Monday

July 28, 2014

July 28, 2014

Total # Posts: 24,000

**Inequalities & Absolute value**

I get -4/3 < x < 1/2, so only (ii) works. In this case, it's easy enough just to substitute in each of the values to see which works in both cases. Always keep in mind the V shape of absolute value graphs. See http://www.wolframalpha.com/input/?i=plot+y+%3D+|2x%2B4|%...

**Math**

Since you are adding 20 to each number, just add 20*21 to the total. Or, thinking of the values as an arithmetic progression, recall that the sum of n terms is Sn = n/2 (T1+Tn) With a=40,d=1, S21 = 21/2 (40+60) = 1050 With a=60,d=1, S21 = 21/2 (60+80) = 1470 Note that 1470 = 1...

**algebra**

figure the common denominator. Then, using that, add/subtract the values: 1/3 + 3/7 21 = 3*7, so you really have (1*7)/(3*7) + (3*3)/(3*7) = (7+9)/21 = 16/21

**algebra**

I'd guess that depends on the size of the tank.

**math**

The smallest such number is 3*5*7 = 105 Since 64 <= 105 < 128 or 2^6 <= 105 < 2^7 That will require 7 digits: 1101001

**algebra**

complex zeros come in conjugate pairs. Just as in the first problem above. So, what do you think?

**algebra**

(x-7i)(x+7i) = x^2+49

**algebra**

(12-2x)(10-2x) = 80 Solve that for x, or just note that 80 = 10x8, so both dimensions are reduced by 2", making a 1" margin all around.

**math**

A1/A2 = (s1/s2)^2 = (2/√2)^2 = (√2)^2 = 2 (B)

**math**

in each suit of 13 cards, there are 5 even cards. That means, there are 8 others. So, P(~even) = 8/13

**Algebra**

just recall that a^2-b^2 = (a-b)(a+b) So, first, make sure that both terms are perfect squares. In this case, they are not. However, if you factor out a 2, you have 2(49-4w^2) 49 is 7^2 and 4w^2 = (2w)^2. So, we now have 2(7-2w)(7+2w)

**math**

look up you standard form for ∫√(u^2-a^2) du Now, if you let u = 2x, you have u^2 = 4x^2 du = 2 dx, so dx = du/2 Also, let a = √3 So, now your integral is 15/2 ∫√(u^2-a^2) du and just go for it.

**math**

a+b+c+d+e = 35 (mean=7) c = 7 (median) e = a+7 (range) a+b+7+d+a+7 = 35 2a+b+d = 21 If a=1, b+d=19 But b<=7 and e=8 1,b,7,d,8 But, if b<=7, and d<=8, no go If a=2, b+d=17 2,b,7,d,9 same problem as above If a=3, b+d=15 d<=10, so b>=5 so we can have 3,b,7,d,10 as ...

**Math**

all the prime factors of c are less than p, so n has 4 unique prime factors. n^2 does not have any new prime factors, so it also has 4.

**algebra**

3.14 * 1/1000 and you can massage that as you will.

**Math**

just replace each expression in parentheses, and you will see that the values are the same. An illustration of the associative property of addition.

**algebra**

mary's age 5 years ago is x-5 1/3 of that is (x-5)/3 3 less than that is (x-5)/3 - 3 Now, that may not be the answer, since it's difficult to parse just who's how old when, with your unusual verb tenses.

**math**

If there are t tourists and r rooms, t = 6r-9 t = 3(r+4) 6r-9 = 3r+12 3r = 21 r = 7 so, t=33

**math**

(ab)^2 = abab If abab = aabb then the middle ba = ab

**math**

y" + 9y = cos2x+sin2x You know that y"+9y=0 has solutions y = a cos3x + b sin3x so the solution here is y = a cos 3x + b sin 3x + (cos2x+sin2x)/5

**Algebra**

first step: expand the polynomial. You will see that x^3 goes away, leaving you with just 3x^2+2x = 85 Now just solve as you normally would: 3x^2 + 2x - 85 = 0 (3x+17)(x-5) = 0

**104B**

500*2.5*r = 40 r = 0.032

**math**

19/3x - 20

**Math**

if x at 7%, then .07x + .08(x+6000) = 7.80 Fix the interest amount and solve for x. And pay more attention to what you type.

**Math**

4c + 5m = 25.50 2m = c+1.75 Now just solve the two equations, using your favorite method. I get (A) assuming a missing decimal point.

**Math - incomplete**

some data missing here. Read what got posted and fill in what got omitted.

