I find it a bit easier not to expand the derivative f'(x) = 2x(4x-15)/(8x-15)^2 Clearly f'=0 when x is 0 or 15/4 So, f'(15/4)=0, and 3 < 15/4 < 5 f'(0)=0 also, but 0 is not in [3,5] The graph at http://www.wolframalpha.com/input/?i=x^2%2F%288x-15%29+for+3...
Sounds like they wanted f'(c) rather than c.
add 1 for each successive integer. So, what is y-3 + 1+1+1+1 ?
Think of the graph for y = x^3 It has no max/min, but just an inflection point at x=0. You function is just the same, only stretched by 2, shifted left by 5, and shifted up by 7.
math - bogus
Two problems: (1) no value given for x (2) I suspect a typo, since there is no "x" term, and two constants.
area of 3x3x3 cube is 6*9=54 area of 2x2x2 cube is 6*4=24 If not joined, total area is 78 The maximum concealed surface area is an entire face of the 2-cube, on both solids: 2*4 = 8 So, the minimum exposed area would be 78-8 = 70
3/5x is not defined for x=0 1 - 3/5 = 2/5 1 - 3/10 = 7/10 If you meant y = 1 - (3/5) x then just plug in the values: 1 - (3/5)(0) = 1 1 - (3/5)(1) = 2/5 1 - (3/5)(2) = -1/5
I'd have to say 90 degrees. If the struck ball has some backward velocity, the striking ball would have to increase its forward speed to compensate.
If there are x bundles, x/3 are morning 2 = afternoon That leaves 2x/3 - 2, of which x/3 - 1 are regional 1 is local 1 is out of state Add them up to get x/3 + 2 + x/3 - 1 + 1 + 1 = x 2x/3 +3 = x 3 = x/3 x = 9
Math - thanks Reiny
I guess I didn't read the question too carefully, and failed to answer it fully.
look at the differences between successive terms: -1 -3 -5 -7 so, the next will be 15-9=6
There are several standard right triangles with integer sides. It will help a lot if you just learn them -- they turn up often in problems, and it's nice not to have to do the calculations every time. 3-4-5 5-12-13 8-15-17 7-24-25 and multiples of those values
advance algebra - oops
Oops mixed up price and quantity p(x) = x(500-x)-35(500-x) = (x-35)(500-x) assuming no extra dolls are made...
profit = revenue - cost revenue = price * quantity. So, p(x) = x(500-x)-35x Now just plug in your data
nice try, but you're mixing things up. Why do you say 120 m^3? m^3 is volume, not are or length! And why multiply the perimeter by the length, anyway? Just take a step back and work things out. The area is length * width The 120m of fencing reaches around the field -- that...
Just translate the words to algebra. Then solve. For example, #3: 3/8 of 768 = 288 5/6 are below senior, so 1/6 are seniors. 1/6 of 288 = 48 Where do you get stuck on the others?
If you mean f'(t) = -8 * 0.8^t, then f(t) = -8/ln(0.8) * 0.8^t + C since f(0) = 90, 90 = -8/ln(0.8) + C C = 90 + 8/ln(0.8) So, f(t) = -8/ln(0.8) * 0.8^t + 90 + 8/ln(0,8) = 90 + 8/ln(0.8) (1-0.8^t) = 90 - 35.85 (1-0.8^t) So, plug in t=10
If you are looking for a complete sentence, What can he do? is the only option. The other phrases are all acceptable in various contexts.
17(4+2*17) = ?
