# Posts by Steve

Total # Posts: 54,365

**English**

Which excerpt from Robert Burns’s “To a Mouse” best conveys understanding and forgiveness? “…An’ weary winter comin’ fast,/An cozie here, beneath the blast…”<<< “Thy wee-bit housie, too, in ruin!/Its silly wa’s ...

**I don't get what you wrotegeometry**

It's the usual octohedron. 8 faces and so on. check out the Platonic solids.

**Math**

the solution is all numbers, since every number is either greater than 3 or less than or equal to 3.

**Math**

If there are m 8-point questions and t T/F questions, you need 8m+3t = 60 m >= 1 and t >= 1 So, clearly m <= 7 since 8*8 > 60 So, just list the possibilities: 1*8=8 and 3 does not divide 60-8=52 2*8=16; 3?44 3*8+12*3 = 60 ok! you might want to check for other ...

**math**

another way to do it is to group the group all the flowers on each table, as in (9+3f)t + 12 Now just plug in the numbers 9*21 + (3*3)*21 + 12 = 390 (9+3*3)*21 + 12 = 390

**Math**

she ate 2/3 of what she had (5/6 cake) or 2/3 * 5/6 = 10/18 = 5/9 of a whole cake

**Math**

assuming you meant h = 35t-5t^2, then just solve 35t-5t^2 = 50 If you get two answers, then that is because the carpet went up higher than 50 meters, and then came back down. I must say, throwing a carpet up more than 50 meters is quite a feat! Was it shot from a cannon?

**English**

Regardless of your answer, 1 and 2 are grammatically incorrect. "what" is a pronoun -- more correct would be "which" to modify the subject. just a pet peeve of mine, like using "if" instead of "whether"

**Math**

the only pairs of factors of 15 are 1x15 and 3x5

**physic**

v = dx/dt = 0.0080 + 0.20t

**Math**

Since the time elapsed is 6 hours, the slopes are (48-58)/6 and (62-67)/6

**Math**

2/5 x + 12 = 1/2 x Now just solve for x.

**physics**

PE = mgh, so 51*g*h = 5997.6 You know g, so now find h.

**Math/ compound interest**

uh, ... 1-10?

**Math, algebra, geometry**

If the fixed cost is f and the per-pizza cost is p, then we know: c+2p = 17 c+4p = 31 now subtract and you see that 2p = 14 now you can find p, and then c. The five pizzas cost c+5p

**math**

the middle bead is #9. So, you have two AP's of 8 terms each, plus the middle bead. That means that 2(8/2 (2+7))+ x = 100 x = 28

**Math**

4 ft = 48 in, so the scale is 1:48 The areas are in the ratio 1:48^2 = 1:2304

**Math?**

n/(2n+5) = 1/3 Now just find n and thus the fraction

**math**

30% of 600 = 180 180+5n = .40(600+5n) Now just find n and thus 5n.

**Math Mysteries....**

#1 Huh? 1:6/12 = 12/6 = 2 How does that relate to what they said? You need to set the words to math: (d-6)/d = 3/4 4(d-6) = 3d 4d-24 = 3d d = 24 check: 18/24 = 2/3 yes. As with most skills, with a little practice it gets easier. #2 n/(2n+5) = 1/3 3n = 2n+5 ... #3 Since 2 and 5...

**Math**

a slightly less flexible but much simpler interface is at wolframalpha.com just type in your function and it takes care of the rest

**Math**

74 = 8*9 + 2

**AP Calculus Help**

v(t) = dr/dt = (1-(1/2)sin(t/2),-3cost) Now just plug in your t value: v(?) = (1-(1/2)(1),-3(-1)) = (1/2,3)

**math**

1.6% = 0.016 so, 0.016h = 1.77 h = 110.6 meters This represents the actual height. No idea what the "usual" height is ...

**math - impatient much?**

Reposted after only 12 minutes?

