Friday

August 1, 2014

August 1, 2014

Total # Posts: 24,054

**Math - Algebra2**

#1 surely you don't have to ask about this one -- the terms get ever larger #2 is simply a geometric series, with |r| < 1, so it converges.

**Math**

actually, you start with one bacterium. You need a function that doubles every time you add 1 to the time. You probably already are aware that this models exponential growth, so what such function doubles as needed? 2^x does the job. So, starting at time x=0, at time x hours l...

**Calculus**

clearly f(x) increases as x increases, since the slope is always positive.

**Math problem or trick**

sounds like it to me, since no one (probably) was wearing both.

**pre algebra**

so, what's the trouble? Just fill in the table x x^2 : x-x^2 0 0 : 0-0 = 0 1 1 : 1-1 = 0 2 4 : 2-4 = -2 and so on for whatever values you want.

**pre algebra**

Write a table for the following quadratic function. y = x - x squared

**pre algebra**

Write a quadratic function rule for the following table x -10 -5 0 5 10 y 80 5 -20 5 80

**algebra**

well, what is 3500 + 200 ln(1000) ??

**Finite Math**

P(even,~8) = P(2,4,6,10,12) = 1/36 + 3/36 + 5/36 + 3/36 + 1/36 = 13/36 P(8) = 5/36 P(odd) = 1-(13/36 + 5/36) = 1/2 So, Fred gets 8*13/36 + 1*5/36 - 2*1/2 = 73/36, or about $2

**Calculus**

what is the slope? (f(x1)-f(x2)) / (x1-x2) both are positive, so the slope is always positive.

**math**

what you mean is .25x = 20 x = 80

**MAT 201**

10 days is 1.33 std below the mean 21 days is 2.33 std above the mean just consult your Z table.

**Science**

most important factor: do not watch the clock!

**Maths**

x y 30 84 90 74 So, every extra 60 trees reduces the yield by 10kg, so y = -(10/60)x + c Since y(30)=84, (-1/6)(30)+c = 84 c=89 y = -x/6 + 89 The total yield is trees * avgyield, so x(-x/6+89) = -x^2/6 + 89x This is just a parabola, where the vertex is at x = 3*89 You can figu...

**Physics**

the police car is moving 20 km/hr faster, and must make up 1.6km. That will take 1.6km / 20km/hr = 1.6/20 hr No idea when that will be...

**ALGEBRA**

First step: sort the values from low to high. mean: add them up and divide by how many values there are median: the middle value -- same number less as greater. If there are an even number of values, take the average of the two center values. mode: The value(s) which occurs mo...

**Math (functions)**

just substitute in 1,2,3,4,... for n 3*1+5 = 8 3*2+5 = 11 3*3+5 = 14 3*4+5 = 17 Or, just start with 8 and keep adding 3 for the next terms.

**Math (functions)**

It is indeed. Since f(x) = 3x-2 for f(1.5), everywhere you see an x, replace it with 1.5 and then do the math.

**chemistry pls help me asap**

.96g of O2 is .03 moles So, since it takes 2 moles of Y to combine with 3 moles of O, and we have .03 moles of O2 (.06 moles of O), we have .04 moles of Y. So, the molar mass of Y is 2.08/.04 = 52

**Algebra**

4x+7 < 11 4x < 4 x < 1 1-x <= -2 -x <= -3 x >= 3 so, x<1 or x>=3 see at http://www.wolframalpha.com/input/?i=solve+4x%2B7%3C11+or+1-x%3C%3D-2

**Math**

3 mi * 15 min/mi = 45 min

**math(urgent)**

what you have done is calculate the first year's growth. Now you have to add the 2nd year: 1000(1+.08)^(2-1) = 1080.00 Then the third year: 1000 1166.40+1080.00+1000.00 = 3246.40 As you can see, for n years, you would have 1000(1+1.08+1.08^2 + ... + 1.08^(n-1)) = 1000(1.08...

**Math**

(1/4) / 3 = 1/12 think about it. If you cut a yard into 4 pieces, and then cut each of those (1/4 yard) into 3 pieces, there are now 12 equal pieces, of 1/12 yard each.

**geometry**

17ft * 17ft * 4 ft = 1156 ft^3 Now to convert that to $, 1156 ft^3 * (1yd/3ft)^3 * $50/yd^3 = $2140.74

**Geometry**

a little inspection (or drawing) will reveal that ABCD is a rectangle with width=3 and height=2 EFGH is a rectangle with width=6 and height=4 Since the width and height have both been scaled by 2, the two rectangles are similar.