You can see some analysis here: http://www.wolframalpha.com/input/?i=sum+3%28-1%29^n%28n%29%28x^n%29 It will probably give you a start on proving the answer.
if the length is x, 2(3/4 x + x) = 100
28' = 853.44 cm 18' = 548.64 cm Easy way, assuming partial pieces are tucked in as needed: (853*548)/(60*40) = 195 Now, you can do several kinds of approximation, requiring whole pieces, etc. One easy way is to round up the lawn area to multiples of 40 and 60: 853/60 =...
just figure how much potential energy (mg ∆h) has been lost. That has been converted to kinetic energy.
consider the takeoff to be at (0,0). The height of the skier is thus y = vt - 4.9t^2 maximum height is thus reached at t = v/9.8 y(v/9.8) = v*v/9.8 - 4.9(v/9.8)^2 = v^2/9.8 - v^2/(4*4.9) = v^2/9.8 (1 - 1/2) = v^2/19.6 Since the max height is directly proportional to the square...
well, what is 2/3 of 18? If that stumps you, what is 1/3 of 18? Just double that.
since density = mass/volume, we have 1112.50g/(5.00cm)^3 = 1112.50/125.00 g/cm^3 # atoms is g * moles/g * 6.02*10^23 atoms/mole So, just look up the atomic weight of copper and plug it in.
enter your data here http://www.gregthatcher.com/Mathematics/GaussJordan.aspx It will show all the details of how the elimination works.
y=2 should immediately be discarded, since fractions with y-2 in the denominator are not defined. The steps should be 3y/y(y-2) - (y-2)/y(y-2) = 4/y(y-2) 3y-y+2 = 4 2y = 2 y = 1
w=2 satisfies the original equation, so I guess your solution is correct. However, the steps should be 2(w-1)/2(w-1) + 4w/w(w-1) = 10/w(w-1) 2w-2 + 4w = 10 6w = 12 w = 2
you want (a+b+c)/3 (a+b)/2 = 45 (b+c)/2 = 43 (a+c)/2 = 50 Add them up and you have (a+b+b+c+a+c)/2 = 45+43+50 (2a+2b+2c)/2 = 138 (a+b+c) = 138 (a+b+c)/3 = 46
16 degrees warmer than it is now.
1/5 - 1/15 = 1/x 2/15 = 1/x x = 15/2
since speed = distance/time, 120/c = 200/j j = c+35 so, 120/c = 200/(c+35) 120(c+35) = 200c 120c + 120*35 = 200c 80c = 120*35 c = 3/2 * 35 = 52.5
how much of the job does each pump do in an hour? 1/12 + 1/16 = 1/x together they take x hours.
how many std above the mean is Z=2? That's how many oz. more than 16 is the box.
just plug those numbers into your amortization formula.
well, what is 30^2?
As usual, draw a diagram. Assuming the plank is just long enough to join the tops of the ladders, there is a 1/2 m overlap on each end, above the sloping side. So, the height is √(2.5^2 - .5^2)
If there were x adult tickets, then there were 340-x students. So, 5.00x + 3.50(340-x) = 1535.00 Now just solve for x...
x = t^2-t dx/dt = 2t-1 y = t^3-3t dy/dt = 3t^2-3 dy/dx = (dy/dt)/(dx/dt) = (3t^2-3)/(2t-1) If the normal to the curve is vertical, the tangent is horizontal. So, dy/dx = 0. That happens when t=±1 So, the normal is vertical at (2,2) and (0,-2) See the graph at http://www...
just convert everything to the same unit, say cm. 1 inch = 2.54 cm, so 176 cm = 176 cm 5'4" = 64" = 162.56 cm 1.8 yd = 64.8" = 164.59 cm and so on For the truck, just look up the conversion for feet-to-meters. 8'6" = 8.5 ft...
the hour hand moves 360° in 12 hours. That is 30° per hour. So, in 1/2 hour, it moves 15°
Write down the facts: 2h+3s = 4.21 3h+2s = 5.24 Now you can solve for h and s, and calculate h+s. Nope, too much work. Instead, just add the two equations, and you see that 5h+5s = 9.45 So, divide by 5 to get h+s = 1.89
maths lit, geography, life science, history, life orientation, english, tswana
quite a variety of things. The question is, what to you enjoy doing? Train yourself in that, now that you have some basic knowledge and study skills.
If Jones borrowed $j at a rate r, he paid 75.00 in interest. So, we see that jr = 75 (3j)*r*2 = 3*2*jr = 6*75 = 300
Read up on these work problems. If Jack can do the job in 6 hours, he does 1/6 of the job in an hour. If together they can do the job in 2 hours, they can do 1/2 the job in one hour. So, you need to add up how much each guy can do in one hour, and the sum is what fraction of t...