**Please Help! Calculus**

v(t) = dr/dt = (-2t,6) (0,12) is on the curve, so at that point, t=2 so, that means v(2) = (-4,6) |v| = ?(16+36) = 2?13

**Math?**

You are told that g = 3p 10g+20p=175 so, 10*3p + 20p = 175 50p = 175 p = 7/2 g = 3p = 21/2 2g+8p = 2(7/2)+8(21/2) = 88

**Math?**

Just plug in the numbers. 3?5 = (7-3)(3+5) = 32 5?c = (7-5)(3+c) = 6+2c so, 32 = 6+2c c = 13

**math**

clearly, that will be 1500 * 1.02^4

**math**

99 + 112 + c >= 415

**Math**

in a triangle, it is the line from a vertex to the midpoint of the opposite side.

**Math**

How long does it take the water to hit the ground? 4.9t^2 = 0.75 t = 0.3912 seconds so, the horizontal speed = 2m/.3912s = 5.11 m/s

**calculus**

First plot the curves. They intersect at (3/2,?/3) and (3/2,-?/3) So, let's just take twice the area for ? in [0,?/3] Now just plug in the functions. The area is ?[0,?/3] (1+cos?)^2 - (2-cos?)^2 d? = ?[0,?/3] 6cos?-3 d? = 3?3 - ?

**Math**

well, 120 = 2*2*2*3*5 Just pick 3 sets of factors from those combinations

**Small changes differentiation**

taking derivatives, you have dT = ?/?(gL) dL Now, to find the % change of T, you take dT/T You would expect it to be about 1/2 the change in L, since you have roughly T^2 = kL 2T dT = k dL

**4 Calculus Related-Rates Problems**

These are all just applications of the chain rule. If y is a function of u, and u is a function of t, then dy/dt = dy/du * du/dt So, now we see what do do: #1 v=4/3 ? r^3 dv/dt = 4?r^2 dr/dt dr/dt = 15/(4?r^2) As expected, if the volume changes at a steady rate, the bigger the...

**Math**

1x(4) - 8x9/-3 1*4 - 72/-3 4 - (-24) 28

**Math 6th Grade**

when a problem says "of" that means multiply 1/2 of a dozen = 1/2 * 12 = 6

**physic**

just do the usual derivative: v(t) = z'(t) = -16.2tk and evaluate at t=3 and t=6 works the same if there are i and j components as well.

**Math**

there are two lengths and two widths, so the perimeter is 13+7+13+7 = 40 2(13+7) = 40 inches

**Java**

can't draw flowcharts here. However, the logic might look like this: define n as a 10-number array sum = 0 i=1 ask for number assign it to n(i) add it to the sum increase i i <= 10? yes, go back to ask again no, print the sum quit

**Maths - huh?**

you wanna try that again so it makes sense?

**Math**

31 are boys so, 31/50 are boys. Just turn that into a %

**Math**

he makes it 2 meters forward every second. So, after 29 seconds, he has gone 58 meters. He makes it out in the 30th second. (29 2/3 seconds, actually)

**Math**

I assume you mean the 5th term is 5. You don't even have to find the 1st term, a; just start at 5 and go backwards, adding 3 each time: 17,14,11,8,5 If you want to do it algebraically, of course, just realize that the 5th term is a+4d = a+4(-3) = 5 a-12 = 5 a = 17

**MATH8**

If by 25/2% you mean 12.5%, then 500 * 1.125 * 1.15 = ?

**math**

since the ratio of sides is the same, 9/5 = x/4

**maths**

I think this will be a good place to start. The answer is given, and you can surely find your way there. https://books.google.com/books?id=uwDfHbyl1IMC&pg=SL22-PA420&lpg=SL22-PA420&dq=Find+the+equation+to+the+cone+whose+vertex+is+the+point+(a,b,c)+and+whose+generating+lines+...

**maths**

probably the intersection of the first two planes.

**Maths**

m+r = 338 m+49 = r/2 m+49 = (338-m)/2 m = 80 check: Minah had $80 and Rohana had $258 Later, Minah had 80+49 = $129 and Rohana had 258/2 = $129

**Math**

42

**math**

p = 2g g = p-20 now just solve for p and g.

**algebra 2**

f(x)=3.8cos(?x20)+2.2 cos(x) has a minimum value of -1 so, f(x) has a minimum value of 2.2 + 3.8(-1) = -1.6

**Educational Technology and Online Learning 7**

copyright is for published material. which of the choices does not fit that category?

