since 729 = 9^3, you are correct. Your method was also correct. 81 = 9^2, so 81^(1/3) = (9^2)^(1/3) = 9^(2/3) and 9^(1/3) * 9^(2/3) = 9^(3/3) = 9 fractional exponents are just like any others. Add them when multiplying, and multiply them when raising powers to powers.
divide 21000g by the number of grams/mole That will give you the number of moles.
7 moles of O2 in every 2 moles of Na2Cr2O7. I assume you have some other data of interest.
PV/T remains constant, so (75.0)(500)/(-185+271) = (55)(221.0)/T T = 28°K Note that we don't really have to convert to L and Pa, because the same conversion factors would be applied to both sides of the equation. The only wrinkle is the °C-°K conversion, becaus...
Anne Frank (another question :/)
Sounds like a question from Connections Academy and Mrs Markly's class.
unless he meant that S18 = 549 In that case, 18/2(2a+17*3) = 549 a = 5 T56 = 5+55*3 = 170 S32 = 32/2(2*5+31*3) = 1648
∛98 = ∛(49*2) sorry, I see no way to simplify it. Now, if you had ∛108, that would be ∛(27*4) = ∛27∛4 = 3∛4
good catch. You are correct h'(0) = 10-0+2-7 = 5 what was I thinking? the answer is 1 if it was supposed to be -2sin(x) instead of +2sin(x)
Calculus - 2nd verse
Ahem: h'(0) = 5*2-0+0-7 = 3
well, what's h'(x)? Use the chain rule: h'(x) = 5g'(x) - 6x + 2sinx - 7 h'(2) = 5g'(2) - 6(2) + 2sin(2) - 7 = 5*2 - 6*2 + 2sin(2) - 7 = 2sin(2) - 9
Z(.674) = 0.25 So, (52-μ)/5 = .674 μ = 52-5*0.674 = 48.63
Converting the data to seconds, we have * fastest: 7439 * mean: 7474 * nedian: 7467 * mode: 7467 * range: 57 * two other fast times: 7493 and 7495 So, we have 7439 x x x x x x (fastest) 7439 x x x x x 7596 (range) 7439 x x 7467 x x 7596 (median) 7439 x x 7467 7493 7495 7596 (o...
If she made x 3-pointers, then she made 3x two-pointers. x+3x = 8 x = 2 So, 2 3-pt and 6 2-pt
If you mean the x-intercepts are at 5 and 15, then y = a(x-5)(x-15) 75 = a(-5)(-15) a = 1 so, y = (x-5)(x-15)
since you give no choices, I'll just say that v = pi r^2 h v = pi (5x+2)^2 (2x+8) expand that as necessary to conform to the format of the choices
h/d = tan 27° so find d when h=875 if flight distance is f, d/f = cos 27° the time needed is thus f/651 hours tanθ = 875/400
(a) 500*2^3 = 500*8 = 4000 (b) 500*2^0 = 500*1 = 500 (c) when 3x=1 or every 1/3 hour (d) 500*2^3x= 32000 2^3x = 32000/500 = 64 2^3x = 2^6 3x = 6 x = 2
well, if you can't pick out the correct choice from my solution, you're in some trouble. Take a good look and see what you can factor out.
(6x)(9x)-π(4x)^2 = 54x^2-16πx^2 = (54-16π)x^2 or about 3.73x^2
C(0) = 0 Naturally, at t=0, there has been no drug added As t->∞, e^-bt and e^-at ->0, so we again have C(∞) = 0 All the drug has been absorbed or eliminated. If C(t) = (500)(8.5)/(3700)(8.5-0.09) (e^-0.09t - e^-8.5t) then max C is at t=0.54
MAT-134 Math XL
intercepts are easiest when x=0, 4y=12, so y=3 when y=0, 3x=12, so, x=4 So, plot the points (0,3) and (4,0) and draw a line through them.
all these are basically the same, so I'll do one for you. If you get stuck on the others, come on back and show ehere you get stuck. z+(1/7)sk = (1/6)yk^2 (1/7)sk = (1/6)yk^2-z (k/7)s = (1/6)yk^2-z s = (7/k)(1/6)yk^2-z s = (7/6)yk - 7z/k
since √81 = 9, I'd say the winner is #2 10 is the largest of 8,10,4,9 largest radius means largest circumference.
figure the slope m between the two points pick one of the points and call its coordinates (h,k) Then, since the slope never changes, the slope between (x,y) and (h,k) is the same for any (x,y) on the line. So, (y-k)/(x-h) = m, the slope between the two given points. This is us...
v(t) = 4-2t dv/dt = -2 There is no local min/max, and v is constantly decreasing, so max v in the interval is at t=0, or v=4
f'(x) = 3x^2+1 g'(2) = 1/f'(g(2)) = 1/f'(1) = 1/4
1.30*10^3 @ W = (-1300,0) 9.90*10^2 @ N30E = (445,857) add the forces to get (-855,857) = 1211 @ N45W Since F=ma, a = 1211/.159 = 7613 m/s^2 in that direction
just solve for t when h=0. It factors nicely, or your good old quadratic formula should do the trick. Did you get 1.5 seconds?
how about -24/30 ?
