Thursday
October 30, 2014

Posts by Steve


Total # Posts: 26,233

trigonometry
Draw a diagram. You have a triangle with angles 30.4°, 137.0°, and 12.6°. At 150 mph, he travels 150mi/hr * 1hr/60min * 1min = 2.5 mi So, now you can use the law of sines to get the distance at first sighting 2.5/sin12.6° = d/sin137° d = 7.82 mi Now, you ...
August 26, 2014

algebra
if x at 11%, then the rest (5900-x) is at 6%. The interest earned is 0.11x + 0.06(5900-x) = 509.00 x = 3100
August 26, 2014

math
v = d/t get d = the distance from the sun to earth. now use v = speed of light t = d/v go for it.
August 26, 2014

Math
10 1/2 = 21/2 so, 3/8 * 21/2 = 63/16 = 3 15/16
August 26, 2014

English
both are syntactically correct, but the first is better. The crime was making fake money. Of course, having made it, you are guilty of making it.
August 26, 2014

physics
depends on how long it took to stop the ball, or how far it traveled while being stopped. Surely you can see that a gentle push (small force) exerted over many meters would do the job, as would a strong force imparted in an instant.
August 25, 2014

Math
I also get 23. So, unless you have transcribed the problem incorrectly, the answer key is wrong. Double check that, and then show your teacher your work. Something doesn't add up, as it were...
August 25, 2014

Physics
The velocity changes by -25 m/s in 0.4 s, so the acceleration is 25/.4 m/s^2 = 62.5 m/s^2 Since F=ma, the force exerted is 65 kg * 62.5 m/s^2 = 4062.5 N
August 25, 2014

math
8(1+.50)(1-.20)(1+.15)(1-.60) = 4.42
August 25, 2014

chemistry help!
5500 acre * 43560ft^2 * 2m * 3.28ft/m * 1s/17600ft^3 = 5500*43560*2*3.28/17600 = 89298s one day is 86400 seconds
August 25, 2014

phys
just look up atmospheric pressure. I know it's 14.7 lb/in^2, but I don't recall its metric value. Anyway, it will be in N/m^2. So, just multiply pressure(N/m^2) * area(m^2) to get force.
August 25, 2014

ALGEBRA
The notation is confusing. To make things more explicit, I'd have written 320km/1hr * 1mi/1.609km = 320/1.609 mi/hr = 198.9 mi/hr That way you can see which units cancel. Using m for mile (from the mph) is confusing.
August 25, 2014

MAth
Well, does x=6 work in the original equation? 5(2*6-10)/2 + 14 = 19 so I guess your answer is correct. The only thing I would change is to include parentheses where things are ambiguous. I'd have said (10x - 50)/2 = 5x - 25 + 14 =19 as in the original equation
August 25, 2014

discrete math
A' U B http://mrithulabanu.blogspot.com/2011/08/venn-diagrams.html A ∩ (B U C) http://onlinemathhomework.wordpress.com/2012/11/19/three-circle-venn-diagram-help/
August 25, 2014

Math
since 12/6 = 2, all the sides of the larger triangle will be double the lengths of the smaller triangle.
August 25, 2014

Math
if the shorter base is b, then we have b + b+10 + 2(2b-3) = 52 Now just solve for b and then the other base and legs.
August 25, 2014

algerbra
clearly a,b,d are out, since they have a positive slope. Of the other two choices, which passes through (0,5)?
August 25, 2014

Math
If .30 = .06x, then x = 5 So, $5 was taxed, and $20 was tax-free
August 25, 2014

algebra
for our purposes, consider h=1. The round trip on each bounce is 2 times the height achieved. So, the total distance traveled is 1 + 2/3 + 2/9 + 2/27 + ... with sums adding up to 1, 5/3, 17/9, 53/27 The round trip distance after the nth bounce is thus 2/3^n The total distance ...
August 25, 2014

Math
Do you mean 21+22+23+...+29 ? If so, note that there are 9 terms of an arithmetic progression. So, the sum is 9/2 (21+29) = 225
August 25, 2014

math
since you could draw all 4 blues before any reds, you will need 6 socks to assure two reds.
August 25, 2014

