# Posts by steve

Total # Posts: 54,960

math
yes

PreCalculus
You know how to find the vertex of a parabola. That will give the maximum height. It hits the ground when h=0. Sol solve that for t.

Math
y^5 + 3x^2 y^2 + 5x^4 = 49 5y^4 y' + 6xy^2 + 6x^2y y' + 20x^3 = 0 y' = -(6xy^2+20x^3)/(5y^4+6x^2y) at (-1,2) y' = -(6(-1)(2^2)+20(-1)^3)/(5(2^4)+6(-1)^2*2) = 11/23

Math
u = lnx du = 1/x dx dv = x dx v = 1/2 x^2 ?u dv = uv - ?v du, so ?x lnx dx = 1/2 x^2 lnx - ?(1/2 x^2)(1/x dx) = 1/2 x^2 lnx - 1/2 ?x dx ...

Math
if f(a) = b then g'(b) = 1/f'(a) Now just plug in your numbers

Math
you can verify your work with any of a number of fine interactive online "Riemann Sum calculator" sites

Math
Alex's score for a game is given by the expression 9-8.2-(-1.9). Beth's score for the game is -8-(-5.4)-1.8. Whose score was higher?

math
bingo

math
just multiply all the numbers by 5. !!

Math
Start by using the product rule and the chain rule y^5 + 3(x^2)(y^2) + 5x^4 = 49 5y^4 y' + 3[(2x)(y^2)+(x^2)(2yy')] + 20x^3 = 0 Now collect all the y' terms, divide, and plug in your numbers.

Java
Sure looks like #2 to me Time to read up on objects and their members.

Math
no, you used 5*2=10 instead of 5^2=25 for the round area.

Math
w/z = 18/2 w = 9z

Physics
I think it would help to know the elevations in the hills and valleys, no? and PE relative to what? Anyway, PE = mgh so knock yourself out ...

math
is there supposed to be a fraction somewhere in there?

math
You're going to have to give a bit more information on the locations of U,V,Y.

math
well, 4d*3 = 12d now what do you think?

Maths
well, 12 minutes is 1/5 of an hour, so what's 1/5 of 50?

Math
using slope-intercept form, y = mx+b so, 53m+b=164 63m+b=214 now solve for m and b or, using point-slope form, since the slope is (214-164)/(63-53) = 5 y-164 = 5(x-53)

math
(a) correct (b) Since NM is not parallel to OB, it cannot be expressed in terms of OB alone. We do know that ON + NM = (OB-OA)/2 OA/2 + NM = OB/2 - OA/2 NM = OB/2 - 3/2 OA (c) OP = OM + 2MN = (2,0)+2(-6,2.5) = (2,0)+(-12,5) = (-10,5) So, P' = (-15,13)

math
3 1/4 - 1 7/8 = 3 2/8 - 1 7/8 = 2 10/8 - 1 7/8 = 1 3/8

math
no, since 3/8 + 2/3 > 1

Math
huh? Looks to me like the domain is all real numbers. The fact that x=0 is included in both parts doesn't really matter, since e^0 = e^-0 = 1 So, since the functions are symmetric, all you need is ?[0,?] 0.5 e^-x dx = 1/2

math
whatever - we can start with log_x(x/4) = log_x(x) - log_x(4) = 1-log_x(4) So, assuming all logs to the same base (x), we can make it 1+log(1/4 * 8/125 * 25/2) = 1-2log5 I suspect multiple typos

Math
what about 11:04 11:13 12:03 and 12:30 and so on?

Differential Equations
?sinx cosx dx = 1/2 ?sin2x dx = -1/4 cos2x Try using that and it should make things less messy.

Differential Equations
So, in the meantime, have you actually tried to solve it? It should not be too hard to plug in your equation and find that y = c1 sinx + c2 cosx - 1/2 x cosx If you still cannot arrive there, try this article, where the example is almost exactly like yours. https://www....

Differential Equations
?? Usually separation of variables is for y' = f(x) g(y) Here, I'd use u=y' and an integrating factor.

Pre-Algebra
Take a loot at gyazo - you can capture a picture on your screen and provide a link to it here. You may have to obfuscate the url since in general they are not allowed here. For example, here is a gyazo link of some pentagons: https://gyazo.com/ed959ca81dc491b313d5cb35a795ee99

American Government
Which of the following are required for a fair trial? the trial is speedy and public the defendant is afforded legal representation the judge issues a gag order to preserve the rights of the defendant. jury members are impartial and residents of the region the trial takes ...

American Government
Thank you very much

American Government
which of the following are examples of civil liberties? select all that apply. A) shooting a person in anger B) protesting on a busy street C) speeding in traffic D) not incriminating yourself in court E) serving in the army My answers are B & D

English
#2 is very haiku-like!

math
Assuming a is the old cost, then the new cost will be a * y/x

physic
clearly you did not make the effort to look up the law. a is the semi-major axis of the elliptical orbit.

physic
well, it looks like M is 82*sunmass find the values for that and G and a and then just plug them in. I assume you can do that much...

