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Posts by steve

Total # Posts: 51,737

math-precalculus
well, you have sec 2? = 3 cos 2? = 1/3 2? = 1.231 or 2?-1.231 so, divide those by 2, and then add ? to get all 4 solutions.

Mathematics - Limits
Hmmm. Using L'hospitals rule, we have the value as (a - 1/2 (1+x)^(-1/2))/2x (1/4 (1+x)^(-3/2)/2 -> 1/8 So, I don't see how we can assign a value to a, because the limit is 1/8 for any value of a. Am I missing something?

Algebra
A = 30 + 0.10m B = 50 + 0.05m see what you can do with those equations.

Physics
recall that v^2 = 2as = 2E/m a = F/m so, s=2

Math
Type in your function here, and it will give you the roots and other info. http://www.wolframalpha.com/input/?i=-0.4x%5E2%2B8.3x%2B4.3 On this one, x^2+3x-10 = 0 you should have factored it: (x+5)(x-2) = 0 Then you would have seen that the roots are -5 and 2, rather than what ...

Math
no square matrix can have 8 elements!

math
not knowing the prices is a bit of a hindrance. However, if the prices were x and y, and there were s seniors, then sx + y(205-s) = 1930 So, plug in your values for the ticket prices, and solve for s.

Math
70 * (1-.25) * 1.06 = 55.65

Math
google Heron's formula

math
see your earlier post

math
solve the equations in pairs: 4x+y=1 2x-y=5 intersect at (1,-3) Now do the same for the other pairs: 4x+y=1 3y+3x=12 2x-y=5 3y+3x=12

inequalities mathh 7a
the monthly fee m is figured by subtracting the entry fee ($100) and dividing the rest by the number of months: m = (700-100)/12 = 600/12 = 50

inequalities mathh 7a
Your keyboard has all the symbols you need to type math problems.

inequalities mathh 7a
ever hear of real math symbols? r/2 - 6 = 14 r/2 = 20 r = 40

math
the two equations are y = 12x y = 120+2x

Math
if you just want to simplify it, add like terms: (14-12)x^2 + (3+11)x + (4-3) 2x^2 + 14x + 1

Algebra
2x^2-3x+1 = (2x-1)(x-1) x^2-6x+1 is a little harder, as it has no rational roots. So, use the quadratic formula to get x = 3±2?2

Math
There are 8 socks, so 3/8 * 2/8

Math
Assuming any number can follow any other, there are 50^3 combinations. If there are some restrictions, then that number will be reduced.

Math
write it as 5*3^n and you have 5*3^0 = 5*1 = 5 5*3^1 = 5*3 = 15 5*3^2 = 5*9 = 45 5*3^3 = 5*27 = 135 starts with 5, not 0

geometry
If she walked on the track, it's an arc of a circle. she walked 2/3 of the circumference. As you recall, the circumference of a circle of radius r is C = 2?r. An arc of a circle of radius r that covers an angle ? is s = r? So, the friend walked through an angle ? such that...

Math
If there are x students, then 3/8 x + 3/5 x + 20 = x now just solve for x

Math
just crank it out... sin(?-30°)+cos(?+30°) = sin? cos30 - cos? sin30 + cos? cos30 - sin? sin30 = ?3/2 sin? - 1/2 cos? + ?3/2 cos? - 1/2 sin? = (?3/2 - 1/2)sin? + (?3/2 - 1/2) cos? = (?3-1)/2 (sin?+cos?) = (?3/-1)/?2 (sin?/?2 + cos?/?2) = (?3-1)/?2 sin(?+45)

Math
if there were a adults, then the rest (8-a) were students. So, adding up the prices, 10a + 8(8-a) = 78

Algebra
correct

Algebra
The terms are powers of 3, so it's a geometric sequence with common ratio 3. So, S10 = 1(3^10-1)/(3-1) = 29524

Algebra
bring it on!

Algebra
(6-x)/(x^2+2x-3) -------------------- (x^2-4x-12)/(x^2+4x+3) (6-x)/(x+3)(x-1) ----------------------------- (x-6)(x+2) / (x+3)(x+1) (6-x)/((x+3)(x-1)) * ((x+3)(x+1))/((x-6)(x+2)) (6-x)(x+3)(x+1) ------------------------- (x-6)(x+2)(x+3)(x-1) -(x+1)/((x+2)(x-1)) -(x+1)/(x^2+x-2...