P = E^2/R = 120^2/15 = 960W
Since the horizontal speed is constant, the time it takes to reach the fence is 8/v The height is h = 4.9 - 4.9t^2 We want h(t) = 2.4 when t=8/v, so 4.9 - 4.9(8/v)^2 = 2.4 v = 11.2 m/s
geometry - incomplete
since I know neither the angles nor their relation to x, you better provide a bit more description of the figure, eh?
so, we know that now there are 12 cards left: 5 even and 6 odd and #1 P(red) = 6/12
area and perimeter
if the length is x and the width is y, then 2x+3y = 1200 a = xy = x(1200-2x)/3 = 400x - 2x^2/3 max area when x = 400*3/4 = 300 So, the field is 300 by 200 Note that as in all such problems, the fencing is divided equally among the lengths and widths.
Algebra (Integer Problem)
x+y+z = 33 y = x+3 z = 4x Now substitute y and z to get x+(x+3)+(4x) = 33 6x = 30 x = 5 so the numbers are 5,8,20
If the altitude is h, then h^2 + 4^2 = 5^2 Looks like h=3
Algebra (Age Problem)
m = 6s m+4 = 4(s+4) so, 6s+4 = 4s+16 2s = 12 s = 6 so, man is 36 check: 40 = 4(6+4)
d = kt 124 = k(2) k = 62 d = 62t d(5) = 62*5 = 310 Or, you can say that since 5 is 5/2 * 2, the new d will be 5/2 * 124 = 310
If there are x gallons of 42% syrup, and y gallons of 95% syrup, then x+y = 3000 .42x + .95y = .55(3000) now just solve for x and y
nope - same old 50-50 chance. Although, given their previous children, I ct the chances are high that they'll have another daughter. There may be something other than random chance at work here.
ummm, how about 16390 + 18000 = ?
no way does 2c flour make 2 muffins I think you meant 2 dozen muffins. If so, then since 120 = 10 dozen, you need (10/2)(2) = 10 cups flour Or, you can say that since 2 dozen uses 2 cups, that's 1 dozen/cup. So, 10 dozen use 10 cups.
assuming Reiny's question is accurate, then 200(50/10) + 100p = 300(50/12)(1.12) p = 4 check: cost = 300(50/12) = 1250 revenue: 200 @ 50/10 = 1000 100 @ 4 = 400 total: 1400 = 1250*1.12
Algebra - Rational Exponents
Just curious how posting a question, waiting for an answer, reading it and posting a reply saved time over just opening your text to the appropriate section and reading that explanation. Just sayin' . . .
If you're trying to prove it, sin(3x) = sin(2x+x) = sin2x cosx + cos2x sinx = 2sinx cos^2 x + (cos^2x-sin^2x)sinx = 2sinx cos^2x + cos^2x sinx - sin^3x ta da
C(x) = 9x for x <= 150 = 9*150+6(x-150) for 150 < x < 210 = 9*150 + 6*59 + 3(x-210) for x >= 210
I'd say C
D looks good but of course, an equilateral triangle with sides of 10, has a height of 8.66 So, the triangle is isosceles, but not equilateral.
5000(1+.03/4)^(4*5) = 5805.92
aww shucks. Reiny is also very good at explaining the solutions he provides.
d=t-15p-20c/2 is correct if you use some parentheses d=(t-15p-20c)/2 now you won't make the mistake your friend did; you will get d = t/2 - 15p/2 - 10c on the other hand, if your friend got d = (t-15p)/2 - 10c then that's ok On #2, d=180 is correct. That answer already...
If the bonus 2% is not paid for the sales making 6%, then she made s = 3900 + .06(39600-36000) + .02(46800-39600) = $4260.00 On the other hand, if she makes 6% on all sales beyond 36000 and an additional 2% on sales above 39600, then she made 3900 + .06(46800-36000) + .02(4680...
2w+2l=300 (w+2l)*50 = 12000 width=60 length=90
algebra - repost
try using more standard one-line notation, such as (x+6)/(x-3) to describe fractions. Note that x+6/x-3 is not the same, since multiplication and division are done first; so that means x + (6/x) - 3
assuming you meant (z-7)/(z+1) = 3/5 then we clear fractions and get (z-7)(5) = (3)(z+1) 5z-35 = 3z+3 2z = 38 z = 19 check: 12/20 = 3/5
since they have no common factors, that wold be 4*19
how about something really simple, like f(x) = 1 for x >= 0 = -1 for x < 0
Excellent graphing help can be had at http://rechneronline.de/function-graphs/ For your example, I'd enter two functions: cos(2x*pi/180) -sin(x*pi/180) and set the x range from -100 to 100 and set the y range from -1 to 1 The pi/180 factor is needed because it plots the an...
The first 24 might all be cinnamon or peppermint. After that, the next three must be licorice, so 27 is the minimum to guarantee at least 3 licorice.
any prime number allows only one array.
1000(1+r)^15 = 39533.32 (1+r)^15 = 39.53332 1+r = 1.2778 r = 0.2778 = 27.78% is that a sane answer? yes, since it doubled over 5 times in 15 years, or every 3 years. The rule of 72 says that a rate of 24% will double about every 3 years.
not only is the premise not necessarily true, but you need to be a lot more particular about which society you're describing.