Math
well, the total circumference is C = ?d = 20? = 62.8 inches, so ...

math
3m+2b = 995 2m+b = 585 Now just solve for m and b (in cents)

Math
total hours: 2 3/4 + 3 3/5 + 5 1/2 = 11 17/20 so, divide that by 3 for each day's work next week

Carpenter
Man. I think you mean 17' elevator (17" isn't very tall!) 90° (vertical) 1.5/x = cos 65° h/17 = sin 65° But these don't look right. Maybe if you explain things a bit more.

Math
volumes are round: ?r^2h = ?*(7/2)^2*2 = 98?/4 = 76.969 in^3 parallelopiped: LWH = 6*9*2 = 108 in^3 should be easy to tell now, eh? areas are round: ?r^2 + 2?rh = ?r(r+2h) brick: LW+2LH+2WH = LW+2H(L+W) Now plug in your numbers and compare

Geometry math
#1,2 no idea #3 correct #4 surely you mean equilateral triangle, unless we're doing spherical trig. Since all the angles are equal, and they sum to 180, what do you think?

Math
Just turn the words into math. A particular Chemistry book costs \$6 less than a particular Physics book c = p-6 Two Chemistry books and three Physics books cost \$123 2c+3p = 123 now substitute and crank it out

Calc Desperate
The graphs intersect at (-3,3) and (0,6) Using vertical strips is easiest, since the upper and lower boundaries do not change. That means we integrate on x. For revolving around the x-axis, that means using discs (washers) of thickness dx, so v = ?[-3,0] ?(R^2-r^2) dx where R=...

Physics
F=mg

Physics
a = GM/r^2

Physics
just plug and chug. The weight is GMm/r^2 and GMm is constant, so (1/(R+H)^2) / 0.94 (1/R^2) It's a bit messy to solve that for H, but since H=kR for some k, we just want to solve for k. H/R = k. (1/((1+k)R)^2) / 0.94 (1/R^2) R^2/(R(1+k))^2) = 0.94 1/(1+k)^2 = 0.94 (1+k)^2...

Calculus
If you meant 2/n^3, yes, since (2n^2 - 1) < 2n^2 (3n^5 + 2n + 1) > 3n^5

Calculus
recall that the Riemann sum is sum f(xi) ?x Here, ?x = 1/n, so the interval has width 1 That means it's not D xi = 0+?(1/n * i) so, it looks like ?[0,1] ?x dx

math
since the volume is proportional to the cube of the linear dimensions, the new h is 14/?2 = 11.11

differential equations
(x^2-1)y'+2y=(x+1)^2 y' + 2/(x^2-1) y = (x+1)/(x-1) now use the integrating factor of e^(?(x+1)/(x-1) dx) and things get simpler.

Math HELP!!!!
33610/60156

physics
time till velocity (v=v0-at) is zero: 3.5/2 - 9.8t = 0 t = 1.75/9.8 That's how long it rose upward. It fell for the same time, so ...

#1 You need to solve 2(x+y) = 60 xy = 125 so, since y=30-x, x(30-x) = 125 x = 5 or 25 #2 It sounds like you want x where x^2 + (2x)^2 = 15^2 #3 it hits the ground when its height is zero, so you need to solve -x^2/40+x+1 = 0 making it a bit more comfortable by clearing ...

algebra 2
First look for low-hanging fruit. A little trial shows P(1)=0, so P(x) = (x-1)(2x^2-x+2) The quadratic formula finds the other two roots. Since cubics are hard to solve in general, if they throw one your way, you know it must have at least one real root, and it will probably ...

algebra 2
the numerator must be a factor of 12 The denominator must be a factor of 4 So the possibilities are ±(12/1), ±(12/2), ±(12/4) ±(6/1), ±(6/2), ±(6/4) ±(4/1), ±(4/2), ±(4/4) ±(2/1), ±(2/2), ±(2/4...

algebra 2
first, put into descending powers: 3x^3+3x^2-27x = 0 Now factor out 3x, leaving 3x(x^2+x-9) = 0 so, clearly, x=0 is one solution use the quadratic formula to find the others. You know they are real, since the discriminant is positive.

algebra 2
if a is a zero of f(x), then (x-a) is a factor. So, you want f(x) = (x-1)(x-2)(x-3)

Algebra
Gayle starts to save at age 20 for an extended vacation around the world that she will take on her 45th birthday. She will contribute \$1000 each year to the account, which earns 1.65% annual interest, compounded quarterly. What is the future value of this investment when she ...

spanish
Translated the question means How many people live in your house?

math
the actual value does not matter replacing h by 4h, we have the new area is b(4h)/2 = 4(bh/2) so the area is increased by a factor of 4

Math - Algebra
the amount halves every 9.45 minutes, so y = a(1/2)^(t/9.45) but,1/2 = e^-0.693 so y = a(e^-0.693)^(t/9.45) = ae^(-0.0733t) where t is in minutes Now use that to evaluate your other questions

math
The midpoint is just the average of the ends. So, it is at (-2+12)/2 = 5 check: -2 = 5-7 12 = 5+7

Honors Geometry
since when does the shorter diagonal bisect the longer?

