Saturday
August 30, 2014

# Posts by Steve

Total # Posts: 24,483

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
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

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

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

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

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

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

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

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

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

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