35+.18x = 71
since sin>0 and cos<0, we are in QII. So, y=1,r=4,x=-√15 sin = y/r = 1/4 cos = x/r = -√15/4 tan = y/x = -1/√15 ...
good graphing help at http://rechneronline.de/function-graphs/
only true if x=0 or x=1
40 in wheel has circumference 40pi inches 50 mi/hr = 52800 in/min so, that's 52800/40pi rev/min or, 52800/40pi * 2pi = 52800/20 = 2640 rad/min
algebra & trigonometry
w(3w+8) = 28 3w^2+8w-28 = 0 (3w+14)(w-2) = 0 w = 2
algebra & trigonometry
x^2+x-210=0 (x-14)(x+15) = 0
10cm + 286(30m+10cm)
If the tree is of height h and at distance d, then (150-h)/d = tan 50° h/d = tan 22° Now you have two equations in two unknowns, so just solve them.
(a) each number is -2 times the previous (b) I suspect a typo, since the signs do not alternate. However, a rule which works is that the nth term is n times the previous term, with sign changing when (n-1) is a multiple of 3.
More Algebra - Dividing Radicals!
2πr = 2π(5/(√2-1) = 2π(5/(√2-1)*(√2+1)/(√2+1) = 2π(5/(√2+1))/(2-1) = 10π(√2+1) (C) is correct
Math PLEASE HELP ASAP AHHHH
-3*7 = -21 -3*8 = -24 -2*11 = -22 and so on you can also use -7*3 = -21 and so on -1*23 and 1 * -23 There are oodles of possibilities
the original area is 12*14 = 168 the square piece is 6x6, with area 36 I assume you can now solve the problem.
Could you find the circumference of a circle using the exact value of pi? Why or why not?
Given: f(x) = X^2-x evaluate: f(sqrt2 + 3) I have worked out this and am stuck: (sqrt2+3)^2 - (sqrt2+3) (sqrt2+3)*(sqrt2+3)- (sqrt2 +3) (sqrt2)^2+ 3sqrt2 +3sqrt2+ 9- (sqrt2+3) 2+6sqrt2 +9-sqrt2-3 and am stuck or wrong here. Ans= SQRT2+6sqrt2 all under radical
of course. A circle of radius 12 as circumference exactly 24π Of course, if you want an exact numeric answer, that's not possible, since the value of π is an unending decimal fraction.
A seagull flies at a velocity of 10.00 m/s straight into the wind. (a) If it takes the bird 18.0 min to travel 6.00 km relative to the earth, what is the velocity of the wind?
solve how? There is no single pair of numbers for (x,y) which will work. They are the equations of lines. Any point on the line will satisfy the equation. Now, if you want to solve each for y as a function of x, then just rearrange things until y is all alone on one side. #7: ...
half-period is 6 hours, so a full period is 12 hours. So, if 2pi/k = 12, k = pi/6. The max-min=1.9-1.1 = 0.8, so the amplitude is 0.4 So, the choice is C or D. The midpoint is (1.9+1.1)/2 = 1.5, so we're still looking at C or D. Since we apparently want a cosine function, ...
ah, a nice related-rates problem. a = pi r^2 da/dt = 2pi r dr/dt when r=3, 8 = 2pi(3)(dr/dt) dr/dt = 4/(3pi) cm/s By the way, da/dt is 8 cm^2/s. That makes the units come out right. cm^2/s = 2pi(cm)(cm/s)
algebra and trigonometry
If the quantity of tickets is x,y,x for t5,10,15 dollar tickets, respectively, then we have x+y+z = 180 5x+10y+15z = 1900 x+z = 2y (x,y,z) = (50,60,70)
a pint's a pound, the world around so, since 16 fl oz is one pint, it should be clear. Extra credit: what's the difference between an ounce and a fluid ounce?
1/5 = 2/10
n/(n+6) = 3/4 n=18 3/4 = 18/24
ah! good one! Looks easy, but there's some algebra and trig identities involved. Rather than slog through it here, I refer you to http://www.wolframalpha.com/input/?i=integral+%28cot4x%29^5+%28csc4x%29^7 and hit the "step by step solution" button.
well, if a pie is divided into 10 pieces, are they larger or smaller than when it's cut into 5 pieces? Smaller denominator means fewer pieces, so each is larger.
1.2 * (32/10)
2(w + 4w+1) = 292
The equivalent resistance from R2 and R3 is 1/R = 1/38 + 1/18 R = 12.214 So, we now have a total R of 16+12.214 = 28.214 ohms That means our current through R1 and the R2R3 network is 6/28.214 = .212 amps Now, divide that current between R2 and R3 and Ix = .212(38/56) = .144 o...
well, since the slope-intercept is y = mx+b I wonder where lies the difficulty???
writing and linear equations
if the angle is x, its supplement is 180-x, so just solve 180-x = 2x x=60 What's all this nonsense about x=4n+12? If you need to find "the number" then just solve that for n, given that x=60.