Math
assuming his contribution was proportional to his profit share, and that the 2:3 ratio is Arham:Babar, then if you divide 3500 into 2+3=5 equal shares of 700, then his Babar's input was 3*700 = 2100.
August 25, 2014

Math
at a growth of r% per year, 1750(1+r/100)^10 = 2625 r = 4.14%
August 25, 2014

Math
6650(1-.06)(1.10) = 6876.10
August 25, 2014

math
see related questions below
August 25, 2014

maths
The large cube is cut into 4x4x4 cubelets. The outside faces on both sides have paint, so only the 2x2x2 inside cubelets have no red paint.
August 25, 2014

Math
I see no way to do this. All you know is the area. There are many isosceles trapezoids that can have such an area, each with a different perimeter. For instance, if the height is 5, then (a+b)/2 = 29 and the slant sides are of length s^2 = 5^2 + ((b-a)/2)^2 So, the perimeter ...
August 25, 2014

Math
you always want x^2/a^2 + y^2/b^2 = 1 So, just divide through so that happens. For example #1: divide by 15 to get x^2/3 + y^2/5 = 1 Clearly, a^2 = 3 b^2 = 5 since a is smaller than b, a^2+c^2 = b^2 3+c^2 = 5, so c^2 = 2 See the graph at http://www.wolframalpha.com/input/?i=...
August 25, 2014

Algebra
The x-intercept is where y=0, so 0+4 = -4(x-2) 4 = -4x+8 -4 = -4x x = 1 How did you wind up with -3? And drop the "like" -- either you got 2 different answers or you didn't.
August 24, 2014

Algebra
21+15 = 36 There are only 25 trays, so 11 must contain both cup and plate. Now you can draw the Venn diagram to see that the intersection of the two regions must contain 11.
August 24, 2014

Math - Old SAT exam
wait a minute. If you multiply j*k*n and any of them ends in zero, the product will also end in zero. Also, if the three are consecutive integers, then at least one of them must be even, so the product cannot end in 9.
August 24, 2014

math
s = 2f-24
August 24, 2014

Math
consider that 2+10+2 = 14 The 2" sides are folded up, leaving the length=10.
August 24, 2014

Ratios and Rates - Last One!
4.5 qt/min * 1 gal/4qt * 60min/hr = (4.5)(60)/4 gal/hr = 67.5 gal/hr You are correct
August 24, 2014

algebra
Better review your motion equation. h = Ho + Vo*t - 1/2 gt^2 the height above the water, using g = 10, is thus h = 30 + 15t - 5t^2 So, just solve for t when h=10
August 24, 2014

Algebra
you know that all points at a distance 5 will form a circle with center at (1,5) and radius 5. So, (x-1)^2 + (y-5)^2 = 25 So, plug in x=4 and you have 3^2 + (y-5)^2 = 25 (y-5)^2 = 16 y-5 = ±4 y = 9 or 1 So, the points are (4,9) and (4,1)
August 24, 2014

Algebra 2. Please Help Someone!!
During the descent, the change in y is -100 the change in x is 5000 so, the slope is -100/5000 = -1/50 = -0.02 The y-intercept is when x=0. That is, at the start of the landing. y=100. so, y = -0.02x + 100
August 24, 2014

Algebra, Please Help!
if you rewrite this, letting u = s+4, then you have 5u^2 - 44u - 9 = 0 (5u+1)(u-9) = 0 u = -1/5 or 9 Now, since u = s+4, s = u-4, so s = -21/5 or 5
August 24, 2014

Alg.2
for x DVDs in a year, the charges are y = 10.00 + 3.95x Now just solve for x when y = 500
August 24, 2014

Algebra 2
c = kN From the data, 14 = 4k k = 7/2 so, c = 7/2 N Now just plug in N=7 to get the cost. cheap tickets! Must be an old problem, or a discount theater...
August 24, 2014

