Posts by Reiny
Total # Posts: 38,877
Basic Numeracy and statistics (math)
Your given equation does not match your given data. If the initial velocity is 800 m/sec, then the equation would be h = -16t^2 + 800t , when shot from ground level. follow "Nonetheless' " suggestion and find the x-intercept 0 = 16t^2 + 800t 16t(t - 50) = 0 take ...
volume of the 5 cm sphere = (4/3)?(5^3) = (500/3)? cm^3 volume of shell = (4/3)?(10^3) - (4/3)?(8^3) = (1952/3)? since the mass is a function of the volume, [ (1952/3)?] / [(500/3)?] = x/6.25 1952/500 = x/6.28 500x = 12200 x = 24.4 kg check my arithmetic
Math - Probability
of the 26 letters, 5 are vowels prob (3 vowels of 3) = (5/26)(5/26)(5/26) = appr .0071 or .01 to the nearest hundredth
I will do the last one, you do the other two G(t)=650e^(0.055t) , tells me the continuous rate is 5.5% with a different base: G(t) = 650(1+r)t pick t = 5, (we can choose anything) in the first: g(5) = 650 e^(.055(5)) = 650 e^(.275) = 855.7449 in the 2nd: 855.7449 = 650(1+r)^5 ...
How many .... what ??? I assume you are asking for the rate of increase of the depth. for the of length 25 m, the depth increases by 2 m so the depth increases 1 m per 12.5 m of length notice the width has nothing to do with it.
Well, the first 4 represents 400 the 4 in the unit position represents 4 what is 400/4 ??
assume an equation of the kind, C = a e^(kt), where C is the consumption, a is the intital amount , t is the number of years since 1945, and k is a constant. given: when t = 0, C = 40, 40 = a e(k(0)) a = 40 so we have: C = 40 e^(kt) given : when t = 25 (1970), C = 27.4 27.4 = ...
simply C(h) = 5h + 10
I assume you want to find the equivalent equation with e as its base, so you want .5 = e^(80r) ln .5 = 80r lne, but ln e = 1 r = ln.5/80 = -.0086643 or P(initial)(1/2)^(t/80) = Pinitial(e)^(rt) (1/2)^(t/80) = e^(rt) take ln of both sides (t/80) (ln .5) = rt divide by t (ln .5...
or even simpler: draw a median from the right-angle to the hypotenuse. proof: let the triangle be A(0,0), B(b,0) and C(0,c) let AD be the median. midpoint of BC = ( (b/2 , c/2) AD = ?(b^2/4 + c^2/4) BD = ?(b - b/2)^2 + (c/2-0)^2 ) = CD = ?( b^2/4 + c^2/4) = AD
Assuming you made a sketch. Let the angle bisector of ?ACD meet BD at E let the diagonals intersect at F In a rhombus the diagonals right-bisect each other. So, in triangle CEF, angle F = 90 angle E = 64, thus angle FCE = 26° which makes angle BCD = 104° and of course...
Proof by contradiction
looks like both Damon and I have a typo in mine: from 4x^2 - 4x + 1 < 0 (2x - 1)^2 < 0 the conclusion is still the same in Damon's from (4x^2+1)/4x <1 NOTE-parentheses VITAL and multiply both sides by 4 x you would get: 4x^2 + 1 < 4x <---- which is the same ...
Proof by contradiction
Some strange math taking place here. first of all, the way you typed it ... 4x^2+1/4x <1 , if you multiply by 4x you would get 16x^4 + 1 < 4x According to your result, I suspect that your question was: (4x^2+1)/(4x) < 1 then 4x^2 + 1 < 4x+1 4x^2 - 4x + 1 < 0 (2x...
