# Posts by Steve

Total # Posts: 49,502

**Algebra**

don't you recognize 8^2 and 9^2 ?

*March 5, 2017*

**Maths**

2(5x+3x) = 128 x = 8 so, ...

*March 5, 2017*

**Algebra**

well, 32 = 2^5 that should help

*March 5, 2017*

**Calculus**

e^(ax) = e^(a/b * bx) = (e^(a/b))^(bx) C = e^(a/b)

*March 5, 2017*

**Calculus**

If I read all those words correctly, you mean ?[-3,3] f(x) dx where f(x) = f1: ?(4-?(x+1)) for -3 <= x <= 1 f2: |x-2|-1 for 1<x<3 Unfortunately, for x < -1 the first piece is complex, not real. Anyway, fix the presumed typo and just plug in the pieces ?[-3,1] f1...

*March 5, 2017*

**math**

Draw the figure. If the height is h, then you have a 40-by-h rectangle in the center, with extra lengths of x and 25-x on the longer base. x^2+h^2 = 56^2 (25-x)^2+h^2 = 39^2 x^2-56^2 = (25-x)^2 - 39^2 x = 224/5 so, h^2 = 56^2-x^2 = 28224/25 h = 168/5 so, the area is (40+65)/2...

*March 5, 2017*

**Math/Calculus**

Consider the set of nested shells of thickness dy. v = ?[0,4] 2?rh dy where r=y and h=218-x = (y+2)^3+2 v = ?[0,4] 2?y(218-((y+2)^3+2)) dy = 8192?/5 as a check, using discs of thickness dx, v = ?[10,218] ?r^2 dx where r=y=(x-2)^(1/3)-2 v = ?[10,218] ?((x-2)^(1/3)-2)^2 dx = ...

*March 4, 2017*

**Calculus**

assuming you mean 1<=x<=5, we have, using discs, v = ?[1,5] ?(R^2-r^2) dx where R=x^(1/5) and r=(x/5)^2

*March 4, 2017*

**Calculus**

each triangle at a distance x from (0,0) has a base of 2y = 2?(64-x^2) So, the total volume, taking advantage of symmetry is v = 2?[0,8] bh/2 dx = 2?[0,8] 2?(64-x^2)*2?(64-x^2)/2 dx = 4?[0,8] (64-x^2) dx = 4096/3

*March 4, 2017*

**Calculus**

Find the volume of the solid whose base is the circle x^2+y^2=64 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=7.

*March 4, 2017*

**calculus**

h^2 = 6^2 + x^2 h dh/dt = x dx/dt when h=10, x=8, so just plug in the numbers 10 dh/dt = 8*2 dh/dt = 8/5 m/s

*March 4, 2017*

**math**

The only way I can make sense of what you wrote is to interpret it as p = mq^3 q = nr^2 p = m(nr^2)^3 = mn^3 r^6 = kr^k p varies directly as the 6th power of r.

*March 4, 2017*

**Calculus AP Exam review explanation pls**

#1. Recall that the average value is 1/? ?[-?,0] 3^cos(x) dx use your calculator to find that the integral is 4.16348 Divide that by ? and you get 1.32528 #2 is just another integral. Just as distance is ? v(t) dt, here the total change in momentum is ? cost dt since ? p = F ?...

*March 4, 2017*

**Algebra 2**

correct

*March 4, 2017*

**math**

35/60 of the circumference of a complete circle of radius 6 cm.

*March 4, 2017*

**math**

The distance between pencil centers on each side is 1 diameter, or 7mm. At each corner there is a quarter-circle, so the entire length is 4*7 + ?*7 = 7(4+?) mm

*March 4, 2017*

**math**

Draw the diagram, with two congruent triangles at the ends. Notice that the two right triangles are 6-8-10.

*March 4, 2017*

**science**

that means that 90% remains, so (1/2)^(t/1590) = 9/10 t = 241.7 years

*March 4, 2017*

**maths**

h/4 = tan45°

*March 4, 2017*

**math**

(2(3x+100)+100)/4 - x/2 = ?

