# Posts by STEVE

Total # Posts: 52,329

Maths
clearly, the fastest has run one complete lap, while the slowest has run only 1/4 of a lap. Then if they started at the eastern side of the track, after 30 seconds they are at the points E,S,W,N in order of speed, fastest to slowest. After 30 more seconds, they are at E,W,E,W ...

maths
well, there were 1100-220=880 mangos, so ...

Calculus 2 - Indeterminate forms
it's quite simple. The rule states that lim f(x)/g(x) = lim f'(x)/g'(x) so, your limit is the same as (ln2*2^x-ln3*3^x)/-sinx(x) now, as x->0, that -> (ln2 - ln3)/0 = ? This is confirmed by the graph at http://www.wolframalpha.com/input/?i=(2%5Ex-3%5Ex)%2F(...

Geometry
the original block has surface 6*2^2 subtract the two circles removed: 2*?r^2 add the curved surface of the hole: 2?rh where r = 1/2 and h=2 the volume is of course 2^3 - ?r^2h

pre calc
draw a diagram. You can see that 5/x = sin ?/3

Pre-Calculus
Since profit is revenue less cost, we have p(x) = 150x - (0.02x^2 + 100x + 3000) now just find the vertex of that parabola.

Calculus
If the base has dimensions x and 2x, then we have 2x^2y = 10 so, y = 5/x^2 So, the cost of the container is c(x) = 12*2x^2 + 5*2xy + 5*xy = 24x^2 + 15xy = 24x^2 + 75/x so, find c(x) when dc/dx=0

pharm
15 mg/ml * 120ml = 1800 mg

Physics
You can easily adapt the example here to fit your problem: http://physics.bu.edu/~redner/211-sp06/class13/class13_rotation.html

math
9+x

Math
still the same: https://www.jiskha.com/display.cgi?id=1500466804

algebra
If your Revenue equation is corrected to read Revenue(x) = 5x then your Profit equation is correct. Not sure about the "need to make" clause. It's just what she makes.

maths
that's better

maths
That's not what I get. Where's your work? Did you try actually using your results to see whether they produce the desired AP?

Math
subtract the inner park from the total area: (350+2w)(200+2w)-350*200 = 74464

Mathematics
You got me. Aside from expanding into Taylor series and dividing, I don't come up with a trick to evaluate it.

Math
since all the sides are equal, the perimeter is just 3 times the length of one side.

Physice - oops
I should have said dynes, not ergs. Ergs are energy, not force.

Physics
Recall that F = ma so, just multiply. Note that the answer will be in ergs, not Joules.

math
homework is 2/3, so revision is 1/3 1/3 * 9/2 = ?

math
well, there are 360 degrees in the whole pie, so ...

math
well, 1/5 of 35 is 7, so ...

arithmetic progression
8/2 (2a+7d) = 56 20/2 (2a+19d) = 260 ...

geometric progression
probably best to first fins a and d: a+4d = 8 a+9d = -7 now subtract, and crank it out.

Math
If the mother is twice as old in x years, then we have 45+x = 2(12+x)

Math
(-6/7+18/28)*-7/5 = (-24/28+18/28) * -7/5 = -6/28 * -7/5 ...

Mathematics
b/g = 3/4 (b-3)/g = 5/8 b+g = 42

Math
well, we do know that (1+.035)^10 = 1.4106 (1+.035/4)^(4*10) = 1.4169 ... e^.035 = 1.4191

geometry
h/27 = sin 47°

Math
a*-1/27=1/18 a=-7/6 Bzzzt. a = -3/2

maths
80*3 = 60*4 = 240

Physics
draw a diagram of the velocities. Recognize an 8-15-17 right triangle?

Math
No one asked how many fruits there are. You just need to give the fraction. Read the question carefully.

Math
3/5 + 1/4 = 12/20 + 5/20 = 17/20 so, what do you think?

Calculus - incomplete
What does the coastline look like? Is it straight? N-S, E-W? All I know for sure just now is that the radar station lies somewhere on a circle of radius 1.5 with its center at the port. Anyway, draw a diagram. It should be clear how to use the available angles and distances to...

math
No way to tell. However, if the function has rational coefficients, then the irrational roots must occur in conjugate pairs. Thus, the other root must be 3-2?2

college algebra
Let x = amount in bonds Then 68000-x is the amount in CDs Now just add up the interest: .08x + .07(68000-x) + .10*68000 = 12040

Science
total energy = PE + KE = mgh + 1/2 mv^2 Now just plug in your numbers

math
8 is 16% of the 50 sampled. That means that 200 is 16% of the whole population. 0.16p = 200 ...

max height reached at t=2 h=0 at t=5 so, 2 seconds rising, 3 seconds falling he got the 3 by seeing how long it takes to fall 144 ft. s = 1/2 at^2

Math
Certainly not English -- the units are metric! To get the width of the path, subtract the inner garden area from the total: 40*25 - (40-2w)(25-2w) = 126

Calculus
the derivative is -x/50 + 50 maximum revenue occurs when that is zero.