1/2 = 1/6 + 1/x Just by inspection, we can see that x=3, so it takes Jerry 3 hours to do the job.
8+4+5 = 17 So, we have 17x = 48 x = 48/17 You can use Heron's formula to find the area of a triangle with sides 8,4,5. Now just multiply that area by (48/17)^2 An odd set of values, I must say.
x^3+2x^2-15x = x(x+5)(x-3) 2x^2-18 = 2(x-3)(x+3) Now just cancel the (x-3) top and bottom
Maths (factor theorem)
27x^3-8y^3 is the difference of two cubes: (3x)^3 - (2y)^3 So, it factors as (3x-2y)(9x^2+6xy+4y^2)
well, 243 = 3^5 32 = 2^5 That should get you started.
(3/4)/(1/6) = 9/2 so, p:q = (9/2)(2/3):(9/2)(1/6) = 3:3/4 p:q:r = 3:3/4:1/2 = 12:3:2
MATH WORD PROBLEM
4 yards = 11 ft 12 in subtract 2 ft 8 in -------------------- 9 ft 4 in
If the border has width w, we need the total area to be twice the garden area: (20+2w)(28+2w) = 2(20)(28) Now just expand, collect terms, and solve for w.
r = b+180 b = .2(r+b) so, b = 60 r = 240 Total beans = 300 oz After the transfer, 30% = 90 oz So, that means that 30 oz of red beans were transferred, added to the 60 oz of black beans already there.
Look at that fraction. The domain is (-1,1). As long as x ≠ ±1, the denominator is not zero. So, the fraction is zero when x=0. On either side of that, y increases, so (0,1) is a minimum. To check, see the graph at http://www.wolframalpha.com/input/?i=1%2F%E2%88%9...
you want to maximize p = .09x + .07y subject to x+y <= 200000 x >= 100000 y >= 50000 A little linear programming reveals x = 150000, y = 50000 p=17000
measure the distance on the map, in cm. Then multiply that by the map scale (18,300,000) to get the real-world distance, in cm. Divide that by 100,000 to get the distance in km.
I predict that the shell lands closer to the shooter than does the bullet! Oh, did you want to ask a question, too? Something tells me you will need to find out how long it takes an object to fall 1.7 meters.
one rotation turns the wheel through 360°, but that's not what matters here. When the wheel turns one rotation while rolling on the ground, it covers a distance equal to the circumference of the wheel. So, since C = πd, a 45-cm diameter wheel covers 45π = 141...
math - oops
Since 17 is prime, N=1
using the well-known proofs that sinx -> x, we can conclude that tan2x -> 2x so we have the limit as (2x-x)/(3x-x) = 1/2
If a shark ate the fish, then, yes, the fish got eaten by a shark. Past tense. However, "gets" can be ok, too. Maybe you are talking about what happens when a fish is near a shark. If the shark is hungry, then what usually happens is that the fish gets eaten by the s...
m = y-7 1/m + 1/y = 1/12 1/(y-7) + 1/y = 1/12 y = 28 so, m = 21 check: working together, in one day they can assemble 1/28 + 1/21 = 1/12 of the whole.
1/2 - 1/4 = 1/x x = 4 Check: water comes in at 1/2 sink/minute water drains out at 1/4 sink/minute net flow: 1/2-1/4 = 1/4 sink/min So, it takes 4 minutes to fill the sink
AB has slope 2 and length √5 mid(AC) = (-1/2,1/2) mid(BC) = (-1,-1/2) so that segment has slope 2 and length √5/2
(2,1)+(1,4) = (3,5) (5,2)+(1,4) = (6,6) So, true
just apply your distance formula. Plot the two points, and join them in a right triangle with legs parallel to the axes; the hypotenuse is the line joining the points.
