# Posts by STEVE

Total # Posts: 50,417

**Calculus**

I suspect a typo, since what you have written is just f(x) = x/(x+x^2) = 1/(1+x) f' = -1/(1+x)^2 f" = 2/(1+x)^3 Anyway, fix that, find f", and recall that f"=0 means an inflection point f" > 0 means concave up f" < 0 means concave down

**calculus**

use integration by parts. That is just the product rule in reverse. d(uv) = u dv + v du u dv = d(uv) - v du ?u dv = ?d(uv) - ?v du ?u dv = uv - ?v du So, here we just let u = (lnx)^2 dv = dx du = 2lnx * 1/x dx = (2lnx)/x v = x ?(lnx)^2 dx = x(lnx)^2 - ?2lnx dx Now repeat, this...

**math**

x >= 15000/12 = 1250 So, consider how long a ride might take, and how long the park is open each day.

**math**

5 divides evenly any multiple of 5. Not sure what you mean by "5 divide into equaly" [sic]

**Help please I am lost, algebra**

if g(14) = -6, then that means you have the point (14,-6) on the graph. Using the point-slope form, then, you get y+6 = -5/4 (x-14) Now massage that to the slope-intercept form: y+6 = -5/14 x + 35/2 y = -5/14 x + 23/2

**Math**

The first model is linear because the changes are constant. In fact, y = x/2 - 1 For the second, check the differences: 1st: 5.1, 20.4, 81.6, 326.4 2nd: 15.3, 61.2, 244.8 If t were quadratic, the 2nd differences would be constant. Since they are also growing rapidly, you ...

**Functions, please help**

2700x+21000 = 83400 just solve for x 2010 is 7 years after 2003, so just plug in x=7 for P(x)

**Physics**

Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B. We know that he is in the water for d/(v/3) = 3d/v seconds, so y = 3d/v * v = 3d. His path is thus ?(d^2+x^2) meters on land, d meters...

**Physics**

Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B. We know that he is in the water for d/(v/3) = 3d/v seconds, so y = 3d/v * v = 3d. His path is thus ?(d^2+x^2) meters on land, d meters...

**Math**

p(red) = (#red)/(#total)

**Math**

start with 7.2 Since 10^0, that is just 7.2x10^0 Now, lowering the power of 10 moves the decimal place to the left, so 7.2x10^0 = 7.2 7.2x10^-1 = 0.72 7.2x10^-2 = 0.072 and so on The number of leading zeroes after the decimal point is 1 less than the negative power of 10.

**Calculus**

every polynomial is continuous and differentiable everywhere. At the midpoint, x = (a+b)/2 f'(x) = 2?x+? So, show that f'((a+b)/2) = (f(b)-f(a)/(b-a)

**calculus**

One way: Theorem of Pappas If the edge goes from (0,0) to (0,1), then the center is at (?3/2,?3/2). The area of the hexagon is 3?3/2. The radius of rotation is ?3/2, so its path has length ??3. So, the volume of the solid is ??3 * 3?3/2 = 9?/2 Another way: calculus. Using ...

**Maths**

I worked it out, and also got a 4th-degree equation in x. So what? Just solve it for x using whatever method works best. I did get z=x rather than z = -2x, but maybe I made a mistake.

**math**

A10-A7 = 3d = 15 Now you know d, so you can get a, and then the terms.

**Math1**

2^24 - 1

**algebra 1**

well, did you check it? -16*36 + 46*6 + 6 = -294 So, stop guessing and do the math! h = -2(8t^2-23t-3) = -2(8t+1)(t-3) So now what do you think?

**calculus review please help!**

#1 ?[0,4] arcsin(x/4) dx = 2?-4 To do this one, let x = 4sin(u) arcsin(x/4) = arcsin(sin(u)) = u dx = 4cos(u) du Now you have ?[0,4] 4u cos(u) du That you can easily do using integration by parts. Note that in changing variables, ?[0,4] f(x) dx = ?[0,?/2] g(u) du #2 Using ...

**Math**

x(?/4) = ?2 y(?/4) = 1 dy/dx = (dy/dt)/(dx/dt) = sec^2(t)/(sect tant) = sect/tant = csc t so at t=?/4, y' = ?2 and the tangent line is y-1 = ?2 (x-?2) y = ?2 x - 1 Note that x^2 = 1+y^2. So, to check the graphs, see http://www.wolframalpha.com/input/?i=plot+x%5E2-y%5E2%3D1...

