Saturday

October 25, 2014

October 25, 2014

Total # Posts: 26,089

**physics**

The boat and its contents are floating, so its general density is less than that of water. So, the boat displaces a volume of water which has the same mass as the boat. But a rock is denser, so it displaces less water. SO, the amount of water displaced drops when the rock ...
*October 1, 2014*

**math**

d and e are obviously out, since they do not start with 3. Of the others, which has terms that increase by 2?
*October 1, 2014*

**Math**

(3*7 + 9*8)/(8*7)
*October 1, 2014*

**math**

350P3 = 350*349*348
*October 1, 2014*

**Math**

why don't you give it a shot? Just start listing them, but don't list any letter twice.
*October 1, 2014*

**Math**

-2(-2)+10 is not 8 use the slope-intercept form: y-8 = -2(x+2) y = -2x + 12
*October 1, 2014*

**Find the pattern**

If you start with #8, you can pin down certain days. Surely you can make some headway in this.
*October 1, 2014*

**Pre-caluclus**

well, I don't know what "7500 1" means, but I'll just call it 7500 and you can fix it as needed. For the inverse, swap variables and solve for y: t = 7500 + 749e^(-0.15y) t-7500 = 749e^(-0.15y) e^(-0.15y) = (t-7500)/749 -0.15y = log[(t-7500)/749] y = -log[(t-...
*September 30, 2014*

**Math**

1 in = 2.54 cm, so you have (2*36 + 2*12 + 5)(2.54) = 256.54 cm Do the other the same way. Next time you get a wrong answer, show your work, and we can fix what's wrong.
*September 30, 2014*

**Math**

wow, didn't get far, eh? Just start solving for y: x = (1+2y)/(1+y) x(1+y) = 1+2y x + xy = 1 + 2y x-1 = 2y - xy x-1 = y(2-x) (x-1)/(2-x) = y Easy, no? The domain of f(x) is all real numbers except where the denominator is zero. That is all values except -1. The domain of ...
*September 30, 2014*

**Math**

But, just to get you started, if there are $x at 6%, the rest (1000-x) is at 9%. So, add up the interests earned: .06x + .09(10000-x) = 750.00 Now just crank it out.
*September 30, 2014*

**Geometry**

the hypothesis comes after "if". so your first answer is correct.
*September 30, 2014*

**Math**

13 and 15 occur most frequently. The center value is 15. Depending on how many other numbers there are, just start putting them on both sides of 15 (the median), making sure they always add up to 15*n, where there are n numbers. And make sure that 13 and 15 occur the most.
*September 30, 2014*

**Math z-scores**

you can play around with Z stuff at http://davidmlane.com/hyperstat/z_table.html It shouldn't take long to answer your question
*September 30, 2014*

**algebra 2**

(ab)^2 - 2^2
*September 30, 2014*

**Precalculus**

P(x) = (x-4)(x+5)^2 now it's easy, right?
*September 30, 2014*

**Algebra 1**

#1, Clearly not true for x=10 Try C if it's supposed to read 4x^2 <= (4x)^2 because (4x)^2 = 16x^2 #2 A, just as in #1. (5x)^2 = 25x^2 >= 5x^2 take a look at wolframalpha.com, where you can plot several functions on the same axes. For example, http://www.wolframalpha...
*September 30, 2014*

**Trigonometry**

The length of the ladder does not matter. We are told that cos x = 1/4 x = 75.52°
*September 30, 2014*

**Math**

4(2x + 3) = 2(3x - 4) 8x+12 = 6x-8 2x = -20 x = -10 Bzzzt 6 - a = 1/3(9a - 18) 18-3a = 9a-18 12a = 36 a = 3 correct 3(4x - 3) - 7x = 5x - 9 12x-9-7x = 5x-9 5x-9 = 5x-9 correct - the same line 4(2x - 3) - 4x 8x-12-4x 4x-12 2(2x-6) 4(x-3) only your first choice is correct
*September 30, 2014*

**Trigonometry**

You have to know the size of the court. Assuming the spike is driven parallel to the side lines, then if the distance to the far line is x, and assuming you want the angle from the vertical (otherwise you'd be asking for the minimum angle), then x/2.44 = tan θ See how...
*September 30, 2014*

