# Posts by steve

Total # Posts: 50,541

**Math**

all those nice right angles and 45-degree angles make things easy. If you draw the figure, you can easily see that 1/2 the diagonal is 2+3 = 5

**geometry**

well any square's diagonal is ?2 times its side.

**Math**

all pyramids have triangular faces and polygonal bases.

**Math**

another prism. All prisms have two bases and some number of (usually) rectangular lateral faces.

**math**

2800 rev/min * 24?cm/rev = 67200? cm/min I'm sure you can convert that to m/s

**Math**

1000*0.60 + 2000*0.80 = ? I'm guessing at the 80c notebook price, but you can use whatever you think it will be.

**Math**

this site should help: http://davidmlane.com/hyperstat/z_table.html

**Math**

prism with 7-sided bases

**math**

using only angles, congruence is not possible. The best you can do is similarity.

**Calculus**

dT/dt = -kT-A dT/(kT+A) = -k dt 1/k ln(kT+A) = -kt + C T(0) = 90 so 1/k ln(90k+30) = C T(1) = 85 so 1/k ln(85k+30) = C-k Solve for C and k, then evaluate t when 1/k ln(60k+30) = C-kt

**Calculus**

dy/dx = x/y y dy = x dx y^2 = x^2 + c using the point (2,1) 1 = 4+c c = -3 x^2-y^2 = 3

**Math Correction**

I forgot that the perpendicular bisector passes through the midpoint of PQ: (3,-2). So, its equation is y+2 = 1/3 (x-3) So, the center of the circle is at (0,-3). Now find the radius, and you're about done.

**sir steve reiny damon bob maths help steve!!!**

(a) the perpendicular bisector of the chord PQ contains the center of the circle. Since PQ has slope -3, the perpendicular will have slope 1/3. So, the line is y-1 = 1/3 (x-2) Similarly, the radius through Q is perpendicular to the line 2x-y=13. Its equation is y+5 = -1/2 (x-4...

**math**

recall that the vertex of a parabola is at x = -b/2a = 480/0.12 = ?

**math**

8+y <= -22

**Maths**

well, .86666666 - .860000 = .0066666 = 2/300 hours so route 2 is faster by 2/300 hours, or 24 seconds

**Maths**

time = distance/speed So, do the divisions and compare the times.

**Mathematics.**

clearly, the whole number part must be as small as possible, so it'd be 2 ?/7 x 3 1/? Now we want as large a denominator as possible, so I'd go with 2 4/7 x 3 1/5 = 8 8/35 Hmmm/ Nope, 3 4/7 x 2 1/5 = 7 6/7

**Math**

I think B is more likely. All the other pairs have two numbers approximately equal. 4.2 is over twice as big as 2.

**science**

draw a diagram. This is nice and easy, since you have a right triangle. The distance traveled by the plane in t hours must form the hypotenuse of the triangle, so (40t)^2 = (20t)^2 + 500^2 t = 25/?3 = 14.434 hours. Now you can figure the distance and the angle ? (west of north...

**Math**

all regular pentagons are similar.

**Math (Calculus II) (Volume Revolution Setup)**

nope - washers, since it's revolving around a horizontal axis, just as in (a).

**Math (Calculus II) (Volume Revolution Setup)**

(a) using discs of thickness dx, v = ? ?r^2 dx where r = y = x(4-x)^2 v = ?[0,4] ?(x(4-x)^2) dx (b) using shells of thickness dx, and taking advantage of symmetry, v = 2?[0,4] 2?rh dx where r=x and h=y=(4-x)?x v = 2?[0,4] 2?x(4-x)?x dx

**variation**

Finally! Your variation description says that L = km/h so, Lh/m = k is constant. So, you want L such that L*50/250 = 40*286/75

**math**

yes, since everything is zero except the -4 at the end...

**math**

x means multiply, so 12n If a number is placed right next to the variable name, it means to multiply. n over 12 = n/12 = n divided by 12

**Geometry**

well, it's half the distance from (9,5) to (-5,5) Note that both points are on the line y=5, so the distance is just 14.

**Math**

since F=ma, a = -8x/4 = -2x x" + 2x = 0 the general solution to this is x = c1 sin(?2 t) + c2 cos(?2 t) so, the frequency is 1/(?2 ?)

**maths(variation)**

you still have not given the first height.

**Math**

I'd say a pentagon in 6 pieces

**Math**

draw the chord. Draw the radius through the center of the chord. Draw a radius to the end of the chord. If the radius of the gear is r, you can see that r^2 = (r-4)^2 + 7^2 r = 65/8

**Geometry**

see your previous post: http://www.jiskha.com/display.cgi?id=1493340120

**Algebra**

y is increasing where y' > 0 y' = -0.08x+4 y' > 0 when x < 50 The average rate of change is (y(50)-y(0))/(50-0) = 100/50 = 2 I don't know what c is supposed to be, but if you're angling toward the Mean Value Theorem, it is where y' = 2

**Calculus**

1/21 is just the 2nd term in the sequence, but is not a partial sum S1 = 1/12 S2 = 1/12 + 1/21 = 11/84 ...