Math
let u = s+4 9u^2-62u=7 9u^2-62u-7 = 0 (9u+1)(u-7) = 0 u = -1/9 or 7 s = -37/9 or 3 Or, you can expand everything and get 9(s^2+8s+16) - 62(s+4) - 7 = 0 9s^2 + 72s + 144 - 62s - 248 - 7 = 0 9s^2+10s-111 = 0 (9s+37)(s-3) = 0
August 24, 2014

physics
d^2 = 600^2 + 200^2
August 24, 2014

Math
I think you mean p = 1.1(1.05)^t Now just plug in various values for t and p to answer questions. For example, after 7 years (1997) p = 1.1 * 1.05^7 = 1.55 How long will it take p to grow by 46%? 1.1*1.46 = 1.1 * 1.05^t 1.05^t = 1.46 t = log(1.46)/log(1.05) = 7.76
August 24, 2014

Math
assuming you meant two days, then that would be 2(1/15 + 1/20) = ??
August 24, 2014

Algebra
Normally, the ^ needs an exponent after it. So, I read it now as 12(6^2/(5^2-4^2)) + 7 12(36/(25-16))+7 12(36/9)+7 12(4)+7 48+7 55 You were ok until the last step. Unless otherwise indicated, multiplication is done before addition. Ah. I see what went wrong; your unbalanced ...
August 24, 2014

Algebra
Your notation is weird. 5^-4 = 1/5^4 = 1/625 No idea what 5^-4^ means, or 6^/...
August 23, 2014

Algebra
correct, though I think you meant (7p)mn = 7p (mn) That little "-" in there seems to indicate subtraction, rather than separation
August 23, 2014

math
Surely you can do this one: √(14-5x) = x 14-5x = x^2 x^2+5x-14 = 0 (x+7)(x-2) = 0 But watch out for extraneous roots. Check both values in the original equation. Hint √4 = 2 √4 ≠ -2
August 23, 2014

math
(3x/x-1)+(2/x)=4 3x*x + 2(x-1) = 4x(x-1) 3x^2 + 2x-2 = 4x^2-4x x^2-6x+2 = 0 x = 3±√7
August 23, 2014

algebra
Vertex at (6,0) y = (x-6)^2 half as tall y = 1/2 (x-6)^2 flipped y = -1/2 (x-6)^2
August 23, 2014

math
Factor the expression (x-8)(x+2) / (x+6)(x+2) = 2 now, omitting x = -2, (x-8)/(x+6) = 2 x-8 = 2x+12 x = -20 4x = -80
August 23, 2014

math
recall that ∫ du/(a^2+u^2) = 1/a arctan(u/a) now note that x^2+4x+13 = (x+2)^2 + 3^2 Nuff said? I get π/12
August 23, 2014

equations
1.25x = 3.5 - 0.4x 1.65x = 3.5 ok?
August 23, 2014

maths
Draw a diagram. If you draw a horizontal line from the top of the 6m pole to where in intersects the 11m pole, then you have a right triangle with legs 5 and 12. You should be able to recognize the ubiquitous 5-12-13 triangle. The tops are 13m apart.
August 23, 2014

calc
As usual, just use the chain rule: Let u = e^3x, and you have d/dx arctan(u) = 1/(1+u^2) * du/dx = 1/(1+u^2) (3e^3x) = 3e^3x/(1+e^6x)
August 22, 2014

Algebra
correct answer, but when typing online where there is no vertical fraction formatting, it's better to use 8/(x-m) That way it will not be confused with 8/x - m Normally, when evaluating expressions, multiplication is done before subtraction, unless parentheses indicate ...
August 22, 2014

Algebra
actually, you already have the difference. What you have done is find the quotient and then simplified it.
August 22, 2014

college algebra
If there are x kg of Brazilian coffee, then the rest (420-x) is Turkish. So, 10x + 13(420-x) = 12*420 x = 140 Note that 140 is 1/3 of 420, meaning that it drags the price down 1/3 of the way from 13 to 10, or $12.
August 22, 2014

math
you want to convert 100 pages to minutes. Your conversion factor is 20 minutes = n pg 20min/n pg = 1 Now multiply vy that to cancel the unwanted units: 100 pg * 20min/n pg = 2000/n min
August 22, 2014

math
Better take a look at http://mathmistakes.info/facts/CalculusFacts/learn/doi/doif.html So, what you have is √(1+(2x)^2)(2) = 2√(1+4x^2) at x=√2, that is 2√(1+8) = 2*3 = 6
August 22, 2014