16y³+16y² +4y = 4y(4y^2 + 4y + 1) = 4y(2y + 1)^2
Vidya mandir rajgoli
Not enough information. We need an angle. Is it a right-angled triangle? Then use Pythagoras
the first as is : 60x + 10y = -16 divide 2nd by 10: -5x - 10y = 5 add them 55x = -11 x = -11/55 = -1/5 plug back into -5x - 10y = 5 -5(-1/5) - 10y = 5 1 - 10y = 5 -10y = 4 y = -2/5
let the base of the first triangle be b let the height of the first triangle be h area of first triangle = (1/2)bh If the sides are tripled the new triangle is similar to the first one, and the height will also be tripled new base = 3b new height = 3h new area = (1/2)(3b)(3h...
c < -1 means that you want all numbers to left of -1, but not -1 itself. This is shown with an arrow to the left of -1 with an open circle around the -1 if the circle is closed or solid, then it would be c ? -1, the -1 would be included so the correct choice is the first one
Draw a straight line 6 units long. Subdivide each unit into 5 parts. Count the parts, there will be 30 of them , since 6 ÷ (1/5) = 6 * (5/1) = 30
Find the area of the first pizza: A = ?r^2 = ?(6^2) = 36? find the area of the smaller pizza take the difference in the two areas
x+y=97 x-y=19 add them up: 2x = 116 x = 58 sub that into the first equation to find y
cylinders are easy: Consider a can of height h, and radius r Visualize taking off both lids of a tin can, you would have 2 circles. Now cut the "sleeve" along the height then fold it flat, and you would have a rectangle of length 2?r and height h So the surface area...
Following the order of operation the way you typed it, and assuming O is the same as 0 1.9(.16) = .25x x = 1.9(1.6)/.25 = 12.16 if you meant: 1.9=0.25/(0.16x) 1.9(.16x) = .25 3.04x = .25 x = .25/3.04 = 25/304
small typo in Steve's answer: last line should be S30 = 30/2 (2k + 29(-k/3)) = 15(-23k/3) = -115k
The missing part is the number of payments. i = .0875/12 = .00729166... n = ? PV = 349000 paym = 5000 5000(1 - 1.007291666..^-n)/.00729166.. = 349000 (1 - 1.007291666..^-n)/.00729166.. = 69.8 (1 - 1.007291666..^-n) = .508958286 .491041713 = 1.007291666..^-n take logs of both ...
1/2, x, 25 are in AP x - 1/2 = 25-x 2x = 51/2 x = 51/4 x+1/4, 32 1/2, and y are in GP, so (65/2) / (x + 1/4) = y / (65/2) y(x+1/4) = 4225/4 y( 51/4 + 1/4) = 4225/4 y( 13) = 4225/4 y = 4224/52= 325/4 check: for AP: 1/2, 51/4, 25 51/4 - 1/2 = 49/4 25 - 51/4 = 49/4 , x is correct...
or let the numbers be x, 3x, and 4x 3x - x = 10 x = 5 the numbers are 5, 15, and 20
17 3/5 ÷ 16 = 88/5 ÷ 16 = 88/80 = 11/10 or 1.1 pitchers
Math- Ms. Sue? Steve? Writeacher?
A(4,2) gives the coordinates of a point labeled A From the origin, it is 4 units to the right and 2 units up . reflection: (x,y) ---> (x+1,y-5) (4,2) ---> (5,-3) reflection across y-axis (x,y) --> (-x,y) (5,-3) --> (-5,-3)
Check Answers PLEASE
Your Venn diagram entries appear correct and are consistent with the 30 students B) is correct C) This a conditional probability P(A | B) ---> read: the probability of A given B = P(A and B)/P(B) for yours: P(Fruit | Salad) = P(Fruit and Salad)/P(salad) = (7/30) / (18/30...
M240 Help please
Hard to type matrices and to line them up properly. Try this effective applet http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
Strange wording of the question. Your choice of answer is incorrect. Since the given point satisfies both equations, both lines must pass through the point (-2,3) check: http://www.wolframalpha.com/input/?i=plot+y+%3D+x+%2B+5+,+y+%3D+%E2%88%922x+%E2%88%92+1
Why not use Google to find out what a limacon looks like? This will lead you to properties and equations of such curves.