**MATH HELP PLEASE**

(5.1 × 10^3) • (3.2 × 10^3) (5.2×3.2)×(10^3×10^3) 16.32×10^6 But that is not scientific notation. The leading number must be at least 1.0, and less than 10, so you need to shift the decimal point and adjust the exponent: 1.632×10^...
*September 30, 2014*

**Trigonometry**

surely you know that cos(180°) = -1 so, arccos(-1) = 180°
*September 30, 2014*

**Pre-Calculus/Trigonometry**

you could eliminate the x by doing some judicious multiplying: 24x-6y = 15 -24x+6y = 14 Now add the equations to get 0y = 29 BZZZT! No solution
*September 30, 2014*

**math**

got me. What is R?
*September 30, 2014*

**College Algebra**

since time = speed * distance, then if her outbound speed was x, then 12/x + 12/(x-10) = 1 x = 30 or 4 Check: 12/30 + 12/20 = (24+36)/60 = 1 The other solution to the equation is x=4. Why is that not useful?
*September 30, 2014*

**Math**

#1 EVERY function has a domain. A function is a relation between two sets: the domain and the range. The domain of any polynomial function is all real numbers. #2 If you mean f(x) = 1/(x+5), then you are correct (except you meant x ≠ -5) #3 correct If you meant √(x+2)
*September 30, 2014*

**Math**

as with any vector of length r on an angle of t, x = r cos(t) y = r sin(t) So, plug in your numbers.
*September 30, 2014*

**math**

98 - (-94) = 98+94 = ?
*September 29, 2014*

**Precalculus**

use the vertical and horizontal line tests. If no line cuts the graph in more than one place, the function is 1-1 and has an inverse. That is, each x value maps to exactly one y value, and vice-versa.
*September 29, 2014*

**horizon elementry**

v = at, so 8 = a(.5) a = 16 m/s^2
*September 29, 2014*

**precal**

ok. now what?
*September 29, 2014*

**Precalculus**

Look at the bottom row of the table, dude!
*September 29, 2014*

**Material Behavior**

I don't know what F is, but dU/dr = Am/r^(m+1) - Bn/r^(n+1) So, plug in r0 and you have dU/dr(r0) = Am/r0^(m+1) - Bn/r0^(n+1)
*September 29, 2014*

**Math**

almost. 3/7 = .4286 so -3 3/7 is 2nd in the list
*September 29, 2014*

**Algebra**

it means it is ill posed. The math is correct, but the problem doesn't take into account real-world conditions. Just ignore it, as this is an algebra class, not a physics class. Still, you might point it out to the teacher, not that it will do any good.
*September 29, 2014*

**Algebra**

well, clearly the temperature is now -247 - 2*11 = -269 The only problem is that hydrogen freezes at -259
*September 29, 2014*

**Math**

36+81 = 9(4+9) or 3(12+27)
*September 29, 2014*

**Geometry**

If the numbers are m and n, and m is even, then m=2k. If the sum is even, say 2x, then 2k+n = 2x n = 2x-2k = 2(x-k) So, it is clear that n is also even, since it is a multiple of 2.
*September 29, 2014*

**math**

2*16 + 2*3 = 38 or, 2(16+5)-4 = 38 why the two ways of writing the expression?
*September 29, 2014*

**Math**

recall that (a+b)(a-b) = a^2-b^2 so, (3+√5)(3-√5) = 9-5 = 4 So, to simplify such fractions, look for the "square conjugate" if you will, of the denominator. 4/(3+√5) = 4(3-√5) / (3+√5)(3-√5) = 4(3-√5)/4 = 3-√5 And do ...
*September 29, 2014*

**Algebra**

recall that (a-b)(a+b) = a^2-b^2 so, (3+√5)(3-√5) = 9-5 = 4 So, to simplify such fractions, look for the "square conjugate" if you will, of the denominator. 4/(3+√5) = 4(3-√5) / (3+√5)(3-√5) = 4(3-√5)/4 = 3-√5 And do ...
*September 29, 2014*