**Help me trig.**

tan(t/2) - sint = 0 (1-cost)/sint = sint 1-cost = sin^2 t 1-cost = 1-cos^2 t cost(1-cost) = 0 cost = 0 or 1 t = pi/2,pi,3pi/2 see http://www.wolframalpha.com/input/?i=solve+tan%28t%2F2%29+%3D+sint+for+t%3D0..2pi

**Calculus**

use the product rule y = sinx tan^3(x) y' = cosx tan^3(x) + sinx (tan^3(x))' for tan^3(x), use the chain rule and you get y' = cosx tan^3(x) + sinx(3tan^2(x) sec^2(x)) Now we can massage things a bit: sin^3/cos^2 + 3sin^3/cos^4 sin^3*cos/cos^3 + 3sin^3/cos^4 tan^3(...

**Algebra**

first step: what does 4x7 mean?

**geo**

well, we know that with center at (h,k) the circle's equation is (x-h)^2 + (y-k)^2 = 100 Since (20,10) is on the circle, at one end of the horizontal diameter, it is clear that the center of the circle is at (10,10). (x-10)^2 + (y-10)^2 = 100 Getting the triangle's dim...

**Algebra**

solve for what? Also, is the denominator m, or (m+1)?

**math/patterns**

Hmmm. That 9 at the start is perplexing. For the other terms, each increases by 5, so the millionth term after the 16 should be 16+5million = 5,000,016. If you can fix the 9 issue, it becomes quite easy.

**Algebra 1B**

log(x^3) = 2

**ALGEBRA**

4√6 / √30 multiply top and bottom by √30 to get 4√6√30 / 30 4√180 / 30 4√36√5 / 30 4*6√5 / 30 4√5/5 Or, 4√6/√30 4√(6/30) 4√(1/5) 4/√5 4√5/5

**Calculus**

just the chain rule y = u^2 where u = tan(v) and v = x^4 y' = 2u u' y' = 2u sec^2(v) v' = 2u sec^2(v) (4x^3) = 8x^3 tan(x^4) sec^2(x^4) and, as usual, you can massage trig functions in various ways.

**Math**

x = 2z y = 2a x < y 2z < 2a z < a

**Álgebra**

raise both sides to the 3/4 power: z+2 = 4^(3/4) z+2 = 2^(3/2) z+2 = 2√2 z = 2(√2-1)

**Geometry**

4v = (4,8) w = (3,-4) so, now just subtract them

**Math, Please Help**

since the terms are number an, then n is any integer from one onward. n>=1. since a4 = a1*r^3, 1024r^3 = -16 r^3 = -16/1024 = -2^4/2^10 = -2^-6 So, r = -2^-2 = -1/4 a6 = a4*r^2 = -16 * 1/16 = -1

**precalculus**

We have a circle and a straight line. So, either the line intersects the circle in two points, or it is tangent at just one point, or it misses the circle entirely. Since y = 4-x, plug that in to get x^2 + (4-x)^2 = 10 x^2 + x^2 - 8x + 16 = 10 2x^2 - 8x + 6 = 0 Since b^2-4ac i...

**Calculus**

easy way: sin2x/cos2x = tan2x so the derivative is just 2sec^2(2x) hard way, using the quotient rule: [2cos(2x)cos(2x) - sin(2x)(-2sin(2x))]/cos^2(2x) 2(cos^2(2x)+sin^2(2x))/cos^2(2x) 2/cos^2(2x) 2sec^2(2x)

**math**

assuming simple interest, 50000*(3/4)*r = 4500 r = 4/3 * 4500/50000 = .12 or 12%

**math**

since you add exponents when multiplying, you just need to find three ways to add numbers to get 11: 5^11 = 5^3 * 5^8 5^11 = 5^0 * 5^11 5^11 = 5^-4 * 5^15 There are lots of other ways; not quite so many if you insist on only positive powers.

**Algebra**

solve just like regular equations, working both at once. -4 <= 3+7x < 24 subtract 3 everywhere to get -7 <= 7x < 21 now divide through by 7: -1 <= x < 3

**Algebra - eh?**

I just see one, and yes, -4 <= 10

**Math**

2900*e^(.04*6)

**Math**

this is just a simple arithmetic progression, with a = 19 d = 1 Since there are 27-9+1=9 rows, S9 = 9/2 (19+27) = 207

**Pre-Calc**

First question: Of the 27 customers, how can there be 25 happy and 3 unhappy? in any case, just some the geometric progression, using the ratio r=3 or 6, as appropriate.

**math - typo?**

just put the clues into symbols: x+y+z = 15000 x = y+z+3000 3x+2y+2z=30000 or, x+y+z = 15000 x-y-z = 3000 3x+2y+2z = 30000 adding the first two, we get x = 9000 so, y+z = 6000 But then 3x+2(y+z) = 39000 Did I miss something? If so, fix it and then apply the same steps.

