# Posts by STEVE

Total # Posts: 49,516

**Calculus - Newton's Method**

well, f'(x) = 1-sinx So plug that into Newton's method. Here is a nice web site: http://keisan.casio.com/exec/system/1244946907

*March 23, 2017*

**calculus**

you will need to use integration by parts, twice. 1st step: u = t^2 dv=sin(2t) dt du = 2t dt v = -1/2 cos(2t) That makes the first integration by parts: ?u dv = uv - ?v du ?t^2 sin(2t) dt = -1/2 t^2 cos(2t) + ?t cos(2t) dt Then repeat, letting u = t dv = cos(2t) dt You should ...

*March 23, 2017*

**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

*March 23, 2017*

**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...

*March 23, 2017*

**math**

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

*March 23, 2017*

**math**

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

*March 23, 2017*

**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

*March 23, 2017*

**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 ...

*March 23, 2017*

**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)

*March 23, 2017*

**Math**

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

*March 23, 2017*

**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.

*March 22, 2017*

**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 ...

*March 22, 2017*

**math**

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

*March 22, 2017*

**Math1**

2^24 - 1

*March 22, 2017*

**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?

*March 22, 2017*

**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 ...

*March 22, 2017*

**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...

*March 22, 2017*

**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.

*March 22, 2017*

**Math**

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

*March 22, 2017*

**maths**

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

*March 22, 2017*

**math real and complex numbers lesson**

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

*March 22, 2017*

**Maths**

x-28 = 42-x

*March 22, 2017*

**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.

*March 22, 2017*

**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

*March 22, 2017*

**trigonometry**

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

*March 22, 2017*

**trigonometry**

use the law of sines.

*March 22, 2017*

**math**

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

*March 22, 2017*

**Maths**

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

*March 22, 2017*

**Maths**

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

*March 22, 2017*

**Math**

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

*March 22, 2017*

**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...

*March 22, 2017*

**Geometry**

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

*March 22, 2017*

**Math**

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

*March 22, 2017*

**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.

*March 22, 2017*

**Math**

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

*March 22, 2017*

**Math**

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

*March 22, 2017*

**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.

*March 21, 2017*

**Linear algebra**

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

*March 21, 2017*

**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...

*March 21, 2017*

**math**

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

*March 21, 2017*

**maths**

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

*March 21, 2017*

**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...

*March 21, 2017*

**Calculus**

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

*March 21, 2017*

**Calculus - Optomization Problem**

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

*March 21, 2017*

**Math**

review the associative property of addition.

*March 21, 2017*

**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)

*March 21, 2017*

**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.

*March 21, 2017*

**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/(...

*March 21, 2017*

**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

*March 21, 2017*

**Maths**

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

*March 21, 2017*

**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.

*March 21, 2017*

**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 ...

*March 21, 2017*

**Math!**

see your other post in the related questions below.

*March 21, 2017*

**physics - eh?**

Try again, but not in gibberish

*March 21, 2017*

**angular velocity/ physics**

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

*March 21, 2017*

**Calculus help**

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

*March 21, 2017*

**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

*March 21, 2017*

**grammar**

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

*March 21, 2017*

**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-...

*March 21, 2017*

**Calculus (related rates)**

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

*March 21, 2017*

**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

*March 21, 2017*

**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 ...

*March 21, 2017*

**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

*March 21, 2017*

**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!

*March 21, 2017*

**Algebra**

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

*March 21, 2017*

**maths**

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

*March 21, 2017*

**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...

*March 21, 2017*

**real estate**

x * 1.06^2 = 140000

*March 21, 2017*

**science**

see related questions below.

*March 21, 2017*

**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?

*March 21, 2017*

**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 ...

*March 21, 2017*

**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?

*March 21, 2017*

**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 ...

*March 21, 2017*

**Math**

correct

*March 21, 2017*

**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...

*March 21, 2017*

**math**

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

*March 21, 2017*

**math**

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

*March 21, 2017*

**math**

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

*March 21, 2017*

**Algebra**

.06^(1/12) = ?

*March 20, 2017*

**algebra**

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

*March 20, 2017*

**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

*March 20, 2017*

**MAATH!!**

correct

*March 20, 2017*

**Math**

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

*March 20, 2017*

**Science**

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

*March 20, 2017*

**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.

*March 20, 2017*

**Physics**

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

*March 20, 2017*

**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.

*March 20, 2017*

**Maths**

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

*March 20, 2017*

**ALGEBRA I**

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

*March 20, 2017*

**Algebra II**

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

*March 20, 2017*

**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...

*March 20, 2017*

**Algebra**

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

*March 20, 2017*

**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

*March 20, 2017*

**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

*March 20, 2017*

**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...

*March 20, 2017*

**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! ...

*March 20, 2017*

**MATHEMATICS**

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

*March 20, 2017*

**Science**

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

*March 20, 2017*

**College algebra**

If the half-life is k years, then after t years, (1/2)^(t/k) remains. Thus, to find k, solve (1/2)^(400/k) = 0.7 600 = 3/2 * 400, or 1.5 half-lives. So, the amount remaining after 600 megayears is (1/2)^(3/2 * 400/k) = (1/2)^(400/k)^(3/2) = 0.7^(3/2) = ?

*March 20, 2017*

**English**

the literary device of foreshadowing is used in which of the following excerpts? They're spoiled and we're spoiled Those screams -- they sound familiar I have a feeling it'll be Africa again before then They're not old enough to do that alone, I explained My ...

*March 20, 2017*