**physics 1**

if the initial velocity was v, v - 3.55*2.13 = 4.90 v = 12.46 m/s the displacement s is thus s = 12.46*2.13 - 3.55/2 * 2.13^2 s = 18.49 m

**math**

we want to approximate ∫[0,4] e^(3√t) sin 3t dt So, divide the interval[0,4] into 8 pieces, each of width 0.5 Now apply each Rule named above, calculating f(x) for each value from 0 to 4, and add up the areas of all the rectangles or trapezoids. There are online ca...

**Heron's formula**

anything to do with the area of triangles. Just look around your home and see what triangles you might be interested in. Painting gables, carpeting a corner of a room, etc.

**Math - bzzzt**

Sorry. If PQ joins the midpoints of AB and AC, then it is parallel to BC and half its length. You cannot have PQ=2 and BC=3.

**Chem**

You have: .0286*.169 = 0.004833 moles of Na3PO4 .0397*.255 = 0.010124 moles of Ca(NO3)2 If the reaction is 2Na3PO4 + Ca(NO3)2 = 2NaNO3 + Ca(PO4)2 then you need 2 moles of Na for each mole of Ca. Since there is extra Ca, you will wind up with .09666 moles of Ca(PO4)2 Just multi...

**algebra 1**

well, the triangle obviously has area = 12 So, the whole outfit has area 6x+12. So, 6x+12 = 150 6x = 138 x = 23

**math**

surely you can count days on a calendar...

**Math**

If you subtract the 2nd equation from the first, you get 4x-3y-4 = 0 4x+2y+5 = 0 ---------------- -5y-9 = 0 now add 9 to both sides: -5y = 9 now divide by -5: y = -9/5 Knowing that y = -9/5, just plug it into either of the original equations and then solve for x. The work is s...

**algebra**

20m

**math**

Just think about it. Every second it travels 1 meter. So, 5 seconds ago it was down 5 meters. now think forward in time for 120 meters above.

**math**

if now is time t=0, then the temperature at any time t is -2t. So, we want -2(-3) and -2(5)

**Math**

that would be 420/12 = ?

**math**

If they were laid out flat, they'd each be 4.8 units long. So, they must be more than that, and since 4.8 is not an acceptable answer, 4.9 is what we have to go with.

**math**

The midpoint of two points is (6,2). One of the points is (3,5). Since the two ends must be equidistant from the midpoint, 3 = 6-3, 9 = 6+3 5 = 2+3, -1 = 2-3 So, (9,-1) is at the other end.

**Physics**

it gained (18-12)=6 m/s in (4-2)=2 seconds, so that is 6/2 = 3 m/s^2 In the first 2 seconds, then, it gained 6 m/s, so it started at 6 m/s.

**geometry**

hmmm. you have the formula. What's the trouble? The same formula applies for ym: (y1+y2)/2 A value midway between two others is just their average: the sum/2.

**10 gr math**

ok. plug in the data and evaluate: the distance between (1,3) and (7,2) is √((7-1)^2 + (2-3)^2)

**Chemistry**

When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...

**algebra**

A. No - the decrease in intensity is not a constant, but depends on the previous intensity. The intensity I of x meters of cable is I = 1500 * 0.964^x C yes you can probably write that one on your own.

**Math**

if there are 8x tools, then there are 3x shovels and 5x rakes. So, 5x = 3x+10 x=5 so, there are 15 shovels and 25 rakes

**Math**

If you can find the midpoint of a line segment know that the slope of the perpendicular is -1/(slope of line segment) remember the point-slope form of a line then all of these problems are straighforward. Review those topics, give it a try, show where you get stuck, if you do.

**Non**

just a note: that's mu sub-k, not "muse of k" µk

**Volume**

Just figure the tank's volume (66.75*132*10) and divide it by 231 in^3, the volume of a gallon.

**algebra**

x^2+8x = x(x+8) Pick any positive value for x and you get a rectangle.

**math**

take a look at the graph of (1+.10/n)^(n) It shows the effective yield of 10% compounded n times per year. It approaches continuous compounding, e^.1 http://www.wolframalpha.com/input/?i=plot+y%3D%281%2B.1%2Fn%29^n+for+n+%3D+1..40%2C+y%3De^.1

**algebra**

solve it just as you would an equation: 42 = -6d -7 = d However, multiplying and dividing by negative values changes the direction of the inequality. So, you have 42 < -6d 7 < -d -7 > d or d < -7 Since you can always add and subtract without changing the direction,...

**science**

I may have messed up the sign change, so double check my math.