Chemistry
what don't you understand? Surely you can at least pick out the elements, and then see which are atoms and which are molecules. And take a stab at the compounds; the ionic ones usually involve a metal and a halogen.

AOOOGAH!! Homework Dump!!
no ideas on any of these? We're not here to do your homework for you...

Physics
a = 2 m/s^2 means that v grows by 2 m/s every second. So, what do you think? v = at

algebra
recall that the vertex of a parabola ax^2+bx+c is at x = -b/2a

Algebra
g(x) is written in the slope-intercept form. Its slope and y-intercept should be obvious. For f(x), note that y changes by 2 when x changes by 1 f(0) = -1 ...

decreased by twice a number
if the number is x, what is twice the number? 2x what is 6 decreased by 3? 6-3 so, what do you think?

Algebra
each element must be identical in the two matrices (you already have 1=1 and 3=3), so you just have to solve 5x-8 = 2 4m-1 = 7m+6 then use those values to fill in the unknown elements.

Calculus
you have a point and a slope, so just use the point-slope form, which you learned in Algebra I: y+4 = 5(x-2)

algebra
?121 = ?

math
0.7x = 3.43 x = 3.43/0.7 = 4.9

math
4/100 x = 0.8 x = 0.8 * 100/4

maths
10/2 (2a+9d) = 220 5/2 (2a+4*2d) = 100

Maths
1,2,4,7 cannot be made I think you can easily show that all the rest are multiples of 3 or 5, or can be made using them and makeable remainders.

KSU
7:3

Math
take logs. 100 log 99 = 199.56 99 log 100 = 99*2 = 198

algebra
Add up the wages: 8x + 11(23-x) = 208

One-to-one function
think about it. If f(1) = 2 and f(2) = 2 how can you pick an inverse g(2)?

Calculus
now you have given even less information than in your last post! There are many many functions passing through (4,-11) tangent to that line. The simplest is, of course, f(x) = (7x-61)/3 Even the next simplest one could be a parabola opening either up or down, and there are ...

math
man, I can't even figure out the question...

well, you have the function. Using it, you can find the initial speed (64 ft/s), maximum height (at the vertex), and how long it takes to hit the ground (when h=0). Incidentally, it is odd that the initial height is given in meters, but the -16t^2 is in ft/s^2.

Calculus
No way to tell, unless you know you are working with something simple, like a quadratic. If y = ax^2+bx+c and you have two points, then you also have 2ax+b = slope of the tangent line Then you have three equations to solve for a,b,c.

Pre-Calc
there are lots of online graphing sites, like desmos, wolframalpha, etc. Find one you like and produce your graphs; see where they intersect.

Math
(2x 3 y2 3z)(3xyz^4)^3 = (18xy^2z)(27x^3y^3z^12) = 486x^4y^5z^13 (2x^3y^2 3z)(3xyz^4)^3 = 162x^6y^5z^13 Or something else, depending on how you have mangled the expression

Math
(-2y4^z3)^2(-xy)^4 = (4y^8z^6)(x^4y^4) = 4x^4y^12z^6

Physics
(0,-6)+(10,0)+(0,5) = (10,-1) I assume you can find vector lengths. The distance, naturally, is just 6+10+5

Chemistry
assuming that is the number of molecules of CO2, then just divide by Avogadro's number: 7.7x10^24 / 6.02x10^23 = 1.28x10^1 = 12.8 moles

physics
1.2x10^-6 / 0.25x10^-12 = 4.8x10^6

Math
I will try to unravel your garbled language, and get x^2 = 100/2 + 12+1 If that's not right, maybe you can fix it up. Not quite sure what "dozen one" means.

Easy Math
f(x) = 1/x g(x) = x^2-5 f?g = f(g) = 1/g ...

Math trigonometry
Assuming you meant 8sin^2?+10 sin? cos?+3cos^2? = 0 (2sin?+cos?)(4sin?+3cos?) = 0 see what you can do with that.

