Wednesday

October 1, 2014

October 1, 2014

Total # Posts: 25,408

**AP Calc. AB**

as x-> 0, 1/x -> ∞ 2^(-1/x) -> 2^-∞ = 0 when x>0 2^(-1/x) -> 2^∞ = ∞ when x<0 So, in those two cases, we have lim x->0+ = 8/(1-2^-∞) = 8/(1-0) = 8 lim x->0- = 8/(1-2^∞) = 8/-∞ = 0 http://www.wolframalpha.com/...
*August 31, 2014*

**AP Calc. AB**

a different problem was recently posted here where the left limit is 2 and the right limit is zero. Tweaking it a bit, we have (8)/(1-2^(-1/x)) which fits your criteria. If you can come up with any function where the left and right limits for some value of x are different, you...
*August 31, 2014*

**Math Compounded daily**

1450(1+.12/365)^(365*1) = 1634.84 Some problems specify that we use 360 days per year. In that case, change the expression as needed.
*August 31, 2014*

**trigonometry**

a circle of radius r has circumference 2pi r, so one lap = 6pi feet So, 20 laps = 120pi feet
*August 31, 2014*

**Algebra 2**

since distance = speed * time, (x+3.5)(5) = (x-3.5)(12) x = 8.5 Now you can easily show how far it went.
*August 31, 2014*

**Algebra 2**

distance = speed * time, so if the plane's speed is x and the wind speed is y, we have 4(x+y) = 5040 5(x-y) = 5040 x = 1134 y = 126
*August 31, 2014*

**Math**

to get the x-intercept, set y=0 and you have -5x = 10 to get the y-intercept, set x=0 and you have 2y = 10 Look at your graph.
*August 31, 2014*

**Algebra**

If the only possible value for x is 3, then the function must factor into (x+3)(x+3) = x^2+6x+9 When they say the only possible value, they mean the only value which makes the equation true. Naturally, x can have many other values, but in those cases, the value on the left is ...
*August 31, 2014*

**Calculus**

at time t hours, the distance d is d^2 = (60t)^2 + (35t)^2 when t=3, then, d=208.39 Since 2d dd/dt = 7200t + 2450t = 9650t at t=3, dd/dt = 28950/(2*208.39) = 69.46 km/hr
*August 31, 2014*

**math**

as usual, you need to find the common denominator. Assuming you meant 2/(m+3) + 1/m the LCD = m(m+3). So, you have (2m + m+3) / m(m+3) = (3m+3) / m(m+3) On the other, I think you have 2/((x+1)(x+2)) + 3/((x+2)(x+3)) so the LCD is (x+1)(x+2)(x+3). That gives you (2(x+3) + 3(x+1...
*August 31, 2014*

**Calculus 2**

Using shells, you have thickness dy, so v = ∫[1,3] 2πrh dy where r = y and h = x = 1/y v = 2π∫[1,3] y*1/y dy = 2π∫[1,3] dy = 2πy [1,3] = 2π(3-1) = 4π That strikes me as odd. Let's try discs (washers) of thickness dx. The ...
*August 30, 2014*

**algebra**

x + x-3 = 21 x = 12
*August 30, 2014*

**Algebra 1**

width: w length: 2w-3 after the changes, we have (2w-3-2 + w-1) = 24 Now just solve for w, the original width.
*August 30, 2014*

**math**

L+M=250 3/5 L = M-40 Now we can substitute for M, and we get 3/5 L = 250-L-40 8/5 L = 210 L = 131.25
*August 30, 2014*

**math**

rotation does not change lengths.
*August 30, 2014*

**Algebra**

12x^2+8x = 4x(3x+2) 9x^2-4 = (3x-2)(3x+2) I think you can see which factor cancels.
*August 30, 2014*

**Math**

If they get shares of x,y,z, respectively, then x = 2/3 y y = 1/4 z x+y+z = 1360 We want to know what y is, so substitute in for x and z: 2/3 y + y + 4y = 1360 17/3 y = 1360 y = 240
*August 30, 2014*