**Precalculus**

|x| is a tricky one, since it changes at x=0. Consider it a |x| = ?x^2. Then, using the chain rule, d/dx ?x^2 = 2x/(2?(x^2)) = x/|x| Note that this correctly captures the change of slope at x=0. d/dx[5(x^2 + 3|x|)] = 5(2x + 3x/|x|) Also, the function is not differentiable at x=0.

**Math**

you don't say whether the radius, diameter, circumference is 28. Anyway, just plug in the formula: A = ?r^2

**maths**

remember the 3-4-5 right triangle? Just scale it up by 2.

**math real and complex numbers lesson**

(7+3,-9+5) = (10,-4)

**Maths**

x-28 = 42-x

**math**

It is true that Anna is not 1000mm taller, but in this case, the "times" indicates a multiplicative factor, and almost no one would interpret it as you have indicated.

**physics/maths help damon or steve or scott**

s(t) = s0 + v0t + a/2 t^2 so, s0 + 6v0 + 18a = 246 s0 + 9v0 + 81/2 a = 246+69 Solve for v0

**trigonometry**

draw a diagram, and you can figure angle T. Then, use the law of sines.

**trigonometry**

use the law of sines.

**math**

x-y = 1/10 y = 4/7 x - 4/7 = 1/20 x = 4/7 + 1/10 = ?

**Maths**

P = R-C break-even when R=C (P=0)

**Maths**

If all were bikes, there would be 70 tyres. There are 9 extra tyres, so that means 9 bikes were replaced with trikes...

**Math**

f(14) = 2*14-2 = 26 26 = m so the first letter is m and so on

**Calcalus**

ln(x^2-15y)=x-y+5 1/(x^2-15y) * (2x-15y') = 1-y' 2x-15y' = x^2-15y - (x^2-15y)y' Now just collect terms and solve for y' to get y' = (x^2-2x-15y)/(x^2-15y-15) So, at (-4,1) that is y'(-4) = (16+8-15)/(16-15-15) = -9/14 Finally, using the point-slope...

**Geometry**

8 * (8 + 1/24) * 34 = ? Or, considering the possibility of a typo, 8 * 8.5 * 34

**Math**

time = distance/speed, so 196/(75+65) = ?

**Maths**

That's elevation, not evolution! Consider the fact that the sides of a 30-60-90 triangle are in the ratios 1:?3:2 and just scale that up for your diagram.

**Math**

so, how many cubes are there? p(cube) is that over 100

**Math**

well you multiply by -4, so B looks good.

**Math**

1) 30cm * ?48m * 12m = 24.94 m^3 ... 3) ?/4 * 3^2 * h = 24.94 Now the rest should not be too hard. Come back if you get stuck.

**Linear algebra**

This is just a standard rotation matrix, explained here: https://en.wikipedia.org/wiki/Rotation_matrix

**Calc AB**

V(t) = 100 + (5t+4) - t^2/2 so you are correct there. V'(t) = 5-t So, you are correct that V is a max at t=5 The average value of a function is (?[a,b] f(t) dt)/(b-a) So, that means that #3 is ?[0,5] (-0.5t^2+5t+104) dt = 337/3 So, you want to find when (-t^2/2 + 5t + 104...

**math**

in 1969: 32000 / 1.0583^45 = ? in 2059: 32000 * 1.0583^45 = ?

**maths**

well, r^3 = 96/12 = 8, so r=2 take it from there.

**Math -- Calculus**

If the printed area has dimensions x and y, then xy=A, so y=A/x The actual page has dimensions x+L+R and y+T+B To minimize the page area, then you want to minimize f(x,y) = (x+L+R)(y+T+B) f(x) = (x+L+R)(A/x + T+B) = (T+B)x + A + A(L+R)/x + (L+R)(T+B) df/dx = (T+B) - A(L+R)/x^2...

**Calculus**

Try changing the equations in your earlier post to reflect the new parameters. How far do you get?

**Calculus - Optomization Problem**

see related questions below. In particular, http://www.jiskha.com/display.cgi?id=1318801288

**Math**

review the associative property of addition.

**College Algebra**

swap variables x = 4-y^2 y = ±?(4-x) But you need to pick the branch where 4-x >= 0. take a look at the graph and I'm sure you can answer the questions. http://www.wolframalpha.com/input/?i=%E2%88%9A(4-x)

**Calculus**

As always, draw a diagram. It is clear that if the length of the rope is z when the boat is x ft from the dock, z^2 = x^2+36 z dz/dt = x dx/dt Figure x when z=10, then just plug in your numbers and solve for dx/dt.

