Posts by Steve
Total # Posts: 53,336
(a+b)²-(a-b)² a²+2ab+b² - (a²-2ab+b²) = 4ab not sure what the logs have to do with anything here.
Rate Problem / College Algebra
since time = distance/speed, if the current's speed is x mi/hr, you have 45/(7+x) = = 45/(7-x) - 4 Now just find x.
If (6-x-x^2) divides g(x), then that means that (3+x) and (x-2) are both factors of g(x) g(x)/(x+3) has a remainder of -27a-3b+27 g(x)/(x-2) has a remainder of 8a+2b+2 Since those are both zero, we have 9a+b = 9 4a+b = -1 a=2, b=-9 g(x) = 2x^3+5x^2-9x-18 = (2x+3)(x-2)(x+3)
try doing this like the other one. Use synthetic division to find the remainders, and set up equations to solve for a,b,p
real: -6 imaginary: -1 time to read that section again ...
well, f'(x) = 12x^2+2x+4 = 2(6x^2+x+2) so, keeping in mind the definition of critical numbers, whet do you think?
|x+5| > 1 x > -4 or x < -6 Mark -5 on the number line You want all the points more than 1 unit away from -5.
their combined speed is R1+R2 Since distance = speed * time, we have D(T) = S-T(R1+R2) extra credit: what is the domain of the function D(T), assuming that time stops when they meet?
the long side is 28 bricks, and the short side is 20 bricks. You will need 2(28+10)+4 bricks. Why the extra 4?
The other side is either ?24 or ?26 One of the other angles is either arctan(1/5) or arcsin(1/5) and the 3rd angle is its complement. So, figure out what's correct, and forge ahead ...
just plug in your numbers and solve for a,b,c. For example, one data point (11,1177) means that 121a+11b+c = 1177 Now write the equations for the other two points, then solve the system of equations. But first, fix your data points, since you have two different values for x=11.
42(x+27)+66x = 1944 you are correct
Math (Pre- Algebra) A
(x,y) -> (x-5,y+8)
#8. 8z = 24, so z=3 (see question 7!) #10 correct, if you meant e^(x+3) = 6 as you wrote it, x = ln 3 The others are all good.
you want to find x hours, such that 5.00 + 5.25x < 6.75x
a = -8 (a+6d)/(a+8d) = 5/8 So, plug in a and solve for d: (6d-8)/(8d-8) = 5/8 ...
x^2 = x*x divide that by x and one of the x's in the numerator cancels out. This illustrates the rule that x^n/x^m = x^(n-m) you subtract exponents because the factors cancel each other out.
so, what's the problem? K(1.3)=20lg(1/(1+(992*0.001)?1.3)^12) no idea what lg are, but use their values and then run the result through any online calculator, such as google or wolframalpha
just as a graph with axes for distance vs time has a slope of velocity (m/s), your graph's slope would be torque/force = N-m/N = m I guess that would represent the length of the arm being twisted to produce the torque.
Mathematics in banking
So, assuming you know about the simplex method, just set up your restraints and the target function. A+B+C <= 90000 A >= 30000 and so on the return will of course be the weighted sum of the expected individual returns.
the % change is found by dividing the amount changed by the original amount: (19-20)/20 = -1/20 = -5%
since the coordinates never decrease, and she started by adding (3,4), she can only make 3 more moves which decrease the x amount added, making her maximum x value 3+2+1+0 = 6 Similarly for y, which can add a max of 4+3+2+1+0 = 10 So, she has to end up at (6,6)
you have a 30-60-90 right triangle. Recall its side-length ratios
as always, a = F/m = (50*9.8)N/(6.0*10^24)kg = 8.2*10^-23 m/s^2
um, 3/5 of them, however many that is ...
1+4i = ?17 cis? where tan?=4 so, ?(1+4i) = ?17 cis(?/2) = 2.0305 e^0.6629i = 1.6005+1.2496i So, we have -1+?(1+4i) = 0.6005+1.2496i (-1+?(1+4i))/2i = 0.3002/i + 0.6248 = 0.6248-0.3002i Now just convert that to polar form.
6 grade math
(3+4)m = 7m when m=0, there were 13+6=19 The 7m/m part was correct. The 19 was how many flies there were at the start of the competition. After that, there were 7 caught each minute.