**Math**

4y(2y^4+3y^2+1) 4y(2y^2+1)(y^2+1)
*September 29, 2014*

**math**

1+1+3 = 5 1+2+2 = 5 And you can shuffle those around, making 3+3 = 6 ways to spin 5
*September 29, 2014*

**math**

well, you have 2.47f+54.1 = 166.21 So, |h-166.21| <= 3.72 166.21-3.72 <= h <= 166.21+3.72 and so on
*September 29, 2014*

**math**

f(x-6)+5
*September 29, 2014*

**7th grade math**

good work
*September 29, 2014*

**Pre-Calculus/Trigonometry**

(3 -1)(2) (5 2)(6) = (0) (22)
*September 29, 2014*

**algebra 2**

10 inconsistent 11 consistent dependent 12 consistent independent
*September 29, 2014*

**Pre-Calculus/Trigonometry**

no solutions to x+y = 3 x+y = 4
*September 29, 2014*

**Math (Trig)**

sin2x+sin4x = 2sin3x cosx cos2x+cos4x = 2cos3x cosx Now divide to get tan3x
*September 29, 2014*

**math**

LCM(9,10,14) = 630
*September 29, 2014*

**AP Calc B/C**

If u = e^x, then (e^x)/(1-e^2x)^3/2 dx = du/(1-u^2)^3/2 Now you can easily find that the integral is u/√(1-u^2) which is what Reiny provided.
*September 29, 2014*

**Math**

If it was T, then T-18-8+1+2+4+5 = 34 T = 48
*September 29, 2014*

**math problem solving**

Looks like 5 to me
*September 29, 2014*

**algebra**

34m + 14 = 30m + 22 4m = 8 m = 2
*September 29, 2014*

**math**

some multiples of 7 and 3 are 21 42 63 84 Looks like they all work
*September 29, 2014*

**DISCRETE MATH**

There are 10 letters, with 3 S's, 3 T's, 2 I's, so 10!/(3!3!2!) = 50400
*September 29, 2014*

**engineering science**

the direction remains the same, and v can be found by conserving momentum: 10(8) + 6(4) = (10+8)v
*September 29, 2014*

**Quadratic Functions**

it means, graph the function, and look where it crosses the x-axis. Those are the solutions to f(x) = 0.
*September 29, 2014*

**Help Please**

Of course not. You just need to find x and y such that x^2+y^2 = 361 So, x and y can be 1,√360 2,√357 3,√352 ... √61,√300 √101,√260 and many, many more.
*September 29, 2014*

**SBGG**

the perimeter of the wheel is 7π cm = .07π = .022 m So, 132 m/min * 1min/60s * 1rev/.022m = 100 rev/s
*September 29, 2014*

**Calculus**

just use the chain rule: let r = log(u) dr/dθ = 1/u du/dθ let u = cos^2(v) du/dθ = 2cosv(-sinv) dv/dθ let v = 4θ dv/dθ = 4 So, dr/dθ = sec^2(4θ) (-2cos4θsin4θ) (4) = -8tan4θ Or, you could just recall that log(cos^2(4θ...
*September 29, 2014*

**math mks**

I see it as what was the temperature at 9 am? -8+15 = 7
*September 29, 2014*

**math**

in theory, the ball will never come to rest, since its bounce height is never zero. But, you can see the height of the nth bounce is 7(2/3)^n So, since the distance traveled is both up and down, the sequence is 7 + 2*7(2/3) + 2*7(2/3)^2 + ... so, if r=2/3, = 7 + 14(r+r^2+...) ...
*September 29, 2014*

**Math**

a^x is an exponential function, for any number a. the quotient (hence the ratio) of two polynomials is called a rational function.
*September 28, 2014*

**Finite**

sounds like real life.
*September 28, 2014*

**math**

the fraction riding bikes is 5/32, so of the 800 5/32 * 800 rode bikes.
*September 28, 2014*