**physics**

dropped stone hits water: 24.4-4.9t^2=0 t=2.23 stone has fallen 6.6m: 4.9t^2 = 6.6 t = 1.16 So, Jill's thrown stone only has 2.23-1.16=1.07 seconds to hit the water: 24+1.07v-4.9*1.07^2 = 0 v = -17.19 m/s
*August 30, 2014*

**Physics Help!!!!**

total distance covered: 20+30+40=90m total time: 30s avg speed: 90/30 = 3m/s final displacement: 20-30+40=30m north avg speed: 30/30 = 1 m/s north
*August 30, 2014*

**Physics**

total distance covered: 20+13+10=43m total time: 45s avg speed: 43/45 = 0.96 m/s final displacement: 20-13+10 = 17m avg velocity: 0.38 m/s away from entrance
*August 30, 2014*

**maths - 2nd take**

what a lot of bother I went to above. The distance from (2,3) to (5,4) is √10. Since the circles are orthogonal at the intersections, the two given points and the centers of the circles form a square, with diagonal √10. So, the side of the square, which is the ...
*August 30, 2014*

**maths**

The line joining the two points is y-3 = (1/3)(x-2) Its midpoint is at (7/2,7/2) The centers of the circles lie on its perpendicular bisector, which is y-7/2 = -3(x-7/2) If the radius of the circles is r, the distance from (2,3) to the second line is r/√2 So, just figure...
*August 30, 2014*

**Algebra 2**

multiply the speed by the time taken. The freight train traveled for 15 hours at 42 km/hr.
*August 30, 2014*

**Algebra 2**

since distance = speed 8 time, we want 42t = 105(t-9) t = 15 So, at 5 am the next day they meet, after having gone 630km. Or, you can consider that the freight train has a 9*42=378km head start, so the express train, traveling 63km faster, makes up the distance in 6 hours, ...
*August 30, 2014*

**Physical Science**

hint: 1 degree is 1/360 of the circumference.
*August 30, 2014*

**Physical Science**

the usual formula s=rθ so, look up the radius of the earth, and multiply that by angle of 1'=0.00029 radians
*August 30, 2014*

**math**

3tanθ = 4, so tanθ = 3/4 That means that sinθ = 3/5 cosθ = 4/5 Now just plug in the numbers
*August 30, 2014*

**Algebra**

z^3 = 8p^3 cis2π z = 2p cis 2π/3, 2p cis 4π/3, 2p cis 0
*August 30, 2014*

**math**

If you label the points A,B,C from left to right, then just show that the slope of AB is the same as the slope of BC. Since B is on both line segments, they are part of the same line.
*August 30, 2014*

**math**

how do you get 306? The perimeter of the kite in cm is 9+9+17+17 Not sure how the inches come into play.
*August 30, 2014*

**math**

count the coins: q = 2h+3 d = q+10 count the values: 10d+25q+50h = 6205 Now you have three equations, and you can solve them to get 113 dimes 103 quarters 50 halves
*August 30, 2014*

**Calculus AB**

correct. The limit from the right is not the same as the limit from the left. But both limits are finite.
*August 29, 2014*

**Calculus AB**

Looking at the graph at http://www.wolframalpha.com/input/?i=%284%29%2F%281-2^%281%2Fx%29%29+ I'm sure you can justify your analysis.
*August 29, 2014*

**vector**

standard differential geometry stuff. You surely have formulas for this in your text. Any google search will provide many discussions of the topic. What do you come up with? We'll be happy to check over your answers.
*August 29, 2014*

**Math - any ideas?**

With that pesky 7 in there, I'm at a loss for any way to combine the terms.
*August 29, 2014*

**Math**

why is the Imperial system any worse than the Cheshire system? Fie on thee, sirrah - hie thee hence!
*August 29, 2014*