Calculus
we have ?/3 h^2(3r-h) = 5?/3 3rh^2-h^3 = 5 3h^2 dr/dh + 6rh - 3h^2 = 0 h dr/dh + 2r - h = 0 dr/dh = (h-2r)/h = 1 - 2r/h ...

MATHS
13601 = 87*156 + 29

science
If there are g grams of gold, then add up the volumes (mass/density): g/19.3 + (9.35-g)/10.5 = 0.690 g = 4.6 So, the % mass of gold is 4.62/9.35 = 0.49 = 49%

calc
draw a diagram. Using similar triangles, if her shadow has height h when she is x cm from the light, then h/500 = 120/x or, hx = 60000 so, h dx/dt + x dh/dt = 0 Now, find h when x = 150, and you know that dx/dt = -60 cm/s; you can then find dh/dt

Math
well, there are 4 sides, right? for the cost, just multiply area by cost/m^2

Math
factor out the ?27 and you have ?27^2 (6 - 1/4)^2 = 27 (23/4)^2 = ...

finite math
well, it is certainly not (a) 30. Note that you can choose any of 6 appetizers. For each of those 6, you can pick any of 8 salads. and so on. So, what do you think?

Math - typo
I hope you caught my top. The total area is (c+d)^3

Math Division polynomials
Note that (c^2+2cd+d^2) = (c+d)^2 That means the area is (c+d)^2 * (c+d) = (c^2)^3 Now, divide the total area by the area covered by one can to get the number of cans needed.

geometry
relative to C=(-1,4), P = (-1,-1) Q = (5,-3) So, scaling those coordinates by 2, P -> (-2,-2) Q -> (10,-6) making P' = (-3,2) Q' = (9,-2) That is, P' = C+2(P-C) Q' = C+2(Q-C)

Computer programming
sum=0 for i = 1..4 {sum += cat[i]} for i = 1..4 {pct[i] = cat[i]/sum * 100}

Math
Too bad you didn't show your work... -16(5^2)+430 = -16 * 25 + 430 = -400 + 430 = 30 How ever did you get 270? 5^2 is not 10

Math
just plug in 5 for t and evaluate it.

Maths
30% = 30/100 = 3/10 = 0.3

Maths
just plug and chug: (4/7+5/21)÷(4/7-5/21) = (12/21+5/21)÷(12/21-5/21) = (12+5)/(12-5) ...

Optional mathematics
(3-4sin^2x) (1-3tan^2x) = (3-4sin^2x) * (cos^2x-3sin^2x)/cos^2x = (3-4sin^2x)/cos^2x * (cos^2x-3sin^2x) = (3sec^2x-4tan^2x)(cos^2x-3sin^2x) = (3+3tan^2x-4tan^2x)(cos^2x-3sin^2x) = (3-tan^2x)(cos^2x-3sin^2x) see if you can finish up from here

math
the product of weight and distance must be equal on both sides, so 60*8 = 80x

geometry
of which lines? I don't mind helping to find answers, but I hate having to provide the questions as well ...

geometry
so, where is P?

Maths
1.20 * 0.90 * 0.95 = 1.026 so he gets 2.6% profit

math
4526.5/4050 = 1.1176 or 11.76% in two years. That means it gets 5.88% each year so, 1 lakh grows by 0.0588 each year ...

math
If all 30 heads are chickens, then there are 60 legs. But we have 86 legs, so there are 26 extra legs. If we replace a chicken with a cow, we get 2 more legs. We need 26 more legs, requiring 13 cows. So, there are 13 cows and only 17 chickens.

geometry
you only show one line.

Math
3*33 + 2*35 + x = 6*34 or, if you notice that 34 is midway between 33 and 35, the extra day had to be a 35, to balance them out.

math
234 = 2m m = 117 so, 117 mangoes, 234 apples ...

Calculus
(a) Apparently you are supposed to find the slopes over the various intervals [a,b]. As always, that is [f(b)-f(a)]/(b-a) Just plug in the numbers. (b) By looking at the way the results approach a single value, that is the estimate of the speed. It should be 50.28

calculus 3
see related questions below

calculus 3
Draw a diagram of the velocities. If the plane's heading is ?, we need the final x- and y-components to be N45W. So, 180sin? - 32cos60 = v sin135 180cos? - 32sin60 = v cos135 ? = 20° v^2 = 180^2+32^2-2*180*32 cos40° v = 157 mph