A line which is perpendicular to the line 3x-2y=3 must look like: 2x + 3y = c but (3,-4) lies on it, so 2(3) + 3(-4) = c c = -6 2x + 3y = -6
we could use CA as the base of the triangle ABC then CA = 4 we could use the distance of B(3,7) from the y-axis as the height height = 3 area of triangle = (1/2)(4)(3) = 6 units^2 so the area of the parallelogram is 12 units^2
What is 1 - 1/5 - 7/10 ?
series help maths steve or reiny
This is called the Harmonic Series and has been the topic of many studies. It comes down to a question of Divergence or Convergence. You will get a finite sum of a series only if the series converges. It has been proven that the Harmonic Series actually diverges. Here are two ...
Do some googling. Find all the teams that Messi played for and make a list of players. Do the same for Diego Costa and the other footballers listed. cross off names that are NOT common, until you end up with a single name.
Math - Calculus
from f"(x)=5x+2 f ' (x) = (5/2)x^2 + 2x + c but f ' (-3) = 3 3 = (5/2)(9) + 6 + c c = ... find c and now you have f ' (x) integrate once more, adding another constant and since you have (-3,6) on it, you can find that constant as well
since the investment grows linearly, you have two points, (0, 3518) and (5,5553) slope = (5553-3518)/(5-0) = 407 looking at the choices, the only one possible is D, since it has a slope of +407 making sure, it is correct .... y = 407x + b and since (0,3518) would be the y-...
slope = (-2-1)/(5-10) = 3/5 y - 1 = ((3/5)(x-10) continue from here to change it to whatever form you need
Permutation: the order matters e.g. In how many was can 8runners finish first, second , and third number of ways = 8*7*6 = 336 or 8!/5! combination: A teacher wants to choose 3 students from 8 to form a clean up crew. The order in which the 3 students are chosen does not ...
Don't try fancy codes here, they don't work. I will read that as $5,000 Pick your "time spot" at 6 years, then 2x + x(1.085)^3 = 5000(1.085)^6 x(2 + 1.08r^2) = 8157.34 x = 8157.34/3.277289... = $2489.05
"The square triangle" ???? So I conclude that you have a square pyramid , and you want the area of the 4 triangles. Let's look at one of them We know its base of 8m We need its height. This height is the hypotenuse of a right-angled triangle formed from the ...
First of all, since you switched your name to "Frustrated Further" I have no way of finding your previous post. Secondly, your first question asks for "the lateral area of the square triangle". This makes no sense. 2nd question: The lateral surface area of ...
let the first term of the first progression be a let the 2nd term of the other progression be b a + 49(8) - (b + 49(8)) = 50 a - b = 50 a+79(8) - (b+79(8)) = a - b = 50 The difference between like term numbers stays the same at 50
After you sketch your triangle, you should see that tanØ = 8/5 <----- opposite/adjacent Ø= appr 58° , using my calculator
You have posted 7 consecutive questions without showing any sign that you have tried any of these. Are you expecting us to simply give you the answer to them? They are not difficult, and are of a basic type in this topic. Follow some of the examples in your text or in your ...
No, you might have come up mysteriously with the answer but it does not follow from what you did. You start off with two lines are are not equations, X^2+2x+3x+20 X^2-x-20 ----> this does not follow from the previous line, then in the third line all of a sudden you have...