**science**

the position falling from a height of h feet is y = h - 16t^2 After t seconds, y=0, so h=16t^2 So, we have (h-16t^2) - (h-16(t-1)^2) = 11h/36 0 - (16t^2 - 16(t-1)^2) = 11(16t^2)/36 32t-16 = 44/9 t^2 11t^2 - 72t - 36 = 0 t = 7.01 So, h = 16t^2 = 786.24 ft

**calc**

first off, I'd use partial fractions: (x^3 -3x^2 -9)/(x^3 -3x^2) = 1 + 1/x + 3/x^2 - 1/(x-3) There are no discontinuities on [4,5], so it's straightforward. The integral is just x + logx - 3/x - log(x-3) so we get (5 + log5 - 3/5 - log2)-(4 + log4 - 3/4 - log1) = 23/20...

**Math**

54° is 3/20 of a full circle. SO, the whole circumference 3/20 c = 9 c = 60

**ALGEBRA - eh?**

cannot parse the "8n 12" part

**math**

The solution of this equation is so complex, I have to assume you're doing numerical methods or something. Take a peek at http://www.wolframalpha.com/input/?i=sin^6x+-sin^2+4x+%3D+sin2x+sin10x for further insight.

**trigonometry**

well, we have h/120 = tan 10°18' h = 21.8 ft

**Maths**

y = 1/x y' = -1/x^2 y'(1/4) = -1/(1/16) = -16 I think you lost a minus sign. And, of course, you have displayed the usual sloppiness with parentheses.

**math**

I don't see any way. Each odd number is of the form 2k+1 Add up 7 of those, and you have a sum of the form 2n+7 = 20 But 2n cannot be 13. The sum of an odd number of odd numbers cannot be even.

**Math**

well, ∫ lnx/x^2 dx = -(lnx + 1)/x recall that ln √x = 1/2 lnx let u = 3-5x^2 and du=-10x dx That gives you ∫ -1/10 2^u du which is just 2^u / ln u Now it's pretty straightforward

**Math**

well, we know that d/dx arccosh u = 1/√(u^2-1) du So just use the chain rule, and note that (2x-1)^2-1 = 4x^2-4x

**physics**

(i) the range for angle θ is R = v^2/g sin2θ (ii) Naturally max height is reached at θ = 45° (iii) given the range, and that horizontal velocity is constant, getting t is easy. So, what do you get?

**Algebra**

y(x) = 3*2^x y(x+1) = 3*2^(x+1) = 3*2*2^x = 2y(x) So, each year y doubles.

**Wood working**

Of course, if each stripe is that wide, there will be no space between them, so the board will just be solid white. Now you have to decide how much blank space to allocate between the stripes, and whether the end stripes will reach to the very ends of the board, or whether the...

**Math-Parabolas**

If you mean y = x^2+9 you can see that since x^2 can never be less than zero, the vertex is at x=0. Since y=9 there, the vertex is at (0,9) Or, recalling that the vertex of y = (x-h)^2 + k is at (h,k), note that we have h=0 and k=9.

**pre cal**

since complex roots come in pairs, we have (x-3)(x+13)(x-(5+4i))(x-(5-4i)) (x-3)(x+13)((x-5)-4i)((x-5)+4i) (x-3)(x+13)((x-5)^2+4^2) (x^2+10x-39)(x^2-10x+41) x^4 - 98x^2 + 800x - 1599

**Science**

Some of the CO2 was lost as a gas. Also, depending on how hot the mixture became, maybe some of the water was lost as steam.

**pre-cal**

However, assuming the chopper starts at (0,h) and the vehicle starts at (0,0), after t minutes the chopper and vehicle are at (2640t,h - 5/33 t) and (4224t,0) So, the line between them has slope (h-5/33 t)/(1584t) Now you have the angle tanθ = (h-5/33 t)/(1584t) so you ca...

**pre-cal - incomplete**

So the helicopter drops 400 feet. How high was it when it started its descent? what is "the vehicle"? Is it a car driving directly underneath the chopper? Did we start at t=0 when the chopper was directly above "the vehicle"? Which angle of depression? chop...

**maths (exponents**

Well, just using brute force, we have b/(b+ab+1) + c/(c+bc+1) + a/(a+ac+1) expand all that over a common denominator, and you get (a^2b^2c + a^bc^2 + 2a^2bc + a^2b + ab^2c^2 + 2ab^2c + 2abc^2 + 6abc + 2ab + ac^2 + 2ac + a + b^2c + 2bc + b + c) / (a^2b^2c^2 + a^2b^2c + a^2bc^2 ...

**Trigonometry**

the angle is x, where cos x = 15/20 the area is 15√(20^2-15^2)

**Algebra**

1.2^-t = 1 / 1.2^t That is clearly not the same as 1 / 2^t recall that x^-a = 1/x^a

**Maths**

Since the diagonals of a rhombus are perpendicular, and all four sides are the same length, the rhombus can be divided into four right triangles with one leg of 5 and an hypotenuse of 8. So, the other leg is √39 So, the area of all four triangles is 10√39 m^2 Multi...