**Geometry**

looks like it to me. Though the phrasing is strange. Better would be the angle of rotation of line l with respect to line m

**Pre-cal**

A) log(x+1)+3logx log(x+1)+log(x^3) log (x+1)(x^3) log(x^4+x^3) B) 2log(np)-3log(p) log((np)^2)-log(p^3) log(n^2p^2)-log(p^3) log(n^2p^2/p^3) log(n^2/p) the base 4 is not important. These steps hold regardless of the base. If the base is not 4, but the 4 is included in the exp...

**Math**

just multiply x and y by 3.

**math**

you can play around with such problems here: http://davidmlane.com/hyperstat/z_table.html

**Algebra**

h(t) = 2+25t-4.9t^2 h=12 when 2+25t-4.9t^2 = 12 t= 0.44 and 4.66 seconds

**Math**

1/x = 1/1 + 1/2 = 3/2 x = 2/3

**math**

12:45 - 6:15 = 5.5 hours That's 1 hour plus 9 additional half-hours.

**Intermediate Algebra**

f(x) = 3x^2-5x+1 g(x) = 2x-5 (fog)(x) = f(g) = 3g^2-5g+1 = 3(2x-5)^2 - 5(2x-5) + 1 = 3(4x^2-20x+25) - 5(2x-5) + 1 = 12x^2-60x+75-10x+25+1 = 12x^2-70x+101 Looks like you messed up on the -5(2x-5) part

**Math 6th Grade**

next time don't list your choice on the same line as an incorrect answer. you are correct

**Math 6th Grade**

look at the number line. -15 is to the right of -21 So, -15 > -21 you are correct, though placing your choice on the same line as an incorrect answer threw me for a second...

**Calculus**

use the chain rule y = f(u(x)) y' = df/du * du/dx here, u = -x, so dy/dx = 5cos(-x)(-1) = -5cos(-x) which, since cos(-x)=cos(x), is -5cos(x) Or, you can note that sin(-x) = -sin(x), so what you have is y = -5sin(x) y' = -5cos(x)

**Math**

can we assume that no student is in more than one group? If so, then we want 190/545 * 360 degrees.

**Trig 2**

Hmmm. I think what we have here is a failure to communicate... The graph of sin(2x) is here. You can plainly see that it reaches its maximum at x = pi/4. http://www.wolframalpha.com/input/?i=sin%282x%29 Not sure what quadratic you are referring to. If you instead meant sin^2(x...

**Trig 2**

sin(2x) is always between -1 and 1. Since sin(pi/2) is the first time that it reaches 1, sin(2x)=1 when 2x = pi/2 That is, when x = pi/4 If you don't know wtf, just take a look at the graph and see where it reaches its maximum.

**alegbra**

what, no calculator? 150((1+.8/1)^(40)-1)/(.80*1) I'm assuming n=1, since you don't say... you can figure the answer, but I seriously doubt there is an 80% annuity out there...

**Trig help**

the period of cos(kx) is 2pi/k So, cos(pi x) has period 2 #2 pi/3

**math**

4/50 * 3/49

**Precalculus**

the center says that the ellipse is (x-2)^2/a^2 + (y+3)^2/b^2 = 1 Since both vertex and focus are at y=-3, the long axis is horizontal. 5-2=3, so a=3 3-2=1, so c=1 b^2+c^2 = a^2, so b^2 = 8 (x-2)^2/9 + (y+3)^2/8 = 1 graph and analysis at http://www.wolframalpha.com/input/?i=fo...

**Geometry**

Euler's Theorem says that OH^2 = R(R-2r) where r is the inradius Hmmm. I'll have to think on how to figure r without knowing a,b,c...

**Math - Trigonometry**

If we label the diagram as follows: P = plane A = point on ground just below the plane B = airport C = town we want to find BC 2.3/AB = tan 32 2.3/(AB+BC) = tan 18 eliminating the AB we have 2.3/tan32 = 2.3/tan18 - BC Now just solve for BC.

**Calculus**

the first place where e^x = x^3 is near x = 1.857 So, we have a narrow strip extending from x=0 out to about (1.857,6.406) The solid is a set of triangles of base e^x-x^3 and height 3 times that. So, the volume of the solid is v = ∫[0,1.857] (1/2)(e^x-x^3)* (3)(e^x-x^3) ...

**Algebra 2 help please**

the angle is in QII, so pi-(2pi/3) = pi/3

**Algebra 1**

rearrange things just a bit and you have 5y^2-20 - y^2z + 4z 5(y^2-4) - z(y^2-4) (5-z)(y^2-4) (5-z)(y+2)(y-2)

**Algebra**

correct

**Algebra**

#1 correct #2 correct, if you consider all the players as identical. good work.

**Algebra 1 Answer Evaluation**

Looks good to me. Did you try plugging in your point to see whether it fits the equation? That's always a good first step.