**Find the pattern problem solving**

taxi: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 ... bike/trike: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 moped: 9 15 21 27 33 39 45 51 57 truck: 1 25 35 55 49 30 taxis 9 mopeds 5 trucks so, 16 humans: 12 bikes, 4 trikes total wheels: 4*30 + 9*2 + 5*6 + 12*2 + 4*3 = 204
*September 28, 2014*

**MATH**

horizontal has slope 0, so y does not change. So, the line is y=8
*September 28, 2014*

**algebra**

If she spends x hours cycling, the rest (8.5-x) is spent running. Since distance = time * speed, 14x + 8(8.5-x) = 101 Now just solve for x and figure 8.5-x
*September 28, 2014*

**math**

28 - 9x = -12 - 11x as you say, add 9x to both sides, and you get 28 = -12 - 2x Now add 12 to both sides and you get 40 = -2x Now divide by -2 and you get -20 = x There's no reason to add 11x to both sides after all the x's are together. If you did do that, you have 28...
*September 28, 2014*

**statistics**

If the distribution is normal, and the std is high enough, the probability could approach 0.5
*September 28, 2014*

**Algebra**

just use the good old distributive property: (2nr - nr^2)r - (2nr - nr^2) . 2r 2nr^2 - nr^3 - (2nr^2 - 2nr^3) 2nr^2 - nr^3 - 2nr^2 + 2nr^3 nr^3
*September 28, 2014*

**math.help pls**

f(x)=(472 - 2x^2)^1/3 so, f(8) = (472 - 128)^1/3 = 344^1/3 f(8+h) = (472 - 2(8+h)^2)^1/3 = (344 - (32h+2h^2))^1/3 By the binomial theorem, that is 344^1/3 - (1/3)(344^-2/3)(32h+2h^2) + a bunch of stuff with higher powers of h Now subtract and you have f((8+h)-f(8)) = (-1/3)(...
*September 28, 2014*

**Math**

that is correct
*September 28, 2014*

**Calculus**

Reiny's solution is cool, using implicit differentiation. You can also do it by noting that 2 = e^(ln 2) So, 2^x = e^(ln 2 * x) and now use the chain rule: d/dx e^u = e^u du/dx, so d/dx e^(ln 2 * x) = ln2 * e^(ln 2 * x) = ln2 * 2^x
*September 28, 2014*

**AP Calc. AB**

clearly, due to conservation of energy, etc., the arrow will strike with the same velocity as it left, but in the opposite direction. just solve 53t - 0.62 t^2 = 0 t(53-0.62t) = 0 t = 53/0.62 = 85.4839
*September 28, 2014*

**Math**

I think you meant 12a^2 - 5a - 2 = (3a-2)(4a+1) After the path, each dimension is increased by 2, so the new total area is (3a-2+2)(4a+1+2) = (3a)(4a+3) Now subtract the original area to get the area of the path: (3a)(4a+3)-(3a-2)(4a+1) now just simplify that Finally, just ...
*September 28, 2014*

**Math**

since C = 2πr, and speed = distance/time, speed = 2π*15000 mi/18 hr = 5236 mi/hr
*September 28, 2014*

**Math**

only if the angles are right angles so that the diagonal satisfies the Pythagorean Theorem. That is, if 80^2 + 32^2 = 86^2 does it?
*September 28, 2014*

**Pre-Calc (Point of Inter.)**

This problem is discussed at https://answers.yahoo.com/question/index?qid=20101127042533AA17HTY
*September 28, 2014*

**Algebra 2**

For x tables and y chairs, we want to maximize p=100x+80y subject to 3x+2y <= 42 2x+6y <= 42 Now use your favorite linear programming tool to find that they make the most with 12 tables and 3 chairs.
*September 28, 2014*

**Pre-Calc (Circles). Please help :(**

the area of C5 = 25π The area of the annulus between C3 and C4 is 16π-9π = 7π so, p = 7/25
*September 28, 2014*

**math analysis**

we want 1/x < ε 1/ε < x So, if x > 1/ε, 1/x < ε
*September 28, 2014*

**High school algebra**

it is well known (and should be noted by you) that 60 mi/hr = 88ft/s So, you have (88/60)(88) = 129 1/15 ft/s
*September 28, 2014*