pick the pair with (x,y) and (-x,-y)
total area = 18*8 = 144 picture area = 14*4 = 56 so, just subtract to get the frame only
dN/dt = 528e^0.4t / (11+e^0.4t)^2 Now just plug in t=4
Do you mean to divide? N(t) = 650/(1+649e^-.5t) What's the trouble? Straightforward evaluation of N or solving for t. That's just algebra. If I have the function right, its graphs is http://www.wolframalpha.com/input/?i=650%2F%281%2B649e^%28-.5t%29%29
simple: p(x) = r(x) - c(x)
John's idea is interesting, but leaves you no closer to the solution. 4x+y=21 7x-4y=8 Consider his multiplication idea, and work it this way: 28x+7y = 147 28x-16y = 32 Now subtract to get 23y = 115 y = 5 now you can find x easily. The other set is even simpler. You know wh...
and then subtract the 18 minutes already walked. Or, consider that there is 1/4 of the way to go. That is 1/3 as far as he's already gone, so it will take 1/3 as long to walk it. That is, 6 more minutes.
yes. care to proofread your posting and rephrase the question?
(12*87+18x)/(12+18) = 90 Now just solve for x
what, you cannot list the samples of size 3? ABC ABD ABE ...
Math - clarify
Hmmm. What does "list price of $100 less 7%, and 6%" mean? Two successive discounts? Also, after all the explanation, I don't see an actual question? What is it you are trying to calculate?
I think it's a divisibility problem, where she meant If a|(b-2c) and a|(2b+3c) the a|b and a|c.
If there are s students, a adults, and g geezers, then s+a+g = 400 8s+10a+7g = 3535 a = s+g-10 Now just solve for the numbers
did you check out the hints I gave on your previous post of this problem? If so, where do you get stuck? The ticket problem is similar. How far do you get on that one?
25^2 = 625
Math (Discrete Math)
271 is prime, so N is a multiple of 271 2014 = 2*19*53, If N = 271*2*2014, GCD(N,2014) = 2*271 and GCD(N,271) = 271 So, it appears to me that 271*2*2014 is the smallest N that fits the requirements
since the ratio of height-to-shadow is the same for both objects, h/29,2 = 3,5/5,2 Now just solve for h.
well, that would naturally be 0.02 * 5270
the figure is really just a sphere of radius r and a cylinder of radius r and height 4r. So, the volume is V = 4/3 π r^3 + πr^2 (4r) = 16/3 π r^3 So, dV/dt = 16πr^2 dr/dt That means that dr dt = dV/dt / (16πr^2) The surface area is A = 4πr^2 + 2...
just list the digits as given, moving the decimal point 9 places to the right, adding zeroes as needed.
the domain is 260 <= x <= 410 the price per chair is 88.00 - 0.02(x-260) revenue is price * quantity, so R(x) = x(88.00-.02(x-260)) = 93.2x - .02x^2 For maximum revenue, just find the vertex of the parabola. For minimum, figure the revenue at the two ends of the domain, ...
revenue is price * quantity, so R(q) = 551q profit is revenue minus cost, so P(q) = 551q - (q^3-60q^2+1200q+760) You should probably graph P(q) to find the max. Take a look here: http://www.wolframalpha.com/input/?i=551q+-+%28q^3-60q^2%2B1200q%2B760%29 If you have calculus as ...
profit P(q) = R(q)-C(q), so P(q) = 510q - (9400+3q^2) dP/dq = 510 - 6p P is maximized when dP/dq = 0, so ...
well, 500 is 25% of 2000, so ...
Just review the definitions of the basic trig functions. Check the diagram, and you can see that the height h can be found using h/220 = sin 36°
your answer looks correct to me. There must have been a typo in the problem, with a spurious "root" tossed in.
assuming that "no students of school A and B would get mixed up" means that each row contains only students from one school, let's find the largest number that divides both 336 and 432. GCF(336,432) = 48 So, school A has 7 rows of 48 and school B has 9 rows of 48
Judging from your experience, I would have to say, YES!
since your speed is 5 km/hr, all the distances must be multiples of 5, since you start counting at the fountain. Or, if the somewhat vague description means that you want the total distance covered, starting at the fountain, then you have to start with 2, and after that, all t...