**Calc**

(a) (f(3+.03)-f(3))/.03 = (3.1209-3)/.03 = 4.03 (b) f'(x) = 2x-2 f'(3) = 4 (c) f(3) = 3 So, now you have a point and a slope. The line is easy to express. (d) Now just plug 2.98 into that line. (e) where is f'(x) = 0?

**Math - Trigonometry**

Recall your basic trig function definitions, in terms of the sides of a right triangle. In this case, x/2 = sin 38°

**Traditional african marriage is an advantage for men only,women**

and what do you mean by "african" or even "African"? Africa is a large and diverse continent, so generalizing such a topic is meaningless.

**Algebra**

Hmm. All the choices appear possible. I guess there's nothing for it but to go through the expansion. I get (A).

**Math**

8y 125d = 8.347 years, so just solve for P in P*e^(.0865*8.347) = 225500

**Algebra**

Assuming the usual carelessness with parentheses, I see it as follows: (y-1)/(x+3) = -3/4 y-1 = -3/4 (x+3) y = -3/4 (x+3) + 1 y = -3/4 x - 5/4 y = -(3x+5)/4

**math**

first step: express the clues algebraically: boys/girls = 2/3 cboys/mboys = 5/3 cboys = mboys+178 Now, we want to find the number of girls. Just for ease of algebra, let's change the above to b/g = 2/3 c/m = 5/3 c = m+178 3c = 5m 3(m+178) = 5m 2m = 534 m = 267 So, there ar...

**Trig**

recall your basic trig definitions, and draw a diagram. You will see that BC/8 = sin 60° BC/8 = 0.866 BC = 6.93 If this gave you difficulties, you have some serious reviewing ahead.

**math**

4/3 pi r^3 = 1200 r^3 = 1200 * 3/(4pi) = 900/pi so now you can find r.

**Geometry**

the radii are in the ratios of A/C = 1/2 B/D = 1/3 so the volumes are in the ratio of A/B = 1/5 A/C = 1/8 B/D = 1/27 So, we want C/D. C/D = A/B * B/D * C/A = 1/5 * 1/27 * 8/1 = 8/135

**Math**

Looks like output increases by the amount the input decreases. So, I'd say y = 162-x Now you can figure out y(10)

**Math**

If the width is w, we have w(40-w) = 384 w^2 - 40w + 384 = 0 since 384 = 4*96 or 8*48 or 12*32 or 16*24 - aha! (w-16)(w-24) = 0 Now you can easily figure the dimensions. Note that width is usually considered to be less than the length.

**Ratio of two triangles**

first:second is 4:1 second:first = 1:4 When you want a ratio, you need to specify which to which The first value is in the numerator, the second in the denominator. The colon (:) takes the place of the word "to".

**Math help practice test**

The sum of all the cans for the 5 days is d + 6 + 3*4 In the above sentence I see all four numbers used. But, I guess technically the 5 is not needed, since all we have to do is add up the numbers of cans. So, assuming d is not 5, then the 5 is n ot needed.

**algrebra - eh?**

got a little copy/paste problem there.

**Acceleration physics**

#1 Keep track of the units. We want time, which is (m/s) / (m/s^2) SO, divide the change in velocity by the acceleration used: -8.9 m/s divided by -2.7 m/s^2 = 3.30 s #2 ok #3 The velocity change by 80 m/s in the W direction. This change took 5.9 seconds, so assuming constant ...

**math**

since time = distance/speed, If Jake's speed is x, 270/x = 270/(x+15) + 1.5 x = 45 So, it takes Jake 270/45 = 6 hours

**Math 4 grade**

if you have 9 squares and 9 digits, that only leaves on digit for each square. I can't see how to add 3 single-digit numbers to get anything greater than 7+8+9=24. Is there a trick, or something missing here?

**math**

well, obviously, one lap is 1/6 of a mile. That should help...

**Math**

as written, I get x^3 - 8/x^2 + 2x + 4 If you mean 11 + (x^3 - 8) / (x^2 + 2x + 4) - x then that's just 11 + x-2 - x 9 recall the factorization of the difference of cubes.

**Algebra**

well since 15 = 3*5, I guess that pretty well solves the problem, no?

**Algebra 1 Answer Evaluation**

correct. good work.

**Algebra 1 (Step-by-Step)**

this has been answered already. Reiny just stated that since x^2 is always positive, there's no real value of x which can produce -7 when squared. Damon actually wrote the quadratic in standard form, applied the formula and gave the complex solutions. http://www.jiskha.com...

**Algebra**

5(w-10)(w+15-10) = 1250 Now just solve for w. length=w+15.

**math - ouch!**

How did I ever get k=3? My Bad!!

**math**

you know that d = kt, meaning that their ratio d/t is constant. Note that in each case, d/t=3 That means k=3. So, d = 3t

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