**Calculus**

I don't know how the liquid can drain and leave the substance behind, if it's dissolved. Maybe it's just in suspension, and the liquid drains through a filter. Anyway, the volume of water at time t hours is v = 60-4t The concentration is c(t) g/L = 100/v(t) = 100/(...

**Calculus**

y = 2?x - 4 since x and y are both functions of t, think chain rule: dy/dt = 1/?x dx/dt Now just plug in your numbers and you have dy/dt = 1/2 * 9

**Maths**

see your other posting -- this is just the same idea.

**Maths**

PQ is 4 units from AD and 6 units from AB. So, The slant height of ?ABP is ?(15^2-6^2) The slant height of ?ADP is ?(15^2-4^2) Now you can easily figure each area, and then the cost.

**Maths**

I have no idea which vertices are VEF, but just draw a diagram and note that the distance from the center pole to the base of the triangle is 1/2 the side length adjacent to the base of the triangular face. Then you can get the (slant) height of the triangle using the ...

**Math!**

see your other post in the related questions below.

**physics - eh?**

Try again, but not in gibberish

**angular velocity/ physics**

500 rotations is 1000? radians, so ? = 1000?rad/10s = 100? rad/s

**Calculus help**

Hmmm. Figured it out in two minutes! Less time than it took you to post the problem, I'd say...

**math**

b/(b+g) = 3/4 g = b-24 b/(2b-24) = 3/4 4b = 6b-72 b = 36 so, g=12 making 48 pupils in all

**grammar**

Extra credit: what's the difference between shall and will?

**Calculus (related rates)**

If the base of the ladder is x feet from the wall, and the ladder reaches up y feet, then we have x^2 + y^2 = 13^2 taking derivatives wrt t, x dx/dt + y dy/dt = 0 Now just plug in your numbers and solve for dy/dt (note that at the moment in question, you conveniently have a 5-...

**Calculus (related rates)**

do this like your earlier one, using the chain rule.

**Calculus (related rates)**

just use the chain rule. Since x and y are both functions of t, dy/dt = (4x+2) dx/dt Now just plug in your numbers

**Calculus**

just crank it out. The acceleration is a(t) = 0.0044875t^2 - 0.17879t + 18.86 a(t) has a max/min when da/dt = 0 da/dt = 0.008975t - 0.17879 da/dt=0 at a=19.9209 a(10.9209) = 17.0792 Since a(t) is a parabola, there is no maximum value, but in the domain [0,50.2], the maximum ...

**Math**

Draw a diagram. If the ladder's length is z, and the base of the ladder is x feet from the fence, then by similar triangles, you can see that z/(x+3) = ?(x^2+9)/x z = (x+3)?(x^2+9)/x dz/dx = (x^3-27) / (x^2 ?(x^2+9)) dz/dx=0 when x=3 z(3) = 6?18/3 = 6?2

**Math Check!**

2975*1.04^2.5 = 3281.48 But, technically, since the interest is not compounded till the end of the year, you might get 2975*1.04^2 = 3217.76 Since that is not listed, I'd go with B So, how did you get D? That's over double the initial amount. Not likely!

**Algebra**

.03b + .10(20000-b) = .08*20000

**maths**

a = 4b .17a + .10b = 234 so, .78b = 234 b = 300

**Math (higher level) 2nd year**

(3x-2)(2x-4) = 14 6x^2-16x-6 = 0 2(x-3)(2x+1) = 0 x = 3 So the bed is 7x2 But you could have guessed that at first, since 2 and 7 are the only factors of 14...

**real estate**

x * 1.06^2 = 140000

**science**

see related questions below.

**Relative Clauses and Pronouns**

all look ok to me. Of course, the purists would write 5. This is the tiger for which the hunters have been looking. Like the small boy who noticed his father had brought the wrong bedtime story, and said: What did you bring that book I don't want to be read to out of up for?

**Calculus**

think of the volume as a stack of discs of thickness dx, and you have v = ?[0,?] ?r^2 dx where r=y=cos(cos(x)) v = ?[0,?] ?cos^2(cosx) dx This is not an elementary integral, so some numeric method is needed. However, using some symmetry, v = 2?[0,?/2] ?cos^2(cosx) dx and you ...

