope ? follow the method I just used in the previous reply to your other question. Let me know what you get.

Quick math help
Slope of given line = 2/8 = 1/4 so the slope of the new line = -4 y = -4x + b , but (4,5) is on it, so ... 5 = -4(4) + b b = 21 y = -4x + 21

Math
profit = 25x - 10x, where x is the number they sell = 15x They want to make a profit of 1000 15x = 1000 x = 1000/15 = 66 2/3 So they must sell 67 cups check: for 67 cups: revenue = 25(67) = 1675 expenses = 10(67) = 670 profit = 1675 - 670= 1005 cents or $10.05 for 66 cups prof...

Quick math help
When the slope of the line changes its sign, that would be a reflection in the y-axis There are many different kinds of reflections, the above is just one of them so y = 3x - 2 ----> y = -3x - 2 , a reflection in the y-axis now down 3 y = -3x-2 - 3 or y = -3x - 5

Quick math help
what kind of reflection ?

Quick math help
f(x) = -6x -10 + 6 = -6x - 4

math
Solving implies that you have an equation. You don't have one. If you mean simplify .... (x^3 y)^2 /(8x^(1/3)) , notice I put brackets in so it makes sense = x^6 y^2 / 2x^(1/3) = (1/2) x^(17/3) y^2 (certainly does not "look" any more simplified)

Precalculus
resultant = 30(cos200, sin200) + 40(cos10, sin10) = (-28.19-10.26) + (39.39 , 6.946 = (11.20 , -3.315) magnitude = √(11.20^2 + (-3.315)^2) = 11.68 miles bearing: tanØ = -3.315/11.2 = ... Ø = 343.5°

Algebra
number of units sold --- x profit = 5x - 1.7x = 3.3x 3.3x = 33000 x = 33000/3.3 = 10000

Math - Oh my gosh please help!
Since this is supposed to be an approximation, I see three days with 4 km each and two days with 2 km each total = appr 16 km so appr 16 km in 5 days or about 3 km/day 32 km in 10 days 96 km in 30 days 100 km in about 31 days

algerbra
Since the + and = signs are on the same key, I suspect you meant 3x-2y = 8 2x+2y = 22 ---->x+y=11 --->y = 11-x sub into the 1st 3x - 2(11-x) = 8 3x - 22+2x = 8 5x = 30 x = 6 then y = 11-6 = 5

calculus
Not sure how your "sign chart" method works, I will solve it the traditional way. x^2 - 2x +6 < 0 Just looking at the graph of y = x^2 - 2x + 6 we can tell that there is no solution. http://www.wolframalpha.com/input/?i=Plot+y+%3D+x%5E2+-+2x+%2B+6

math
I will assume the left side is supposed to be absolute value ... |3x+12| ≥ 21 3x+12 ≥ 21 OR -3x-12 ≥ 21 3x ≥ 9 or -3x ≥ 33 x≥ 3 or x ≤ -11

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