**math**

no way to tell what is his mass? what is his weight on earth? something, eh?

**Physics**

time for the carbon would be dilated, or slowed by the usual relativistic factor. So, multiply the half-life by that.

**Pre calc**

Draw the triangle in QIV so that r = 3 x = 2 y = -?5 tan? = y/x = -?5/2 ...

**MATH**

well, your equation has a typo (it has two = signs, and that 84x cannot be right!). Aha -- it appears that you have duplicated the equation 4x-3y = 8 Clearly (1,4/3) does not fit, but (1,-4/3) does work, since 4(1)-3(-4/3) = 4+4 = 8 4(3/2)-3(-2/3) = 6+2 = 8 4(-4)-3(-8) = -16+...

**physic**

It's easy if you (a) draw a diagram (b) review your trig functions Then it's clear that if the height is h, h cot17° - h cot20.9° = 928 Now just find h.

**math**

because (a+b)^2 ? a^2 + b^2 sqrt is not a linear operator

**algebra**

correct, if ?5 is one of two bisectors of ?1. Of course, you don't give much context, do you?

**Math**

Of course, it is not possible to make a "complete" graph of a parabola on finite graph paper. If y = x^2-2x-8 then clearly the y-intercept is -8, since that's what you get when x=0 x^2-2x-8 = (x-1)^2 - 9 So the vertex is at (1,-9), which is the lowest point on ...

**Trigonometry**

draw the triangle. Review your basic trig functions: opposite = ?11 adjacent = 5 hypotenuse = 6 csc = hypotenuse/opposite

**Physics**

if you mean the recoil speed, then just conserve momentum (mv) 6v = 0.025*615

**math**

check to be sure you don't want 3 + 9 + 27 + 81 + 243 4 + 16 + 64 + 256

**Geometry**

no problem. How about asking an actual math question?

**Physics**

work = force * distance so, how far did he move?

**Algebra**

Well, revenue must equal costs, so if they sell t tickets and f fans get free bats, we have 4t + 1200 = 2100+1900+3f

**calc 3**

s = ?[0,2] ?((18t)^2 + (18t^2)^2) dt = ?[0,2] 18t?(1+t^2) dt = 6(5?5 - 1)

**Calculus**

if the interval is [a,b] and there are n equal subintervals, then the ith x value is a + i times the subinterval width, less 2/3 of that width. xi = a + (b-a)/n * i - (b-a)/n * 2/3 = a + (b-a)/n * (i - 2/3) and the sum is as usual n ? f(xi)*(b-a)/n i=1

**math**

6n + 4*2n = ?

**MATHS**

(a) ?x | A(x) any ideas on the others?

**math**

1/2.5 = 15/x x/2.5 = 15 x = 2.5 * 15 ...

**L.A 8TH**

the triangles are congruent. This is in fact almost the definition of congruent. Take a look at your text. two triangles are similar if their angles are equal. Also, they are congruent if their sides are equal, as described above.

**Math**

I'll work with a vertical axis, just because it makes me more comfortable with the derivatives. For y = x^2/4 (x^2 = 4y), at x=a, the slope is x/2, so the normal has slope -2/a For y = x^2+k, at x=b, the slope is 2b, so the normal has slope -1/(2b) So, the equations of our...

**Math**

Eh? How can two parabolas with a common vertex and a common axis of symmetry have two distinct normals? This should get you started... https://math.stackexchange.com/questions/524130/common-normal-parabola-problem

**math**

The four points are (0,b),(?b,0),(0,-b),(-?b,0) Now use your favorite method to find the base length and altitude, or sides and angles, etc. to find the area of the rhombus.

**Math**

what you do is translate so that the desired point becomes the origin. Then rotate as usual, and undo the translation afterwards. Each of these operations can be described using a matrix, and the whole shebang can be performed at once by using the product of the three matrices...

**Math**

correct. y = -x^3, which is a polynomial, not an exponential.