**Math**

Hmmm. It doubles every day. 6 = 4 * 1 1/2, so it must have taken the last 2 days to double twice from 1 1/2 to 3 to 6 inches. I say it took 28 days. I'd have stopped at .25 = 2^(t-30) -2 = t-30 t = 28 Not sure what went wrong after that.
*August 29, 2014*

**math**

didn't we just do one of these with different numbers? Follow the same steps.
*August 29, 2014*

**maths**

since distance = speed*time, if the still-water speeds of the men are a and b, (a-.5)(5) = 10 (b+.5)(3) = 10 5a - 5/2 = 10 3b + 3/2 = 10 b-a = (10 - 3/2)/3 - (10+5/2)/5 = 1/3
*August 29, 2014*

**math**

draw horizontal and vertical lines from the two points to form a rectangle. The distance between them is just the diagonal of the rectangle. That is why the distance formula is d = √(10^2+2^2) = √104 The distance formula is just the Pythagorean theorem value.
*August 29, 2014*

**math**

For the x-coordinate, C is 6 units to the right of E For the y-coordinate, C is 2 units above E So, since E is the midpoint, the other endpoint is 6 to the left and 2 below E, or (-7,-2) Algebraically, you know that if the ends are C and D, (Cx+Dx)/2 = Ex (Cy+Dy)/2 = Ey, so (5...
*August 29, 2014*

**math**

the roots are x = (8±√(64-4m))/2 = 4±√(16-m) So, we have 4+√(16-m) = 4-√(16-m) + 4 2√(16-m) = 4 √(16-m) = 2 16-m = 4 m = 12 So, the function is x^2-8x+12, and the roots are 2 and 6
*August 29, 2014*

**Markups and markdowns**

p(1-.30) = 20.00 Now just solve for p
*August 29, 2014*

**math**

since cot 30 = √3, the ratio of the horizontal distance x to the height h is x/h = √3 so, if the height is increasing at 2 m/s, the man approaches the wall at 2√3 m/s
*August 29, 2014*

**Calculus**

I see the typo as specifying feet. In metric units, g=9.8, or roughly 10, so Jacke, redo the calculations, with g=10 and get the correct answer.
*August 28, 2014*

**Math**

Just start with the left-most digit of each number, and compare corresponding digits. The first time one is greater than the other, that number is the greater. You know that, say, 6 > 2 So, if your two numbers are something like 7836219 7832... you can immediately see that ...
*August 28, 2014*

**Advanced Math**

yes. As long as the GCF is not 1, then since the GCF divides both numbers, it divides their difference. For three numbers, extend the method as for two. Fins all the prime factors and their powers, and pick the highest power of each prime that appears in all three lists. 3 is ...
*August 28, 2014*

**Math Problem (please help)**

break-even is where cost=revenue. So, you want to solve for x where 42.25x + 30000 = 64.95x Next, you want 64.95x = 42.25x + 30000 + 100000
*August 28, 2014*

**math- help needed badly**

If I understand true bearings as relating to true north, then we have a diagram where L is the light A is the initial observation point B is the second observation point In 20 minutes, the ship has traveled 4 miles. AB=4 ∠A = 60.3-37.3 = 23° ∠B = 180-(60.3-20...
*August 28, 2014*

**Math**

try checking some of the related questions below.
*August 28, 2014*

**Math**

since the parabola opens downward, its maximum is at the vertex. As you recall, the vertex of ax^2+bx+c is at x = -b/2a In this case, that is x = 30/6 = 5. I expect you can evaluate P(5).
*August 28, 2014*

**Maths**

since 7+9 = 16, n+2 = 16 I expect you can figure out now what n is.
*August 28, 2014*

**Sorry, Emma.**

AT last someone who meant what she wrote, rather than just being careless with parentheses. However, I'm surprised that given my solution, you did not just fix my function and apply the same logic.
*August 27, 2014*