If we set t=0 at 2 pm, we have a right triangle at time t hours later, such that the distance z between the ships is z^2 = (5(t+1))^2 + (10t)^2 = 125t^2 + 50t + 25 if we want z not to be changing, then we need dz/dt = 0 2z dz/dt = 250t+50 dz/dt = 50(5t+1)/z clearly dz/dt=0 ...
the domain of all polynomials is all real numbers. the domain of rational functions is wherever the denominator is not zero. 3x^2+2 is clearly a minimum when x=0, so the range is [2,?)
twice as many men, 1/2 as much time ...
revenue = quantity * price and of course, profit = revenue - cost just plug in the numbers given you
3/8 * 4/5 = 12/40 = 3/10 "of" just means "times"
If there are x erasers, then x + 2x + (2x)^2 = 45 x = 3 ...
#2 When blade 1 is vertical, blades 2 and 3 are at angles 30 and 150 #3 when blade 2 is 7m above the axle, then its angle from the vertical is arccos(7/8). Blade 3 is 120 degrees from that angle. #4 If you mean the blades are rotating at 60°/s = ?/3 rad/s, then since s = r...
x(61-x) = 320 x^2-61x+320 = 0 solve that, using the quadratic formula
sorry. -4 + -12 = -16 -4 - -12 = -4 + 12 = 8 I guess there was a typo somewhere.
there is no change involved. If there are x houses in total, then .80x have garages 60% of those have two-car garages, so 40% have garages that are not two-car. .80x * .40 = 56 x = 175
(3?12 - 8)/(?9-?6) since a^3-b^3 = (a-b)(a^2+ab+b^2), multiply top and bottom by (?9^2 + ?(9*6) + ?6^2) then you have (?36 - 6?2 - 6?3)/3
hmmm. that is the point...
2005-2002 = 3 So, in 3 years, Jamal will be 21+3 = 24 so, Malcolm will be 8 ...
clearly the output is 8 times the input. 7*8 = 56
finish the triangle. You have x = 5 y = -2 r = ?29 Now recall that sin? = y/r cos? = x/r tan? = y/x and so on.
geometry - incomplete
surely you jest ...
of the total number of houses x, .80*.40 x = 56
all your answers are correct. C could be written better online as 10p-75 >= 50
just describe the picture, mentioning the lines and angles. For example Given lines l (AB) and m (CD), a transversal crosses them, intersecting line l at P line m at Q angle 1 is APQ etc. Then we can reproduce your diagram.
Math - homework dump?
Looks like one to me ...
a = (40m/s)/(10s) = 4 m/s^2 F = ma
posting a second time will not speed things up if no one happens to be looking... For the perimeter, you surely know that it is the sum of the sides. So, if the are n sides, you have 4.05n = 486 the weights add up to 45(1 + 1.09 + 0.95) = ?
59.4mi * 1760yd/mi * 1m/1.094yd * 1km/1000m = 95.56km
Maths, Physics, Resultant force
|F1+F2| = ?((1.2*10^8)^2+(5.0*10^7)^2) = 10^8 ?(1.2^2 + 0.5^2) = 1.3*10^8 N So, you want d such that GMm/d^2 = 1.3*10^8 Now just plug in G and the masses and crank out d.
2cos2x = ?3 cos2x = ?3/2 2x = 30°,330° + 360n x = 14,165 + 180n x = 15°,195°,165°,345° You are correct ?3 sin2x + cos2x = 0 ?3 sin2x = -cos2x tan2x = -1/?3 tan < 0 in QII,QIV and so on as in the other problem.
College Algebra. Please Help.
factor out all the perfect squares. Even powers are perfect squares. ?(27a^13/(b^12) = ?(9a^12 * 3a/b^12) = 3a^6/b^6 ?(3a)
Assuming he worked 4 full days, and x hours on Friday (the holiday), then 13*8*4 + 26x >= 650
it is a parabola, with its axis along the x-axis, rather than the y-axis. Note that y = ?x is only the top half. y^2 = x shows both halves.
so far, so good ... dy/dx = 3/(1+(x/2)^2) * 1/2 = 3/[2(1+x^2/4)] = 3/[8(x^2+4)]
no. at least, not with rational coefficients.
4.5x10^9 = 4.5 billion years. so, one half-life has passed...
Use a graphing calculator to solve the equation -3cost=1 in the interval from.0<theta<2pi Round to the nearest hundredth.