**Calculus**

well, 3n/(8n+9) -> 3/8 as n->?, so if that's what you meant to say, then you're off. But the series clearly diverges, since the terms do not tend to zero.

**calculus**

just separate the variables as usual dy/dt = -1/50 (y-17) dy/(y-17) = -1/50 dt ln(y-17) = -1/50 t + C y = c e^(-t/50) + 17 y(0) = 87, so c=70 y(t) = 17+70e^(-t/50)

**Precalculus -- Systems of Equations**

substituting for x, we have (2y+8)^2 + y^2 = r^2 5y^2+32y+64-r^2 = 0 For that to have one real solution, the discriminant must be zero: 32^2-4(5)(64-r^2) = 0 r = 8/?5

**Geometry**

of course there's an equation. 5/8 y + y + 1/4 y = 180 y = 96 so, x = 60 and z = 24

**Calculus Help Please**

looks good to me. Of course, the series is ? ? 1/k! f(k) (x-2)k The (2n)! series is for cos(x) k=0

**science**

4m = 50*12

**math**

assuming a linear function, the slope is (25-10)/(5-2) = 15/3 = 5 ft/yr

**calculus help please!**

then it's just like the one I showed first. divide and hen integrate.

**calculus help please!**

correct. So, just do it... ?[0,5] F(t)-E(t) dt = ?[0,5] (t+7)/(t+2) - ln(t+4)/(t+2) dt ?(t+7)/(t+2) dt = ?1 + 5/(t+2) dt = t + 5ln(t+2) For ?ln(t+4)/(t+2) dt, you're in trouble. It is not doable with elementary functions. You sure there's no typo? ?ln(u)/u du = 1/2 ln^...

**maths (variation)**

#1 done below #2 s = kt^2 so, s/t^2 is constant. You want 648/t^2 = 1800/15^2 #3 p = kq^2/?r so, p?r/q^2 is constant p?9/25 = 16?9/64 Kinda dumb to give you the same r value...

**maths (variation)**

E = a + kL a+20k = 1.4 a+30k = 2.0 Now just solve for a and k, and then go for L=50

**Calculus**

?[-1,2] x^2 dx = 3 so far, so good For the horizontal strips, you need the width on the left side as 1-?y, since that is the distance from x = -1 to the parabola. Just as it is 2-?y on the right side. ?[0,1] (1-?y)) dy + ?[0,4] (2-?y) dy = 1/3 + 8/3 = 3

**calculus review please help!!**

I'd say so, yes.

**calculus review please help!!**

not so. ?[0,2] t^2+2t+1 dt = t^3/3 + t^2 + t [0,2] = (8/3 + 4 + 2)-0 = 26/3

**Pre-Calculus**

1.1 times as many pens are sold each year, so after t years the sales will be 2000 * 1.1^t To get the sum of all sales, do the integral ?[1,5] 2000 * 1.1^t dt You need to check on how to integrate a^t for any constant a

**physics**

ok

**chemistry**

you are told that 1 mole of gas fills 22.4 Liters so, how many moles of H2 were produced?

**physics**

well, 7/10 the mass of the wood is submerged, so ...

**Maths**

10/.092 = 108.69 so, ...

**math**

There are 36 possible outcomes. How many of these are even and not 2? Well, of the 36 outcomes, half are even and half are odd. But you want even?2, so throw out 1,1. That leaves just 17/36 Just to be sure, list all possible successes: 13 15 22 24 26 31 33 35 42 44 46 51 53 55...

**Calculus**

(12x+6)(3x^2+3x+5)^7 dx = 2(3x^2+3x+5)^7 (6x+3) dx Let u = 3x^2+3x+5 du = 6x+3 dx so, now your integrand is just 2u^7 du not so hard now, eh?

**math-precalculus**

the amplitude is (87-73)/2 = 7 the center line is (87+73)/2 = 80 y = 7sin(k(x-h))+80 since y(8) = 0, y = 7sin(k(x-8))+80 since the period is 24 hours, 2?/k=24, so k = ?/12 y = 7sin(?/12 (x-8))+80 so, when is y=77?

**Calculus**

dr/dt = 3 r = 3t + c since r(0) = 0, r = 3t a = ?r^2 da/dt = 2?r dr/dt ...

**Math, Algebra, Graphing Systems of Linear Equation**

I'm confused by your impatience and reposting the same problem...

**Math, Algebra, Graphing Systems of Linear Equation**

try playing around here, where I have plotted the first pair... http://www.wolframalpha.com/input/?i=plot+3x%2B2y%3D-6,+x-4y%3D-16 since your lines have different slopes, the have to intersect. You must have plotted them wrong. 3x+2y = -6 x-4y = -16 2y = -3x-6 -4y = -x-16 You ...

**6th Grade Math (Please Help It's Getting Late)**

$60 is the discount, not the price.

**math**

starting when? 6 degrees each minute, however.