**AP Calc. AB**

If you mean f(x)=x^(3/8), then the slope at any x is f'(x) = 3/8 x^(-5/8) So, when x=4, f'(4) = 3/8 * 4^(-5/8) = 0.157
*August 27, 2014*

**Math**

P(1+.10/12*15)=20000 P = 17,777.78
*August 27, 2014*

**Precal**

for degrees, the boundaries are at 0,90,180,270,360 for radians, that is 0,pi/2,p,3pi/2,2pi Assuming you can work with fractions, there should be no problem. What are your responses?
*August 27, 2014*

**Math**

at $2/week, it takes 7 weeks for the sister to save $14 more. So, in those 7 weeks, Rina has saved 4.50*7 = $31.50
*August 27, 2014*

**Honors Algebra II**

well, from the first equation, y = (6x-20)/4 Substitute that into the second and you have 3 = (18/5)x + (21/10)(6x-20)/4 x = 2 So, y = -2
*August 27, 2014*

**Math- urgent**

t+b = 21 - counting burgers 1/4 t = 1/3 b - weighing burgers t=12 b=9
*August 27, 2014*

**Algebra**

Thank you
*August 27, 2014*

**Algebra**

So in an equation if there is an alphabetic entity the equation is open? My answer is yes
*August 27, 2014*

**College Algebra**

3/3 + 2/3 = 5/3 Divide $21 into 5 parts, and A pays for 3 and B pays for 2. 21/5 = 4.20 A pays 3*4.2 = 12.60 B pays 2*4.2 = 8.40 total: $21.00
*August 27, 2014*

**algebra**

20x + 14*24 = 16(x+24)
*August 27, 2014*

**Algebra**

if there are x dollar increases, then the revenue (price * # cars) is (4800-800x)(x) = 4800x - 800x^2 That's just a parabola, so the maximum revenue is at the vertex.
*August 27, 2014*

**Algebra**

ummm, 40*12, don't you think? The capacity of the tank does not make any difference.
*August 27, 2014*

**math**

(a) 200+25*10 = 450 -- you are correct (b) 200*1.15^10 = 809.11 (c) Hmm. seems kind of odd. If you tabulate the amounts held after n passes, n Mary John 0 200 200 1 225 230 John has more after a single pass, and gains faster and faster on every pass thereafter. You sure that ...
*August 27, 2014*

**math**

sounds good to me. Move either of the other coins to the other end of the line, and now the dime is at the end of the line.
*August 26, 2014*

**Math-help please**

since the same scale applies to both height and width, 220/25 = x/10
*August 26, 2014*

**math**

certainly not geometric. The numbers are 201,207,... The common difference is 6. Normally, numbers divisible by 3 have a difference of 3, but you need to skip the even ones, making the difference 6.
*August 26, 2014*

**math**

out = 100 + 5*in
*August 26, 2014*

**Advanced Math**

all data are already integers 3,4,6,6,6,6,7 5,8,9,12,12,18,21 No idea what "opposite" means, unless you mean negative.
*August 26, 2014*

**Calculus**

f◦g = f(g) = g^2-3 = (5x+2)^2-3 g◦f = g(f) = 5f+2 = 5(x^2-3)+2 f◦f = f(f) = f^2-3 = (x^2-3)^2-3 g◦g = g(g) = 5g+2 = 5(5x+2)+2 the domain of all polynomials is all real numbers.
*August 26, 2014*

**math**

1 * 26^3 * 10^4 = 175760000
*August 26, 2014*

**math**

correct
*August 26, 2014*

**math - eh? eh?**

I have no idea what your final line 2x6 is supposed to mean. The only equation I see is x^2-x^2=x which is nonsense. Better repost the original problem.
*August 26, 2014*

**math**

a = b+15 a-5 = 4(b-5) a=25 b=10 5 years ago, a was 20 and b was 5
*August 26, 2014*

**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*

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