Algebra
y = 3/(2x) so we want the minimum of 10x + 3/5 * 3/(2x) = 10x + 9/(10x) take the derivative and you have 10 - 9/(10x^2) set that to zero and you get 100x^2 - 9 = 0 (10x-3)(10x+3) = 0 x = ±3/10 So, at x = 3/10, y = 5 and 10x+3y/5 = 3+3 = 6
August 22, 2014

math
g'(1/2) = 4(1/2)(2-1/4) = 2(7/4) = 7/2 So, g is increasing at x = 1/2 Have you looked at the graph? http://www.wolframalpha.com/input/?i=4x^2+-+3x^4 Clearly only (b) is true
August 22, 2014

math
g' = 8x-12x^3 = 4x(2-x^2) g" = 8-36x^2 g' changes sign in x<1, so not (a) g'=0 and g"≠0 at x=0, so (b) g" changes sign, so not (c) so, (b) is the only true statement
August 22, 2014

math
you are correct
August 22, 2014

math
exactly 75%=3/4 implies the number is a multiple of 4, so the candidates are 40,44,48 exactly 1/6 implies it is also a multiple of 6, so 48 students
August 22, 2014

Math
9 clearly cannot be on a corner, so we have X9X X7X XXX Now, the only choices along the top are 1,2, so we have 192 X7X XXX 8 cannot be on a corner, because then we'd need 2,2 or 1,3 twice. It must be on one of the sides: 192 87X 3XX Now, 3+9=12 and 2+10=12 We still need ...
August 22, 2014

Algebra
(x-1)/(x-3) = √(17-x) (x-1)^2/(x-3)^2 = (17-x) x^2-2x+1 = -x^3+23x^2-111x+153 x^3-22x^2+109x-152 = 0 No rational roots here, so you will need to resort to a graphical or numeric method to get the desired accuracy. http://www.wolframalpha.com/input/?i=x^3-22x^2%2B109x-152
August 22, 2014

math
If the first basket has x and the second has y, x = 4/3 y x = y+3 x = 4/3 (x-3) x = 4/3 x - 4 1/3 x = 4 x = 12
August 22, 2014

algebra
P e^(.0855*(8+125/365)) = 225500 P = 110502.63
August 22, 2014

algebra
Assuming you want to factor it, grouping is probably the easiest way: 4ax+8a-10x-20 2(2ax+4a -5x-10) 2(2a(x+2)-5(x+2)) 2(2a-5)(x+2)
August 21, 2014

Algebra
sure. You can have any positive number of rows or columns.
August 21, 2014

Math
2 2/5 % = 12/5 % = (12/5)/100 = 12/500 = 3/125
August 21, 2014

math
(3/4 mi)/(9/8 mi/hr) = 3/4 * 8/9 hr = 24/36 hr = 2/3 * 60 min = 40 min
August 21, 2014

Geomentry
assuming RST are collinear, RT = RS+ST, so 8y+4 + 2x-2 = 64 2x = 64-8y-4+2 2x = 62-8y x = 31-4y Assuming the y is a typo, 8x+4 + 2x-2 = 64 10x = 62 x = 6.2
August 21, 2014

math
6/4
August 21, 2014

Math
Get the w stuff all alone G-4x-4/3 = 1/2 w Now multiply by 2 and you have 2(G-4x-4/3) = w
August 21, 2014

math
Because you have added 0 hudredths. Adding 0 of anything leaves the result unchanged. 10.6 = 10.60 = 10.6000000000000000000
August 21, 2014