NOW: John --- x Juan --- x+5 6 years ago: John --- x-6 Juan --- x+5-6 = x-1 x+5 + x-1 = 25 take over
C is inversely proportional to D ---> C = p/D B is inversely proportional to C ---> B = qC so B = q/(p/D) = (q/p)D A is directly proportional to B --> A = rB A = r(q/p) D looks like A is directly proportional to D
no, you are multiplying when multiplying powers with the same base, keep the base and ADD the exponents since -4+5 = 1 x^-4×x^5 = x^1 or just plain x
#1 -15 > -21 #2 correct #3 your choice is ordered from smallest to largest, but they wanted largest to smallest I think you have a typo, D would be it if it had been 4,6,7,-10, -15 #4 my choice would be B
typo - Mathematical Proof
my last 2 line should say: if n is odd, then n+6 is odd, since odd + even ---> odd
I assume you are allowed to use the basic rules of addition and multiplication of odds and evens odd + odd ---> even odd + even --->odd even + even ---> even so if 5n + 1 is even: given then 5n is odd: odd + 1 ---> even odd*odd ---> odd odd*even ---> even ...
You would be solving: .5sin(?t/5) = .1sin(?t/4) 5sin(?t/5) = sin(?t/4) getting a "feel" for the question, I ran it through Wolfram, had to change the t to x http://www.wolframalpha.com/input/?i=plot+y+%3D++.5sin(%CF%80x%2F5)+,+y+%3D+.1sin+(%CF%80x%2F4)+from+0+to+3%CF...
x+y = 80 x-y = 5 add them: 2x = 85 x = 85/2 = 42.5 take over
Make a sketch, dropping perpendiculars from the shorter parallel line to the longer Let that height be h You now have a rectangle 24 by h, and two triangles. One has hypotenuse 6, height of h, let its base be x The other has hypotenuse 8, height of h, and base of 10-x from the...
subtract the first from the second: -3xy + y^2 = 12 x = (12 - y^2)/(-3y) or (y^2 - 12)/(3y) sub into the first: (y^2 - 12)^2 / 9y^2 + y^2= 13 (y^2 - 12)^2 + 9y^4 = 117y^2 y^4 - 24y^2 + 144 + 9y^4 - 117y^2 = 0 10y^4 - 141y^2 + 144 = 0 y^2 = (141 ± ?14121)/20 y^2 = appr ...
or, without finding the angle, projection of u on v = (u dot v)/|v|^2 * v = (1.6*-2.1 + 3.3*-.5)/?(4.41+.25)^2 * v = appr -1.0796 v = appr 2.26i + .539j ----> given as choice b), same as Steve's answer
Unless you have a model of a football field, you must have meant 204 m, with a breadth of 24 m 2L + 2(24)= 204 solve for L
Due to the nature of the question, I will assume that you have been introduced to the circle on an x-y grid and the right-angled triangles with sides x and y and radius r, and have learned the definition of the six trig functions in terms of x, y, and r cot¤ = 7/8 ----&...
What is 10x9x8 ?
Precalculus - check
recall that y = loga u y' = (1/lna)*(1/u)*(du/dy) I will assume that you have r(t) = log4 (t + ?t) r ' (t) = (1/ln4)*( 1/(t + ?t) )*(1 + (1/2)t^(-1/2) ) = (1/ln4) (1 + 1/(2?t) )/(t + ?t) if we multiply top and bottom by 2?t = (1/ln4) (2?t + 1)/(2t^(3/2) + 2t) or ...
Area = ?r^2 d(area)/dt = 2?r dr/dt given: dr/dt = 4 find: d(area)/dt when r = 7 d(area)/dt = 2?(7)(4) = 56? miles^2 / hour
Ganett, that negative answer should not have made sense to you. form 2.00x + 6.50(1133-x) = 3836.50 2.00x+7364.50-6.50x = 3836.50 -4.5x = -3528 x = 784 1133-x = 349 x had to be a positive whole number, since it stands for the number of tickets
math (venn diagrams)
We do not know how many have phones and are in the chorus, label that percentage as x and place in the intersection of the two circles. so we have : 70+60-x+15 = 100 x = 45 now you have all the entries, so what is your answer ?
