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.
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...
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.
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.
Write a table for the following quadratic function. y = x - x squared
Write a quadratic function rule for the following table x -10 -5 0 5 10 y 80 5 -20 5 80
well, what is 3500 + 200 ln(1000) ??
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
what is the slope? (f(x1)-f(x2)) / (x1-x2) both are positive, so the slope is always positive.
what you mean is .25x = 20 x = 80
10 days is 1.33 std below the mean 21 days is 2.33 std above the mean just consult your Z table.
most important factor: do not watch the clock!
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...
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...
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...
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.
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
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
3 mi * 15 min/mi = 45 min
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...
(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.
17ft * 17ft * 4 ft = 1156 ft^3 Now to convert that to $, 1156 ft^3 * (1yd/3ft)^3 * $50/yd^3 = $2140.74
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
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(...
first step: what does 4x7 mean?
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...
solve for what? Also, is the denominator m, or (m+1)?
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.
log(x^3) = 2
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
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.
x = 2z y = 2a x < y 2z < 2a z < a
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)
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
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...
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)
assuming simple interest, 50000*(3/4)*r = 4500 r = 4/3 * 4500/50000 = .12 or 12%
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.
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
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
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.
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
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...
just multiply x and y by 3.
you can play around with such problems here: http://davidmlane.com/hyperstat/z_table.html
h(t) = 2+25t-4.9t^2 h=12 when 2+25t-4.9t^2 = 12 t= 0.44 and 4.66 seconds
1/x = 1/1 + 1/2 = 3/2 x = 2/3
12:45 - 6:15 = 5.5 hours That's 1 hour plus 9 additional half-hours.
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...
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)
can we assume that no student is in more than one group? If so, then we want 190/545 * 360 degrees.
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...
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.
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...
the period of cos(kx) is 2pi/k So, cos(pi x) has period 2 #2 pi/3
4/50 * 3/49
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...
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.
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
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)
#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.
(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.
Hmm. All the choices appear possible. I guess there's nothing for it but to go through the expansion. I get (A).
8y 125d = 8.347 years, so just solve for P in P*e^(.0865*8.347) = 225500
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
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...
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.
4/3 pi r^3 = 1200 r^3 = 1200 * 3/(4pi) = 900/pi so now you can find r.
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
Looks like output increases by the amount the input decreases. So, I'd say y = 162-x Now you can figure out y(10)
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.
#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 ...
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?
well, obviously, one lap is 1/6 of a mile. That should help...
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.
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...
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!!
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