Math
you are correct that V=1/2 b x h x l Unfortunately, you have not given a value for l

Math
sorry. You have the area of the triangular base. Now you need the length (or height) of the prism. V = Bh here, "h" is the height of the prism perpendicular to the base, not the height of the triangular base. The volume of prisms is always Bh.

Math
well, you have to know what h is, right?

MATHS
just replace each value with its scaled equivalent. (2cm)(1.5cm) --> (2*5km)(1.5*5km) = (10km)(7.5km) = 75 km^2

MATHS
A MAP HAS A SCALE OF 1 CM = 5 KM On a map, a forest is shown as a rectangle measuring 2 cm by 1.5 cm what is the real area of the forest

Math
6x = x + 2.5 x = 0.5 now use that to get the lengths.

Math
LW = A So, you want W such that 18W = 27*10

math
1/B + 1/25 = 1/15

geometry
I assume you meant (x+3)/3 = (y+2)/2 x/3 + 1 = y/2 + 1 ...

Calculus 2
time for you to step up with some work. Just plug in your formula: s = ?[1,6e] ?(1+y'^2) dx so, first step: what is y'?

logical reasoning
start off as in the example, using some small values. You will see a pattern developing.

Algebra
#5 might also be x^3+7 depending in just what is in the cube root

Algebra
#5 (x+7)^3 #8 ?(5x)(?x-5?5) = x?5 - 25?x (?5)x(?x-5?5) = x?(5x) - 25x not sure either one is any simpler #10 add exponents: 7^(1/3 + 2/3) = 7^1 = 7

math
well, 3 tails out of 5 events = 3/5

trignimetery
csc^2? = 1+cot^2? = 1 + 1/tan^2? so, csc? = ?(1+1/tan^2?) or ?(1+tan^2?) ---------------- tan?

maths
2x - 3/x = 5 2x^2 - 3 = 5x ... or (2x-3)/x = 5 2x-3 = 5x ... Pick the one that you meant to type...

Math
recall the Pythagorean Theorem. Then solve for x in (x+1)^2 + (x+3)^2 = (x+5)^2

MATh Methods
You gonna do any of the work here? #1. profit = revenue - cost They gave you the formulas for both, so just plug and chug: 1.5x^2 - (20 + 5x) = 800 Remember that x is 100 liters #2. Just start with what they tell you: c = 10 + kh^2 32.50 = 10 + k*3^2 -- find k. Then use that ...

Algebra 2B
Not sure what you want. Do you mean that g is replaced by the previous value of g, so that g(n+1) = -2|g(n)-2|+4 ?? Otherwise, how do you get any looping activity?

Math
well, 243 = 3^5 Note the pattern in the number of pieces 1 = 3^0 3 = 3*1 = 3^1 9 = 3*3^1 = 3^2 ...

math
well, just add it up: .05x + .03(x-1600) = 144

Calculus 2
using discs of thickness dx, v = ?[0,?/2] ?r^2 dx where r = y = cosx v = ?[0,?/2] ?(cosx)^2 dx = ?^2/4 using shells of thickness dy, v = ?[0,1] 2?rh dy where r=y and h = x = arccos(y) v = ?[0,1] 2?y*arccos(y) dy = ?^2/4

Calculus 2
The curves intersect at (0,0) and (6,36). So, using discs (washers) of thickness dy, v = ?[0,36] ?(R^2-r^2) dy where R = 8-y/6 and r = 8-?y v = ?[0,36] ?((8-y/6)^2-(8-?y)^2) dy = 360? using shells of thickness dx, v = ?[0,6] 2?rh dx where r=8-x and h=6x-x^2 v = ?[0,6] 2?(8-x)(...

Math
Need a little help. I was asked to find perimeter of a rectangle, which I did and got an answer of 66. Now I have to convert it to feet. That's where I'm stuck. What is the perimeter of the actual patio in feet? 2 cm=1ft P=2(12+21)=66cm

Math
a=2c=3p a+c+p=88 now just solve for a,c,p

Algebra 2
Hmmm. time = distance/speed ...

Algebra
As written, it is -(5)-1 = -5-1 = -6 So, maybe you meant -(5)^-1 = -(5^(-1)) = -(1/5) = -1/5

Math
since B's density is 11.3/13.6 that of A, the volume needed is 13.6/11.3 * 50 cm^3

Math
If the base is b, then (b/2)/6 = tan 48° Then each of the two equal sides s is 6/s = sin 48° Now the perimeter is just b+2s

algebra 2
y = 4x + 14 y/4 = (4x+14)/-4 = 4x/-4 + 14/-4 = -x - 7/2 you are correct now.

Maths
If AC is the revenue function, then the marginal function is its derivative: 0.0002q-0.02-(5000/q^2) If not, what is AC?

pre-alg
yes

At any rate, I assume you can find the area of a triangle, given its sides. The surface of the pyramid is just the sum of the areas of the triangular faces.

which sides are the triangular base? Is one value the altitude, or a slant height?

since you don't give me any of the dimensions, how can I possibly guess?

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