height = 5(330) m = 1650 m !!!!! Exactly where are you on earth? https://www.google.ca/webhp?sourceid=chrome-instant&rlz=1C5CHFA_enCA690CA690&ion=1&espv=2&ie=UTF-8#q=tallest+buildings+in+the+world&*
30/7 m = 3(10/7) m 20/7 m = 2(10/7) m So If I went to a tile store and asked for 6 tiles of 10/7 m units on each side, I could do this by laying 3 tiles along the length and 2 tiles along the width. This is an absurd question. You cannot decide on the size of the tile that you...
did that yesterday http://www.jiskha.com/display.cgi?id=1490974553
Your rule is correct, so the sum of the odd-place digits = 1+7+x+1 = x+9 sum of even-place digits = 3+2+4+3 = 12 difference : x+9 - 12 = 0 x = 3 is 13723413 divisible by 11 ? YES, 13723413 = 11(1247583)
I think you have a typo. 31:5 kg is not a unit of weight, did you mean 31.5 kg? If so, then just use a ratio .... zinc/31.5 = 7/9 9zinc = 220.5 zinc = 220.5/9 = 24.5 kg notice : 24.5 : 31.5 = 245 : 315 = 7 : 9
I used http://www.calculatorweb.com/calculators/loancalc.shtml and got a payment of $3404.53 , but I learned nothing about the actuarial math involved. From your data: Present value = 140000 n = 5(12) = 60 i = .16/12 = .013333... (ridiculously high rate for current rates, time...
R = a(x) + b(y^2) case 1: R = 21, x = y = 1 21 = a + b case 2: R = 48, x = y = 2 48 = 2a + 4b or 24 = a + 2b subtract them: 3 = b then in a+b=21, a = 18 R = 18x + 3y^2
And I am confused by your question. What does "using (y-h^2 (y-k)^2=r2 " have to do with it. First of all you typed it incorrectly, should be using (y-h)^2 + (y-k)^2=r^2 that would be the equation of a circle with centre (h,k) and radius r. But you simply wanted the ...
Because it is rotated about the line y = 2 , not y = 0 , which would have been the x-axis
Estimate ?? The standard simple formula and a good calculator gives you the answer in less than a minute. i = .08/12 = .006666... n = 30(12) = 360 P( 1 - 1.00666..^-360)/.00666.. = 200000 P = $ 1467.53
I have a strong feeling that you meant: (x-1)/(3x-3) = (x-1)/( 3(x-1)) = 1/3 , as long as x?1 the way you typed it, it would be (2/3)x - 3
"the geometric mean of two numbers x and y is 6" ---> (xy)^(1/2) = 6 xy = 36 goemetric mean of x,y,9x,9y = ( (x)(y)(9x)(9y) )^(1/4) = ( 81x^2 y^2 )^(1/4) = (81 (xy)^2 )^(1/4) = (81(1296))^(1/4) = 3(6) = 18
Assume the cost will be a function of the surface area SA. radius of can ---- r height of can ---- h V = ?r^2 h = 640 h = 640/(?r^2) SA = 2?r^2 + 2?rh = 2?r^2 +2?r(640/(?r^2) = 2?r^2 + 1280/r d(SA)/dr = 4?r - 1280/r^2 = 0 for a min of SA 4?r = 1280/r^2 r^3 = 320/? r = appr 4....
Assuming that S8 means Sum(8), and you are dealing with a geometric sequence ..... ( a(r^8 - 1)/(r-1) ) / ( a(r^4 - 1)/(r-1) ) = 97/81 (r^8 - 1)/(r^4 - 1) = 97/81 (r^4 - 1)(r^4 + 1)/(r^4-1) = 97/81 r^4 + 1 = 97/81 r^4 = 16/81 r = ± 2/3
similar question here, just change the numbers http://www.jiskha.com/display.cgi?id=1362948858
Math - Quadratic Equations
Mark now is x^2 at some time in the future, Mark is 10x so the change in time is 10x - x^2 Peter's age will change by that same number so Peter's age will be x + 10x-x^2 = 11x - x^2 but 3x = 11x- x^2 x^2 - 8x = 0 x(x-8) = 0 x = 0 , not likely or x = 8 So Mark is now 64...