**Calculus**

Each semicircle resting on the x-y plane has radius x=?(16-y^2). Adding up all the slices, and using symmetry, we have v = 2?[0,4] 1/2 ?r^2 dy = ??[0,4] (16-y^2) dy = 128?/3 bobpursley's solution is much more intuitive and geometric, though, eh?

**Calculus**

Hmmm. Let me take a stab at it. AT (-4,1) we have ln(x^2-15y) = ln(1) = 0 Hmmph. Can't make out a reasonable interpretation that is zero on the right. Anyway, regardless, let's just say that it is ok as it is. Then we have, taking derivatives of both sides, using the ...

**Math**

correct

**math**

Since the axis of symmetry is x=3 and the y-intercept is E, the parabola is f(x) = a(x-3)^2 + E since E is the y-intercept of the parabola, E = -7/2 f(x) = a(x-3)^2 - 7/2 Now you know that (7,0) is on the parabola, so a(7-3)^2 - 7/2 = 0 16a = 7/2 a = 7/32 f(x) = 7/32 (x-3)^2...

**math**

well, ?5 ? 2.236 I assume you can mark that on the number line. . .

**math**

{1,2}?{2,3} = {1,2}?{2,5} I'm sure you can handle the Union one...

**math**

I believe exterior angles are 180 - interior angles. Their sum is 360.

**Algebra**

.06^(1/12) = ?

**algebra**

L(L-3) = 46.75 solve for L and W, then P = 2(L+W)

**Science**

you'll probably get a faster response from google: https://www.google.com/search?q=What+are+the+uses+of+reactivity+series&ie=utf-8&oe=utf-8

**MAATH!!**

correct

**Math**

720 = 36*20 so, count the good ones here and multiply by 20 to estimate the larger amount.

**Science**

KE = 1/2 mv^2 and that's "wrecking" ball, but it does wreak havoc ...

**maths**

Now, use the fact that v(0) = 10 (4t^5/5)-(8t^3/3)-9t+v0 = 10 at t=0 So, v0 = 10, and thus v(t) = (4t^5/5)-(8t^3/3)-9t+10 Now go on to x(t), using x(0) to find the constant of integration.

**Physics**

Adding 20cm^3 of liquid added 20g of mass, so the density is 20g/20cm^3 = 1 g/cm^3

**calculus**

y" = 4 y' = 4x+c y'(1)=10, so 4+c = 10 c=6 y' = 4x+6 No do the same to move on to y.

**Maths**

4/5 the time, so 5/4 the workers: 80 so, another 16 are needed.

**ALGEBRA I**

1st step: write a function for each company. For example, Rider: y = 50 + 0.50x now what?

**Algebra II**

assuming a linear rate of depreciation, the car loses $3900/year. So, after x years, its value is v(x) = 16800 - 3900x

**Math**

Assuming you meant f(x)=-2x*4^(x-1)+3 the domain of all polynomials (-2x) is (-?,?) the domain of all exponentials is (-?,?) so, the domain of f(x) is likewise (-?,?) now work with the ranges in like wise. x -> (x-h) translates right by h y -> (y-k) translates up by k y...

**Algebra**

compare Bh to 1/3 Bh in each case for volume similarly for area

**Math**

just plug your points into x^2/a^2 + y^2/b^2 = 1 then solve for 1/a^2 and 1/b^2

**Math**

The direction numbers for the last two points make the line from t=0..1 x = 2-t y = 0-t z = -1+4t So, backing up to z=3, -1+4t = -3 t = -1/2 a = x(-1/2) = 5/2 b = y(-1/2) = 1/2

**Calculus - Integrating**

The problem is that you did not have du in your integrals. You lacked the extra 2x dx in your integrands. u = x^2+1 du = 2x dx x = ?(u-1) So you have ?x/?(x^2+1) x dx = 1/2 ??(u-1)/u du which isn't really much better Try using a trig substitution: x = tan? x^2+1 = tan^2...

**math**

s = t^3-9t^2+3t+1 v = 3t^2-18t+3 = 3(t^2-6t+1) so, solve for t when v=-24 a = 6t-18 then plug in that t to find v and a. what is your problem with minus signs (-) ? over- and under-score really are ugly! x^2 cosy - siny = 0 Surely you can plug in the point to verify it fits! ...

**MATHEMATICS**

plug your numbers into the formulas found here: https://www.google.com/search?q=cone+area&ie=utf-8&oe=utf-8

**Science**

2Mg + O2 -> 2MgO now convert to moles for amounts needed