Math
In that case, there is no way to tell. You must know how many rows, and how many seats in each row. And who cares which day it was?
August 21, 2014

math
Looks like $1.25 for the first 1.5 miles, and $.45 more for every 1/2 mile beyond that. So, since 2 5/8 = 1 1/2 + 1/2 + 1/2 + 1/8, the charge is $1.25 + 0.45 + 0.45 + 0.45 = $2.60 Now work on the other parts.
August 21, 2014

math
we know that (2x+12)^2 + x^2 = (2x+18)^2 expand all that and solve the quadratic, and you get x = 30 check: 30^2 + 72^2 = 78^2 That's just 6 times a 5-12-13 triangle
August 21, 2014

math
x^2-2x+1 - 4 x^2-2x-3
August 21, 2014

Algebra
correct!
August 21, 2014

physics
In terms of x & y, 186@E23°N = 171.21,72.68 327@N43°W = -223.01,239.15 Add them up: -51.80,311.83 That is 361.10 at 99.43° or, as a heading, 361.10@N9.43°W
August 21, 2014

MAth
Nope. Treat || like parentheses for grouping. Then, when everything inside has been evaluated, apply the absolute value: |13|-7x|-2+8|/6 13-7x|6|/6 13-7x6/6 13-7x1 6
August 21, 2014

physics
The swimmer's direction should be the hypotenuse of the diagram. Then, the current makes the resultant velocity perpendicular to the bank. The angle is thus upstream at an angle of arccos(1.5/3.76)=66.5° relative to the bank. That makes the speed relative to the shore...
August 21, 2014

math
For m minutes, A: 25.00+0.10(m-30) B: 20.00+0.12(m-30) So, just solve for m when A=B The language used for this problem is rather odd. Not at all what I'd expect from a school text.
August 21, 2014

math
since 7y=28x, y = 4x 6x+4(4x) = 40 22x = 40 x = 20/11 x^2 = 400/121
August 20, 2014

Math
just subtract his initial loss from the subsequent profit: 1580-415 = ?
August 20, 2014

Algebra
sounds good. You might also note that for an exponential function y = f(x), log(y) is linear.
August 20, 2014

Geometry - eh?
Hard to say. Just noting the degrees separating the hands tells nothing about the actual time. And, since you don't specify which hand is at 70 degrees, that's no help either. Want to rethink the question?
August 20, 2014

Math
If you mean (225-256)^2 that's just (-31)^2 = 961 If you mean 225-256^2 that's -65311
August 20, 2014

Algebra
easy. Note that y^3 / y^10 = y^3 / y^3*y^7 The y^3 factors cancel, and you are left with 1/y^7 Or, use the rule that in division, you subtract exponents, so y^3/y^10 = y^(3-10) = y^-7 = 1/y^7
August 20, 2014

college algebra
It's already factored! Want to rephrase the question?
August 20, 2014

maths
what do meters have to do with anything? If the equation is 3 cos x = 25x, that's one thing. If not, fix the equation, but leave the m^2 out of it.
August 20, 2014

MATHH
The slope of the line joining those two points is (4+7)/(3-2) = 11 But, you are supposed to find the slope of any perpendicular line. That is -1/11.
August 20, 2014

math
1. reflect through the x-axis 2. reflect through (0,0) 3. a translation, but you are missing a sign.
August 20, 2014

math
You have a/b = 4/5 a/c = 6/11 You want b/c = (b/a)/(c/a) = b/a * a/c = 5/4 * 6/11 = 30/44 = 15/22
August 20, 2014

math
B gains 100 yards every minute. So, after 10 minutes, B has lapped A once. C gains 100 yards on B every minute, so after 10 minutes C has lapped B. Thus, after 10 minutes, A has gone 7 laps, B has gone 8 laps, C has gone 9 laps, and all are even again.
August 20, 2014

Math
-8 is less than any of them. All the negatives come first. The || values are all positive. So, (C) is correct
August 20, 2014

Geometry
In an equilateral triangle, the median is the same as the altitude. If the side is s, the median is √3/2 s. Each median extends from a vertex to the midpoint of the opposite side.
August 20, 2014

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