**Algebra**

since PV=kT, if T is constant, then P and V are inversely proportional. Halving the pressure doubles the volume.

**Math**

|x| + 5 = 18 |x| = 13 x = ±13 |x+3| < 5 x+3 < 5 if x >= -3 x < 2 so, -3 <= x < 2 or x+3 > -5 if x < -3 x > -8 so, -8 < x < -3 result: -8 < x < 2 |-3n|-2 = 4 |-3n| = 6 |3n| = 6 since |-3n|=|3n| 3n = ±6 n = ±2

**mathematics**

(e + 1/e)^4 = e^4 + 4e^3/e + 6e^2/e^2 + 4e/e^3 + 1/e^4 = e^4 + 4e^2 + 6 + 4/e^2 + 1/e^4 for the 2nd one, since the terms alternate in sign, every other term cancels out, leaving just 2(e^4 + 6 + 1/e^4)

**mathematics**

if wire 2 is 9, and wire 3 is x, then we have 9 = 2x-3 x = 6 the perimeter is just 5 + 9 + 6 = ?

**math - trig/pythagoras**

x^2 + (2b)^2 = (6b)^2 x^2 + 4b^2 = 36b^2 x^2 = 32b^2 x = 4b?2 Now recall that area = bh/2 and just do the multiplication

**Math**

1) m = 6t m+20 = 2(t+20) 6t+20 = 2t+40 t=5 So, Mary is 30 in 20 years she will be 50, which is 2*25 2)5W = 2*10W = 4*15W = 8*20W 3) makes no sense, either the question of the answers

**Math**

taxes: 40% of 50000 = 20000 So, they had 30000 left to spend In 1994 they spent of their $40000 Others-10000 Food- 4000 Housing- 10000 Total: 24000 That leaves 6000 for savings

**Math - Need Pattern**

ummm, which pattern?

**Alg 1 -Further explanation PLEASE**

If the points given are those of P(x), then f(x) has the same values, with the exception of (1,-3). f(x) contains (1,3) since |-3|=3, and the range of f(x) is all the distinct values of y.

**Math**

ah, actually I misspoke. Since 3+2i is also a root, we have p(x) = (x-(3-2i))(x-(3+2i))(x-a) = (x^2-6x+13)(x-a) So, now just solve for a: p(0) = -13a = -52 a = 4 p(x) = (x^2-6x+13)(x-4) = x^3-10x^2+37x-52

**Math**

peter is 30 lbs lighter than john. So, j + j-30 = 235 Odd; I expected an integer answer... as for the polynomial, who knows? I see no question there. And LaTex doesn't do well here. And p(x) cannot be monic with real coefficients and have a complex root.

**maths**

x^(3/2) = x^(1 + 1/2) = x * x^(1/2) = x?x so, 20^(3/2) = 20?20 = 40?5

**physics**

1200rev/min * 2?/rev * 1min/60s = 40?Hz 40?Hz * 3s = 120?*6cm = 720?cm

**MATH**

or, convert all to decimals. Then it is easy to see.

**Calculus**

So, with limits a and b, that will be n-1 ? f(a+(i + 1/3)*(b-a)/n)*(b-a)/n i=0

**math**

one way is to check the lengths of the sides. Call the longest c, and the others a and b. If c^2 = a^2+b^2 then you have a right triangle. For example, GH^2 = (3+2)^2 + (-1-1)^2 = 29 Now fin the other side lengths Another way is to find the slopes of the sides. If two of the ...

**mtap**

assuming the diagonals are equal, 3x+2 = 5x-8 x = 5

**Math**

r^6 = 39366/54 = 729 = 3^6 a = 54/3^2 = 6 ... for the factorials, just use any online calculator. geez.

**Algebra II**

Note that since 8 = 2^3, 8a^-3 = 2^3/a^3 = (2/a)^3 so, (8a^-3)^-2/3 = (a/2)^2 = a^2/4 You are done, and you are correct.

**Math**

well, you know that 1 ft = 12 in 1 yd = 3 ft = 36 in So, just do the math

**maths**

the nth term is (1 + .07/12)^n after 5 years, the balance is thus 25000(1+.07/12)^(12*5)