**Geometry**

the midpoint is just the average of the two ends, so its coordinates are x = (-4+9)/2 = 5/2 y = (-2-6)/2 = -4 So, M = (5/2,-4) It would be better had you posted your work, so we could verify accuracy or note mistakes. Also, answer keys are sometimes wrong, so that's always...
*September 28, 2014*

**maths**

assuming a constant rate of cooling, it will take x total minutes, where 300 - (300-200)/3 x = 70 x = 6.9 So, in 3.9 more minutes it will have cooled to 70°F
*September 28, 2014*

**geometry**

The two radii are r and 14-r, so πr^2 + π(14-r)^2 = 160π (assuming the strange character is supposed to be pi) r^2 + 196 - 28r + r^2 = 160 Now just solve for r.
*September 28, 2014*

**Calculus Minima Problems**

if she lands a distance x from the closest point on shore, she is 6-x from the village. So, she will row √(x^2+36) km run 6-x km So, her travel time will be t = √(x^2+36)/10 + (6-x)/20 dt/dx = (2x - √(x^2+36)) / 20√(x^2+36) Since the denominator is ...
*September 28, 2014*

**math**

since the figure is isosceles, the diagonals are equal. So, 8x-7 = 5x+2 Now, just solve for x and evaluate the length.
*September 28, 2014*

**trigo**

Ah. If you just wanted to verify that cos 3x = 4cos^3 x - 3cos x, then consider cos 3x = cos(2x+x) = cos(2x)cos(x) - sin(2x)sin(x) = (2cos^2(x)-1)(cos x) - (2sin x cos x)(sin x) = 2cos^3(x)-cos(x) - 2sin^2(x)cos(x) = 2cos^3(x) - cos(x) - 2(1-cos^2(x))cos(x) = 2cos^3x - cosx - ...
*September 28, 2014*

**trigo**

If you want to know the solutions to 4cos^3x - 3 cos x = 0, cos x (4cos^2 x - 3) = 0 so, cos x = 0 or cos x = ±√3/2 You should recognize those values, as they come up often.
*September 28, 2014*

**algebra**

Been there, done that, half an hour ago. It helps if you check your previous posting before doing it again... http://www.jiskha.com/display.cgi?id=1411871416
*September 27, 2014*

**math**

A square is the largest area for a given perimeter, if all sides are included. In this case, one side is not, so suppose the side parallel to the wall has length x, and the other sides have length y. x+2y = 24 The area is a = xy = (24-2y)y = 24y-2y^2 You know that this is just...
*September 27, 2014*

**geometric sequence**

ar + ar^4 = 7/2 ar^2 + ar^5 = -7 divide and you have r(1+r^3) / r^2(1+r^3) = -1/2 1/r = -1/2 r = -2 So, a = 1/4 Check. The sequence is 1/4 -1/2 1 -2 4 -8 -1/2 + 4 = 7/2 1 + (-8) = -7
*September 27, 2014*

**algebra**

Work with the total cost of each part of the mix. They have to add up the the final cost. So, if there are x lbs of $8 coffee, the rest (60-x) has to be the $4 coffee. 8x + 4(60-x) = 5.25(60) x = 18.75
*September 27, 2014*

**Algebra 1**

just collect terms with the same power and then simplify: 6-t-t^4 + 9t+t^4 = (-1+1)t^4 + (-1+9)t + 6 = 8t+6 It is customary to list the highest power first, and then descend. Notice how the t^4 terms vanish because -1+1 = 0
*September 27, 2014*

**algebra**

well, just plug in your numbers: f(35) = 0.019*35^2 + 35 + 14 = 72.275 and so on with other values
*September 27, 2014*

**Algebra**

Since the fence is mentioned, you really should check to see that the ladder will clear the fence. Using the given distances, and similar triangles, if the ladder lies on top of the fence, it will reach up to a height h, found by 9/8 = h/10 h = 12.5 In this case, the ladder ...
*September 27, 2014*

**physics**

5π/4 what about it? It's just a number. It is much easier to use in calculations than its decimal approximation of 3.927
*September 27, 2014*

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