**Physics**

well, KE = 1/2 mv^2

**Math**

each octave up doubles the frequency

**computer science**

sum=0 max=0 min=9999 for i=1,12 read amount month[i] = amount if amount < min then min = amount if amount > max then max = amount sum += amount end for avg = sum/12

**MAth**

looks good to me.

**MAth**

I'd say the one which is not showing two sets of data.

**physics**

just add up the KE before and after the collision.

**Mathematics**

As long as we're dividing by zero, what about 0/0? Why is it undefined? Suppose there is a value x such that 0/0 = x Then, multiplying by zero, we get 0 = 0*x But that is true for any value of x. So there is no particular value we can say is equal to 0/0.

**Please help with MATH**

why not post your solution to the first part, and we can see why this change is important?

**geometry**

32 * 26? in * 1ft/12in = 217.817 ft

**math**

correct. a person can determine the miles walked. After that, the calories follow.

**Math**

.03 * 27700

**math**

there are only 2 colors. 3 socks must have two of the same color...

**math**

correct

**Math - Calculus**

Actually, the shape does not matter for this question because it asked about the rate of flow through the channel. I suspect there were other parts where we'd have to work with the volume or depth in the bay, but not here.

**Math - Calculus**

just find the derivative dd/dt the shape of the bay does not matter for this question.

**math**

just divide and you get x+4 + 9/(x-2) So, as x gets huge, the 9/(x-2) vanishes, and the graph approaches the line y = x+4

**Math(Calculus)**

well, x^2-4 has a minimum at x=0, so e^(x^2-4) will as well. since x^2-4 has an absolute max at x=±2, so does e^(x^2-4) But, as long as this is calculus, dh/dx = 2x e^(x^2-4) dh/dx=0 at x=0 (minimum)

**Algebra**

Since F=ma, a = 8x/m. So, we have a(x) = -8/m x v(x) = -4/m x^2 + c1 s(x) = -4/3 x^3 + c1*x + c2 v(0) = 0 and s(0) = 10, so s(x) = -4/3 x^3 + 10 For the damping, just work with v(x) = -4/m x^2 + 8v and follow through to get s(x)

**Calculus**

Since the y-axis is also the axis of symmetry for the curves, we can just take one side and revolve it. This will be easiest using shells of thickness dx: v = ?[0,2] 2?rh dx where r=x and h=(8-x^2)-x^2=8-2x^2 v = ?[0,2] 2?x(8-2x^2) dx = 16?

**Math**

x = 3+4cos? y = 2+4sin? since cos^2? + sin^2? = 1, (x-3)^2 + (y-2)^2 = 4^2

**grades**

no way to tell all we know is that 15 students got above 74% and 15 got below 74%

**math**

x grows by 2 the slope is 2, so y grows by 4. so, y=2+4=6 or, more formally, (y-2)/(3-1) = 2

**Math**

each term is calculated using the previous term, not the next one!

**Calculus - Fundamental thm of Calc**

that would be ((1/4)(x^2)^2?1)^15 * 2x = 2x(x^4/4 - 1)^15

**Calculus - Related Rates**

Let the distance on the road be x. Then the distance z to the house is z^2 = x^2+25 z dz/dt = x dx/dt z(1) = ?26 ?26 dz/dt = 1 * 65 ...

**Calculus Help**

google hole in sphere. You will find many excellent discussions.

**Math**

well, you have a base perimeter of 30. So, the base of each triangular lateral face is 30/4 = 7.5 Now you can see what the side edges of the pyramid are, and there are four of them. let 'er rip...

**math**

reimburses? Did the doctor pay the patient something?

**maths**

L = km/h^2 So, Lh^2/m = k is constant You want L such that L*50^2 = 40*h^2/175 If you will supply the original height, then you can solve for L.

**math**

I don't see any graph ...

**algebra**

#1 The line of symmetry of y=x^2 is the y-axis (x=0). Similarly, for a translated parabola y=a(x-h)^2 + k the axis of symmetry is the line x=h. So, for y = -2x^2+3 the axis is x=0 #2 same for |x|. So, for y = 1/3 |x| - 2 the axis is x=0 #3 Huh? This stumps you? P(4,-4)-->(-...

**math**

I suspect there was meant to be a question in there somewhere, but I couldn't see it ...

**Math**

not mixed numbers. As a fraction, 87.3/8.73 = 10*8.73/8.73 = 10/1 = 10 In case you wanted individual fractions, 87.3 = 873/10 8.73 = 873/100

**Math**

I think Natavia is right. If P = 1/26 that is the theoretical probability. No mention is made of actually performing the experiment.

**Math**

recall that alternate interior angles between parallel lines are congruent. Draw a line through one vertex parallel to the opposite base. the rest is easy.

**Math**

4 * 1/4 = 1

**Math**

6 * 2/3 = 4

**Math**

4/12 = 2/6 = 1/3

**Intermediate Maths**

(a) 12(1/2)^(t/5700) = 10 t = 1499.3 years (b) 12(1/2)^(1599.3/5700) = 9.879 grams