Thursday

September 18, 2014

September 18, 2014

Total # Posts: 25,054

**math**

what's to explain? Write the facts in symbols: p^2 + (p+5)^2 = 625 Now just solve for p and find p+5
*September 2, 2014*

**math**

(x+y)y = 70 (y-x)x = 12 now proceed
*September 2, 2014*

**algebra**

good work. Just for the future, recall that the domain of all polynomials is all real numbers.
*September 2, 2014*

**math**

221 = 13*17 you can use that to answer your question, rather murkily stated.
*September 2, 2014*

**Physics**

try C(x) = 4.00 + 0.40⌈10x⌉
*September 1, 2014*

**Geometry**

clearly, HJ+JK=HK, so x/4 + 3x-4 = 22 now just solve for x and evaluate the distances
*September 1, 2014*

**KIPP Believe**

divide the 740 into 20 equal parts of x each. There are thus 17x students and 3x faculty. So, 17x+3x=740 20x=740 x=37 So, there are 17*37 = 629 students 3*37 = 111 faculty
*September 1, 2014*

**Math Proof**

we want to show that |x1 + x2 + ... + xn| <= |x1| + |x2| + ... + |xn| Let's take n=3 We know that the inequality holds for n=2, so now we have |(x1+x2)+x3| <= |(x1+x2)| + |x3| But, we already know that |x1+x2| <= |x1|+|x2|, so we now have |x1+x2+x3| <= |x1|+|x2...
*September 1, 2014*

**Math**

Only the student can tell what was intended. We've provided two solutions, so our work is done here.
*September 1, 2014*

**Math**

Not quite 9^(1/2) = 3 but (n^4)^(1/2) = n^2 so the answer is 3n^2
*September 1, 2014*

**Math**

looks good to me.
*September 1, 2014*

**MA 112**

for a proportion, the two ratios must be equal So, a = a+b which can only happen if b=0. But, we cannot divide by zero, so a/b and (a+b)/b would both be undefined.
*September 1, 2014*

**math**

the numerator is a whole number, and it is multiplied by the other whole number.
*September 1, 2014*

**Math**

I get x^2+x-6 in the numerator, so better double-check your math.
*September 1, 2014*

**Math**

If there were x liters to start, then we have the following table: month water at end of month 0 x 1 x/2 + 1 2 (x/2 + 1)/2 + 1 = x/4 + 3/2 3 (x/4 + 3/2)/2 + 1 = x/8 + 7/4 ... n x/2^n + (2*2^n-2)/2^n = (x + 2*2^n-2)/2^n So, at the end of the 5th month there were (x+62)/32 = 4 x...
*September 1, 2014*

**math**

A. You can factor out 3/√x to get 3/√x (x^2-3x+2) 3/√x (x-1)(x-2) Or, if you don't want that extra 1/√x, now you can divide by it to get 3(√x - 1/√x)(x - 2) or 3(x-1)(√x - 2/√x) B. xy(x^2-4) xy(x-2)(x+2)
*September 1, 2014*

**math**

what is #x ?
*September 1, 2014*

**algerbra**

okay - your turn. Check the solutions to your other problems, and take a stab at it.
*September 1, 2014*

**algerbra**

Hint: graph the two lines. Note where they intersect.
*September 1, 2014*

**algerbra**

Using elimination, double the first equation and rearrange things a bit to get 6x+4y = 8 5x-4y = 3 Now add them up and it's clear that 11x = 11 and the rest is easy
*September 1, 2014*

**math**

If x at 10%, the rest (8900-x) at 9%, then calculate the interest: .10x + .09(8900-x) = 831 x = 3000
*September 1, 2014*

**math**

You need the Binomial Theorem: (a+b)^n = a^n + n a^(n-1) b + ... So, you have (3x-2)^3 = (3x)^3 - 3(3x)^2(2) + 3(3x)(2^2) - 2^3 = 27x^3 - 54x^2 + 36x - 8 (4x+5)^2 = (4x)^2 + 2(4x)(5) + 5^2 = 16x^2 + 40x + 25 Subtract them to get 27x^3 - 70x^2 - 4x - 33
*September 1, 2014*

**MA112**

Look at the common factors on both sides d(a-b) = b(c-d) What you want to do now is unclear, but go for it.
*September 1, 2014*

**math**

as with the other, just plug in the value for x: -2(4^2) + 5(4) - 10
*September 1, 2014*

**math**

That would be 3(-2)^2 - 2(-2) + 5 = 3(4)+4+4 = 20
*September 1, 2014*

**algerbra**

If there are no typos, then 8 = 6x-4 means x=2 So, that means that -3(2)-4y=2 y = -2
*September 1, 2014*

**algebra**

the equation for the height is h = 80 + 960t - 16t^2 As you recall, the vertex (maximum height) is at t = 960/32 = 30 Now just figure h(30)
*September 1, 2014*

**math packet**

(4)(-3/5)(10/-9) = -120/-45 = 8/3
*September 1, 2014*

**math**

one of my favorite sequences. Thanks for sharing.
*September 1, 2014*

**math**

just solve for p in -2000p² + 2000p + 1700 = 5000 The problem is that D has a maximum of 2200 when p = 0.5 I suspect a typo somewhere. Is D the monthly demand, or the weekly demand?
*September 1, 2014*

**math**

x^2 + (x+4)^2 = 20^2 Think of a scaled-up 3-4-5 triangle.
*September 1, 2014*

**Algebra 2**

Rearrange things a bit and you have 2m^2-8m + 6n^2-5n^2 2m(m-4) + n^2 It's kind of a strange problem; is there a typo in there somewhere?
*September 1, 2014*

**PRE CALC**

Just list the facts as given: u+f+t = 39 t = u-16 u+5f+20t = 208 Now just solve as usual
*August 31, 2014*

**math**

length=2w 2(w+2w) = 60 ...
*August 31, 2014*

**math**

If q quarts are to be drained, then .40(12-q) + 1.00q = .60(12) ...
*August 31, 2014*

**algebra**

S = P(1 - 0.25)
*August 31, 2014*

**stats**

since 2500 is exactly the mean (0 std away), look up P(Z < 0) in your standard table. Or, just consider the data and pick what seems reasonable in that case.
*August 31, 2014*

**math**

If x L are added, then .01(40) + .04x = .02(40+x) ...
*August 31, 2014*

**Math**

see related problems below
*August 31, 2014*

**physics**

(E).893J
*August 31, 2014*

**Math**

When you solve for a variable, you want it all by itself: P = I/rt r = C/2π
*August 31, 2014*

**Algebra**

#1 correct #2 If y=1, 4y-2=2 and 3*2 is not 18 You should have done 3(4y-2) = 18 4y-2 = 6 4y = 8 y = 2
*August 31, 2014*

**AP Calc. AB**

well, since -0 = 0 and -8 = -(8), it should not be hard to make the required change to the function I provided. I mean, you do remember your basic algebra, right?
*August 31, 2014*

**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*

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