*March 3, 2017*

**math**

x/y = a/b (x+y)/y = x/y + 1 = a/b + 1 = (a+b)/b the rest follows

*March 3, 2017*

**math**

let's say that for each ounce of 5-cent rice, you buy k ounces of 6-cent rice. 7(1+k) = (5+6k)(6/5) k = 5

*March 3, 2017*

**calculus**

h' = 3/20 ?x the length of cable is s = 2?[0,20] ?(1+h'^2) dx = 2?[0,20] ?(1+9x/400) dx = 44.2 ft Now figure the weight.

*March 3, 2017*

**Calculus**

dy/(y-2) = x^4 dx ln(y-2) = x^5/5 + ln(c) y-2 = c e^(x^5/5) y(0)=0, so c=-2. y = 2-2e^(1/5 x^5) I suspect you did ln(y-2) = x^5/5 + c y-2 = e^(x^5/5) + c That still does not give your answer. Too bad you didn't show your work ...

*March 3, 2017*

**Calculus**

correct. I'd probably have written it y = 1/16 (x^2 + 11)^2

*March 3, 2017*

**Algebra**

It moved 60° in 10 minute. 11:00 t0 11:40 is 40 minutes. 4 times as long, 4 times as many degrees: 240°

*March 3, 2017*

**chemistry**

10/3 the volume, 3/10 the concentration.

*March 3, 2017*

**chemistry**

0.1L * 0.1M = 0.01 moles Now just convert that to grams.

*March 3, 2017*

**Algebra**

Assuming f is quadratic, start with y = (x-2)(x-4) y(3) = -1 So, multiply it by 2 and you have y = 2(x-2)(x-4) = 2(x-3)^2 - 2

*March 3, 2017*

**Algebra**

many functions meet those criteria, but one of them is given roots: y = (x - (1+?2))(x-(1-?2)) = x^2-2x-1 That has a y-intercept of -1. So, multiply it by 4. It has the same roots, but now y(0) = -4.

*March 3, 2017*

**MATHEMATICS**

correct.

*March 3, 2017*

**Algebra 2**

the y-intercept has noting to do with the asymptotes. Unless the asymptote is the y-axis, in which case there is no y-intercept.

*March 3, 2017*

**Mathematics**

4 painters paint 1 room in 12/3 = 4 hours 1 painter paints 1 room in 4/4 = 1 hour Now you can answer the questions.

*March 3, 2017*

**Math**

too bad you couldn't be bothered to show your work. start: $x CD: 18, leaving x-18 dress: half that, leaving x/2 - 9 lunch:11, leaving x/2 - 20 book: 1/3 of that, leaving (2/3)(x/2-20) = x/3 - 40/3 gas: 12, leaving x/3 - 76/3 CD: 1/4 of that, leaving (3/4)(x/3 - 76/3) = x/...

*March 3, 2017*

**Calculus AP Exam review explanation pls**

#1 a = ?[0,3] (3x-x^2) dx = 9/2 #2 Using either discs or shells, v = ?[0,4] ?(2-x)^2 dy = ?[0,4] ?(2-?y)^2 dy = 8?/3 or v = ?[0,2] 2?(2-x)y dx = ?[0,2] 2?(2-x)x^2 dx = 8?/3 #3 I can't make out the function, but the total distance traveled is the arc length of the path ...

*March 3, 2017*

**Math**

the diet looks linear to me. 1/80 lb/day. A cup of coffee cooling is non-linear. The amount of temperature drop depends on the difference in temperature between the coffee and the room. The cooler the coffee gets, the more slowly it cools. Or radioactive decay is non-linear. ...

*March 3, 2017*

**maths binomial expansion**

1/0! x^(1/3) (y/2)^0 + (1/3)/1! x^(-2/3) (y/2)^1 + (1/3)(-2/3)/2! x^(-5/3)(y/2)^2 + (1/3)(-2/3)(-5/3)/3! x^(-8/3)(y/2)^3 + (1/3)(-2/3)(-5/3)(-8/3)/4! x^(-11/3)(y/2)^4 = x1/3 + 1/6 x-2/3 y - 1/36 x-5/3 y2 + 5/648 x-8/3 y3 - 5/1944 x-11/3 y4

*March 3, 2017*

**physics 11**

the horizontal speed is constant. So, how long does it take to fall 36 meters? h(t) = 36 - 4.9t^2 As to the distance of the boat, it depends on the goal: hit or no hit?