**maths**

I see a lot of perfect cubes there 8x^3 - 27y^3 = (2x-3y)(4x^2+6xy+9y^2) Hmmm. No joy there. wolframalpha.com factors it, but I can see no motivation for trying (2x-3y+5) as a factor.

**math**

area of ABCD = ab area of ABCD+path = (a+2c)(b+2c) area of path = (a+2c)(b+2c)-ab

**Calculus help**

for multiple periods per year, just divide the interest rate and multiply the number of years. (b) P = 2000(1+.057/12)^(12*10) and similarly for other divisions of the year into multiple parts.

**Algebra**

C is correct

**calc**

Note that since (x-3)^2 = x^2-6x+9, what you have is ∫√(25-(x-3)^2) dx If u = x-3, du = dx, and it's just ∫√(25-u^2) du which you should know. If not, just use the trig substitution u = 5sinθ The answer can be seen at http://www.wolframalpha.co...

**Algebra**

continuously: A(t) = 1000*e^.08t daily: A(t) = 1100(1+.08/365)^(365t) so, when are they equal? When 1000 e^.08t = 1100(1+.08/365)^(365t) t = 10,873 years. continuous compounding is so close to daily compounding (1.08328% vs 1.08327%) that it takes a long time to overcome the l...

**MATH**

look at the differences: 2,3,5,7 My guess is that the next difference will be 11, the next prime. If not for the 2, I'd have said odd numbers were the differences.

**maths**

The formula must have a typo. If not, you are saying that r(x) = 600x, or $600 per person. I suspect that the problem is incorrectly stated. It appears that the $20 discount is only being applied to those people in excess of the 25-passenger price break. That explains the -20x...

**maths**

40m north and 40m south cancel out, leaving only the 30m east.

**maths**

draw a diagram, and you will see a 3-4-5 right triangle. So, the final displacement is 5, the hypotenuse. The direction (measured from due east) is x, where tan(x) = 40/30

**maths**

-j x i = k

**maths**

zero

**maths**

|A+B|^2 = 2^2 + 2^2 - 2(2)(2)cos 120°

**math**

.327... = 327/999 = 109/333 1000x = 327.327327... x = 0.327327... 999x = 327

**Maths**

(i) 3*b = 2*3+b = 6+b b*5 = 2*b + 5 = 2b+5 so, 6+b = 2b+5 b = 1 (ii) 3*d = 6+d d*(3*d) = 2d+(6+d) = 3d+6 d*3 = 2d+3 (d*3)*d = 2(2d+3)+d = 5d+6 so, 3d+6 = 5d+6 d = 0

**math**

first, note that if u = 6x, you have 1/6 ∫ sin^5 u du = 1/6 ∫sin^4(u) sinu du = -1/6 ∫(1-cos^2 u)^2 (-sinu du) If v = cos u, then dv = -sinu du, and you have -1/6 ∫(1-v^2)^2 dv just expand that and it's a regular old polynomial.

**Physics . pls help me :)**

we need to find where the cars have gone the same distance. So, 0 + 0t + (1/2)(2)t^2 = 30 + 4t that is, t^2 - 4t - 30 = 0 t = 7.83 Just plug that value in for t to see where they met.

**math - eh? eh? eh?**

that cannot possibly be how the question was presented. why not post it as it was given?

**mathematics**

well, just plug and chug: u = ln(x^2+y^2) - ln(x+y) ∂u/∂x = 2x/(x^2+y^2) - 1/(x+y) ∂u/∂y = 2y/(x^2+y^2) - 1/(x+y) x ∂u/∂x + y ∂u/∂y = 2x^2/(x^2+y^2) - x/(x+y) + 2y^2/(x^2+y^2) - y/(x+y) = 2(x^2+y^2)/(x^2+y^2) - (x+y)/(x+y) = 3 so...

**mathematics**

the volume is just |u•v×w| That's pretty straightforward. What do you get?

**mathematics**

assuming you meant t=π/6 The unit tangent vector T(t) = r'/|r'| = cot(t) i - tan(t) j ------------------------- tan^2(t) + cot^2(t) The unit normal is T'/|T'| = -(csc^2(t) i + sec^2(t) j) ---------------------------------- csc^4(t) + sec^4(t) which at t = ...

**mathematics**

find a line in each plane the cross product of those two vectors is perpendicular to them both. Then translate the vector so it passes through P.

**mathematics**

for all x ≠ -3, (x^2-9)/(x+3) = x-3 So, the limit as x->0 is just -3. How did you get -6?

**shizo homework dump**

if you're going to just dump your homework, at least use a consistent name... Lots of problems, no evident effort displayed on your part.

**maths**

R(x) = 120x if x <= 25 100x is 25 < x <= 40

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