The Earth because Earth has a strong enough force to hold the moon and satellites
Make it clear whether you mean (-2/5)x - 9 < 9/10 -2/(5x) - 9 < 9/10 -2/(5x-9) < 9/10 It makes a difference, and as you can see, online text formatting does not fully reflect what you thought you were saying...
what you got was 6 <= -10 not a likely answer
as always, your earnings is (# items sold) * (price for each item) how hard is that?
well, you have the mass and the volume, and you clearly know that density = mass/volume what is the problem?
polynomials and roots have no asymptotes. Surely your algebra book shows the graphs of all of these.
A = 4?r^2 dA/dt = 8?r dr/dt v = 4/3 ?r^3 dv/dt = 4?r^2 dr/dt when r=10, we have -3?/2 = 400? dr/dt dr/dt = -3/800 dA/dt = 80? * -3/800 = -3?/10 You are correct
p^(1/m) = E 1/m lnp = lnE m = lnp/lnE
no way to tell, unless the radius and height of the cone are the same as those of the cylinder. Then, as you surely recall, the volume of the cone is 1/3 the volume of the cylinder.
sin ?/6 = 1/2 since sine is negative is QIII and QIV, we have 2x = 7?/6 or 11?/6 that should help.
homework dumps with no work from you are generally not well received here ...
14-5-10+8 = ?
4(t-9) = t+57-9 t = 28 So, Tony is 28 and Elizabeth is 85 9 years ago, they were 19 and 76 76 = 4*19
If we assume a polynomial-like function, then we know that it will look kind of like a quartic. It is concave up on both ends, and has a bump in the middle where it is concave down. It has minima at x = -5 and x=3, and a maximum at x = -2 Since f"(x) = (x+3)(x-1) = x^2+2x...
I assume you want the integral, but it's not clear just what you are working with. (tanx+cotx)(tanx+cotx) = tan^2x + 2 + cot^2x = tan^2x+1 + cot^2x+1 = sec^2x + csc^2x = 1/(sin^2x cos^2x) so 1 over all that is just 1/4 sin^2(2x) = 1/8 (1-cos(4x)) and that's easy to ...
3/8 x = 135 ...
90 = 10(2+7) 90 = 9(4+6) = (2+7)(4+6)
Trisha uses her credit card to pay for new tires that ended up totaling $527.89. She can pay off up to $200 a month. The card has an annual rate of 22.5%. How much will she pay in interest? 22.5% / 12 = 0.01875 interest per month 1st month 527.89 x 0.01875 = $9.90 interest 527...
Brooklyn opened a store credit card to purchase a sofa for $849. She put the entire purchase on the credit card. Her APR is 19.99% and the minimum payment is 5%. Assuming she makes only minimum payments, what is the remaining balance on her card after 3 months? 849 x (0.1999...
Sorry, that is $125.78
Tabitha opens a credit card in which the minimum payment is 13%. Her current balance is $1,450, not including the finance charge, and the APR is 14.5%. Assuming she makes a payment of $500 this month, how much will the minimum monthly payment be for the next month? .145/12=....
list them, with the decimal points aligned. Then it should be easy.
the zeroes must divide 18, so try the easy ones first. A little synthetic division shows that f(x) = (x+2)(x^2-9) I'm sure you can take it from here ...
10000 * 0.92^50
you want n such that 10+0.10n < 5 + 0.25n
duh - half as much (one half-life)
Explain which companies would advertise APR over APY and describe how this would help them attract customers.
nope. 60 years is 3 half-lives, so 1/8 will remain.
since "many" is vague and unspecified, #6 in no way implies #1. For example, #6 might be: I have 100 books. You have 1000 books. We both have "many" books, but #1 is clearly false. Still, in the context of these sentences, maybe #6 means #1, since we seem ...
well, 24 = 4*6, so the amount left will be (1/2)^6 = 1/64
Maths - incomplete
How much older is Siphon now?
1/1.15 + 1/0.85 = 2.046 So, he gained 4.6%
how are these matrices?
10/7 as much, right?
blue + blue+4 = 8
96 * (1/2)^(t/8) = 50 t = -8 ln(50/96)/ln2 = 7.53 hr I assume that 96 and 50 are both either ng/L or mg/L 7.53 hr makes sense, since after 8 hrs the amount will be 1/2 * 96 = 48 mg/L