*March 3, 2017*

**maths**

v = 4/3 ?r^3 r = ?(3v/(4?)) a = 4?r^2 = 4? * (3v/(4?))^(2/3) = ?(36?v^2) so, for your sphere, a = ?(36?*9000^2) = 900?(4?) ? 2092

*March 3, 2017*

**Math**

6490 * (71/59) = ?

*March 3, 2017*

**Struggling on math please help :(**

just keep adding/subtracting 360° 47+360 = 407+360 = 767° 47-360 = -313 - 360 = -673°

*March 3, 2017*

**Rpcc**

horizontal velocity is constant. vertically after t seconds, v = -9.8t

*March 3, 2017*

**maths trigonometry,**

Always start by finding the reference angle in QI. Then you can work with angles in the standard position (with one corner at (0,0) and lying on the x-axis). tan ?/4 = 1 tan? is positive in QI and QIII so, the solutions are ? = ?/4 and ?+?/4=5?/4 cos ?/3 = 1/2 cos? is negative...

*March 3, 2017*

**maths trigonometry**

(2cos? + 1)(tan? - 1)=0 see your other post, where you have taken the next step.

*March 3, 2017*

**calculus**

as it stands, I think there's something wrong. you want dt/dx = 0 but since ?n is always >= 0, that means that ?(x^2+a^2) + ?(b^2+d^2) = 0 since even powers are always non-negative, that means that x,a,b,d are all zero. and 0 is not in the interval (0,d)

*March 3, 2017*

**calc**

1/f = 1/p + 1/q 0 = -1/p^2 dp/dq - 1/q^2 dp/dq = -p^2/q^2

*March 3, 2017*

**Maths**

same question: how many 1cm cubes does it take to fill a 6cm cube?

*March 3, 2017*

**math**

Since the 30th minute is at the end of the 1st quarter, there is a 3/4 probability that he missed the goal.

*March 2, 2017*

**math**

350.5 is one possible value

*March 2, 2017*

**Calculus**

read the question carefully. v(0) = 3 you want v to be three times its initial value. 3*3 = 9

*March 2, 2017*

**math**

first, 80% interest is too weird to be real. second, I can't quite figure out just what you're asking. Take a look at what you wrote...

*March 2, 2017*

**Calculus**

well, the line has slope 3. So, where does the curve have that slope? y' = 2e^x = 3 x = ln(3/2)

*March 2, 2017*

**maths**

I'd say separation of variables, since you can write it as dy/y^2 = -(t+t^3) dt ------------------------------------------- next is just direct integration, since you already have dy/dt as a function of t. ------------------------------------------- The last is of the form...

*March 2, 2017*

**calculus-snell's law**

try this discussion: http://dev.physicslab.org/Document.aspx?doctype=3&filename=GeometricOptics_LeastTime.xml

*March 2, 2017*

**math**

D because you did not show the data ...

*March 2, 2017*

**math**

actually, since there is only one variable, there is no direct variation. If you meant -4+7x+4 = y then y = 7x is a direct variation.

*March 2, 2017*

**Maths**

using a weekly rate for simple interest, you want p*rt = 1500 50000*(.06/52)t = 1500 t = 26 makes sense, since you will earn 6% of 50000 = 3000 in a year.

*March 2, 2017*

**calculus**

ok, Sam/Maggie, see whether you can set up the needed integrals, and show what you tried.

*March 2, 2017*

**calculus I**

at x=h, the tangent line to the parabola is y - (3-h^2/10) = (-h/5)(x-h) y = -h/5 x + 3+h^2/10 So, find where the line intersects the circle, and find h so that there is only one solution. It might be useful to pick a value of x close to what you expect, and then use an ...

*March 2, 2017*

**geometry**

tan 36° = 0.7265 x^2+y^2 = 25^2 y = 0.7265x x^2 (1 + 0.7265^2) = 25^2 x = 20.2258 p = 2(x+y) = 2(20.2258 + 14.6949) = 69.8414

*March 2, 2017*

**linear approximation**

You want to pick a value of cos(x) where x is near 2?/13, and you know what it is. you know cos(?/6) = ?3/2. 2?/13 = ?/6 - ?/156, which is pretty close to ?/6. cos(2?/13) ? cos(?/6)+(-sin(?/6))(?/156) = ?3/2 - (1/2)(?/156) = 0.8560 the true value is 0.8855 That seems kind of ...