Time = distance/rate let the equal distances be x km individual times are: x/20, x/60, and x/120 hours total time = x/20 + x/60 + x/120 = (6x/120 + 2x/120 + x/120) = 9x/120 hrs avg speed = total distance/total time = 3x / (9x/120) = 40 km/h
let cosx = t, then your equation becomes 4t^2 - t - 3 = 0 (4t + 3)(t - 1) = 0 t= -3/4 or t = 1 cosx = -3/4 or cosx = 1 now follow the steps I used for your previous post when you were Sara http://www.jiskha.com/display.cgi?id=1490924093
log2 (x+5) + log2 (x-1) =4 , x > 1 or else the log .... would be undefined log2 ( (x+5)(x-1) ) = 4 (x+5)(x-1) = 2^4 x^2 + 4x - 5 - 16 = 0 x^2 + 4x - 21 = 0 (x + 7)(x - 3) = 0 x = -7 or x = 3 So x = 3, the other root is extraneous
I sent it through Wolfram the way you typed it Even Wolfram had trouble understanding what you meant: http://www.wolframalpha.com/input/?i=solve+15(5%5Ex-2)%3D8%5E2x%2B1
No extraneous root here. Just a simple equation.
I went through a very similar question for you in your previous post. Using a "Web Loan Calculator" and being asked to put the answer in a webpage input box will not allow you to learn how to do this type of problem.
Saturn was never made by Dodge, and has not been manufactured since 2009, anyway .... I will assume you want to find the monthly payment. i = .0325/12 = .002708333... n = 48 PV = .95(20800) = 19760 P( 1 - 1.00270833..^-48 )/.00270833.. = 19760 I got P = 439.56
From p(-2)=5 and p(1)=14 we have two points (-2,5) and (1,14) so, 3(-8) + a(4) -2b + 7 = 5 4a - 2b = 22 ----> 2a - b = 11 3(1) + a(1) + b(1) + 7 = 14 ---> a + b = 4 adding: 3a = 15 a = 5, then b = -1 a+b = 5-1 = 4
recall cos 2x = 2cos^2 x - 1 4cos2x - cosx-3 =0 4(2cos^2 x - 1 ) - cosx - 3 = 0 8cos^2x - 4 - cosx - 3 = 0 8cos^2 x - cosx - 7 = 0 (cosx - 1)(8cosx + 7) = 0 cosx = 1 or cosx = -7/8 cosx = 1 ---> x = 0 or x = 2? cosx = -7/8 ---> x = ? - cos^-1 (7/8) or x = ? + cos^-1 (7/8...
simple case of tan 22° = height/15 height = 15tan22 = ....
Did you make a sketch? What are the dimensions of the tub with a 3 ft border around it? What is the area of that rectangle? What is the area of the tub? subtract the two areas. let me know your choice.
if 5/8 are girls, then 3/8 are boys let the number of girls be 5x , and the number of boys be 3x 5x = 3x + 10 2x = 10 x = 5 number of girls is 25 and boys is 15 total in chorus is 40 fraction of chorus kids to whole student body = 40/178 = 20/89 I don't get the point of ...
Keith and 10 and Sally has 3 times as many. What is 3 x 10 ??
Anna's cards --- 5x Jane's cards ---- 3x Tina's cards ----- 2x 5x + 3x + 2x = 120 10x = 120 x = 12 plug back into my definitions
done, see your previous post of this btw, I notice you had to find the dimensions as well as the minimum cost but once you have r, just go back into h = ...
let the radius of the cylinder be r, let the height of the cylinger be h ?r^2h = 1000 h = 1000/(?r^2) Cost = .05(2?r^2) + .03(2?rh) = .1?r^2 + .06?r(1000/(?r^2) = .1 ?r^2 + 60/r d(Cost)/dr = .2?r - 60/r^2 = 0 for a min cost .2?r = 60/r^2 r^3 = 60/(.2?) = 300/? carry on, find r...