*March 2, 2017*

**calculus**

using shells of thickness dx, and taking advantage of symmetry, v = 2?[0,1] 2?rh dx where r=1-x and h=y=?(1-x) v = 2?[0,1] 2?(1-x)?(1-x) dx = 4??[0,1] (1-x)^(5/4) dx = 16?/9 using discs (washers) of thickness dy, we have v = 2?[0,1] ?(R^2-r^2) dy where R=1 and r=1-x v = 2?[0,1...

*March 2, 2017*

**Math related rates**

if the water depth is h, the radius of the surface is 2/3 h. So, the volume of water is v = 1/3 ?r^2 h = 1/3 ? (2/3 h)^2 h = 4/27 ?h^3 dv/dt = 4/9 ?h^2 dh/dt plugging in the numbers, 3/2 = 4/9 ?*2^2 dh/dt dh/dt = 27/(32?) Too bad you didn't bother to show your work...

*March 2, 2017*

**Algebra 1 - Help!?**

think about it. If a line has a nonzero slope, it extends forever, both left-right and down-up. So, the domain and range are both All Real Numbers. To sketch the graphs, just pick two values for x, figure the corresponding values for y, plot the two points, and draw the line ...

*March 2, 2017*

**maths**

(?*14.642 km)/(50/60 hr) = 55.2 km/hr

*March 2, 2017*

**math**

Your mistake happened early. You said 5x+3y=2 eq.2 X=-3y/5 but really x = (2-3y)/5

*March 1, 2017*

**Precalculus**

it's an exponential function.

*March 1, 2017*

**math**

I'm not talking about angles, but sides. Remember the Pythagorean Theorem? a^2 + b^2 = c^2

*March 1, 2017*

**math**

LM = ?(5^2+3^2) = ?34 LN = ?(4^2+1^2) = ?17 MN = ?(1^1+4^2) = ?17 So, it is isosceles. But since ?17^2 + ?17^2 = ?34^2 17+17 = 34 it is a right triangle.

*March 1, 2017*

**math**

Somehow you messed up the final answer. It is just 15w^3 + 25w^2x - 5wx^2 There are no wx terms anywhere.

*March 1, 2017*

**math**

pyramids have a base and one top vertex prisms have two parallel bases. so, ...

*March 1, 2017*

**Calculus**

As above, using discs of thickness dx, v = ?[0,ln3] ?(R^2-r^2) dx where R=y and r=1 v = ?[0,ln3] ?((e^(x/2)^2-1^2) dx = ?[0,ln3] ?(e^x-1) dx = ?(2-ln3) or, using shells of thickness dy, v = ?[1,?3] 2?rh dy where r=y and h=ln3-x v = ?[1,?3] 2?y(ln3-2lny) dy = ?(2-ln3)

*March 1, 2017*

**calculus- optimization**

base = 2x height = y = ?(4-x^2) a = 2x?(4-x^2) da/dx = 4(2-x^2)/?(4-x^2) da/dx=0 when x = ?2 so, max area is 2(?2)?(4-2) = 4

*March 1, 2017*

**Math**

don't know about the triangles, but the rectangles' areas are clearly in the ratio 25:240

*March 1, 2017*

**Math**

well, which is larger/smaller?

*March 1, 2017*

**math**

the other angles are 11x and 17x. So, 11x+17x+40 = 180 find x, then you can get the other angles.

*March 1, 2017*

**Math**

as always, draw a diagram. Label the lighthouse L, and the two ship positions S and N. Draw an E-W line from L to SN, intersecting at P. SP = 15.5 cos40° PL = 15.5 sin40° PN = PL cot54.9° The ship has sailed a distance of SP+PN

*March 1, 2017*

**Math**

(6x^3y)(8x^2y^4) = 48 x^5 y^5 now just plug in your values...

*March 1, 2017*

**Math plz help**

rewrite them all as just radicals, and then it is easy to compare them: 1. -?18 2. ?9 3. ?12 4. -?28 or, convert to decimals, but that's more work...

*March 1, 2017*

**Math**

3^4?2 81?2 4?(81^2/16 * 2) 4?(6561/8) somehow I doubt that's what you were after if by 4?n you mean 4th root (?n) I'm also confused. 3^?2 is trés bizarre. Try again using ^ for exponents and ? for square root, and ? for 4th root.

*March 1, 2017*

**Math**

just subtract the exponents of y. y^7/y = y^6 take it from there.

*March 1, 2017*

**Math**

do you mean (7^3)?32 or 7^(3?32) ? in either case, just type it in at wolframalpha.com

*March 1, 2017*

**Math**

I suspect you mean p = 100(0.5)^(t/20) So, plug in t=30

*March 1, 2017*

**Math**

You could go through the math of finding the side lengths of all six sides, and comparing them, but these are easy to figure out if you just plot the points. Then its easy to see that ABC is a 3-4-5 right triangle. Now take a look at DEF.

*March 1, 2017*

**Math**

You are correct. Whoever said it was 0.402 was nuts. Or there are some serious typos in the problem.

*March 1, 2017*

**Chemistry**

Would the percent yield of Ni(NH3)nCl2 be high, lower, or unchanged if you made the following procedural changes? a) You performed the synthesis reaction at 100 degrees instead of 60 degrees b) you dissolved the NiCl2*6H2O in 50 mL of distilled water instead of 10mL c) You did...

*March 1, 2017*

**Trigonometry**

A = (ab sinC)/2 so, how do you get C? sinA/a = sinB/b Now, having A and B, C is easy, since they add up to 180°

*March 1, 2017*

**Math**

if xy is constant, it's inverse. xy=k If y/x is constant, it's direct. y=kx So, take a look and see what you find.

*March 1, 2017*

**Aditi**

There are 4C2 = 6 ways to choose the two required biographies. That leaves 8 other books, with 8C2 = 28 ways to pick them. So, there are 6*28 = 168 ways to pick 4 books as required.

*March 1, 2017*

**Trigonometry**

after t hours, the distance d between the hikers is d^2 = (.24t)^2 + (.17t)^2 - 2(.24t)(.17t)cos109.167° so, find t when d = 0.0568182 I get about 10 minutes. The radios aren't much use, I guess...

*March 1, 2017*

**Geometry**

eq. 1 says 2y = 3x+23 use that in eq. 2 and you have 5x + 3x+23 = -17 for elimination, this web site gives all the details: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

*March 1, 2017*

**Geometry**

since ?x^2 = x, you want to factor out all the perfect squares. 224 = 16*14 so, ?224 = ?(4^2 * 14) = 4?14

*March 1, 2017*

**Calculus**

google is your friend. You can find what you need here: http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeProofs.aspx

*March 1, 2017*

**maths**

a + ar^4 = 34 ar * ar^2 * ar^4 = 512 a(1+r^4) = 34 a^3 r^7 = 512 Looks kind of messy, but since the only factors of 34 are 2 and 17, it appears that a=2 and r=2 I think the second condition should have used the 4th term, rather than the 5th. If so, then since 2^9=512, that ...

*March 1, 2017*

**calculus**

if w has a max at t0, dw/dt = 0 at t0. so, (f'(t0)(c+t0)-f(t0))/(c+t0)^2 = 0

*March 1, 2017*

**Maths**

p(man) = 3/4 p(woman) = 1/4 ...

*March 1, 2017*

**Maths**

doing selection without replacement, the chance is 1/5 * 1/4 * 1/3 = 1/60 or, since there are 5P3 = 60 permutations of 3 of the 5 letters, and only one of them spells BED, the chance is 1/60

*March 1, 2017*

**Calculus**

I assume you have drawn a diagram of the situation. The length z of cord when the kite has flown to a horizontal distance x is z^2 = x^2 + 135^2 so, z dz/dt = x dx/dt Find x when z=285, and you can find dz/dt.

*March 1, 2017*

**calculus**

Think of the solid as a stack of thin squares. At a distance y from the origin, the square has side 3y. So, add them all up and the volume is ?[0,3] (3y)^2 dy

*February 28, 2017*