Calculus
Are you looking for a piecewise function? If so, a simple step function will do the job. f(x) = 0.1 for 0 <= x < 1 0.2 for 1 <= x < 2 0.4 for 2 <= x <= 2.5 You can do similar things with sloping lines, but you will get trapezoids or triangles to work with. If...

math
nah - that's what I got.

math
the distance traveled is the same: 126 km. So, since distance = speed * time, 6(b-c) = 126 4.5(b+c) = 126

Algebra Help ASAP
all correct. good work

One more question Calculus
the acceleration graph is apparently a(t) = 10-t so, that gives us v(t) = 10t - t^2/2 + C v(0)=0, so C=0 so, now we have s(t) = 5t^2 - t^3/6 + C s(0) = 10, so C = 10 s(t) = 10 + 5t^2 - t^3/6 s(30) = 0 So, the final position is 10 ft behind the starting line. However, the total...

Calculus Please Check my answer
You have found the net rate of change of the water (since E and F are measured in pints/minute) at t=5, not the amount of water. dA/dt = F(t)-E(t) = (t+7)/(2+t) - (ln(t+4))/(t+2) Unfortunately, ln(t+4)/(t+2) does not integrate using elementary functions. Also, without knowing ...

Calculus really quick check
I agree.

Math
If the bus's speed is x, then since time = distance/speed, 180/x = 240/(x+15)

math
I hope your answer to #5 is (b)

Calculus Please Check my answers
?[1,x] 2t+2 dt = t^2+2t [1,x] = (x^2+2x)-(1^2+2*1) = x^2+2x-3 ?[0,x] ?(4-t^2) dt = 1/2 ?(4-t^2) + 2 arcsin(t/2) [0,x] = 1/2 ?(4-x^2) + 2arcsin(x/2) - (1/2 ?(4-0) + 2 arcsin(0)) = 1/2 ?(4-x^2) + 2arcsin(x/2) - 1 The domain is clearly [-2,2] The range is [-?-1,?-1] http://www....

math
6*5*5 = 150 ft^3 Now just convert ft^3 to liters.

Math
well, you have the formula. So, v = s^3 = (3/4 in)^3 = 27/64 in^3

Math
If x passed both, then 45+52-x = 64

geometry
42

algerbra
all correct You can write >= for "greater than or equal" same for <= as intervals, the domain and range are x?[0,?) and y?[2,?)

Calculus Please Check my answers
Come to think of it, I changed my mind. g'(0.2) = f'(0.4)*2 = -8

Calculus Please Check my answers
#1 not D, since f' is always increasing, f" cannot be zero anywhere. So, no inflection points. I like C, since f'(0) = 0. f has a minimum, since f" > 0 and thus f is concave up. g(x) = f(2x), so g'(x) = f'(2x)*2 g'(0.2) = f'(0.2)*2 = 2*2 = ...

caculus
the length z of cord is z^2 = x^2 + 60^2 z dz/dt = x dx/dt when z=100, x=80, so 100 dz/dt = 80 * 5 dz/dt = 4

Math
a:p = 2:1 = 10:5

Math
2 negatives negative to odd power is negative

Math
log16 - 2logx

Math
what is the mean proportional for any two numbers?

math
consider a hexagon. The triangle's sides join alternate vertices of the hexagon.

maths
you want to divide the length into 9 equal parts. Place z 4/9 of the way from x to y.

Calculus Please Check my answers
#1 ok #2 4^x grows faster than any polynomial #3 I think more likely (-4,0), as in y = 2sin(pi/4 x) http://www.wolframalpha.com/input/?i=2sin(pi%2F4+x)

English
A little-known fact is that "shall" is used for first person: I shall arise and go now. "will" is used for 2nd and 3rd person. They will have a great time. These are reversed in the imperative mood. That is why the Ten Commandments read Thou shalt not steal...

Math
For the code, something like count=0 for i=1..2000   with student[i] do {     read   name,sex,score     pct = score*5/2     sub45 = false     if pct < 45 then   &...

math
surely you meant If the diagonal of a square is 14 m, what is the area? well, if the diagonal is d, the area is d^2/2 because if the square's side is s, the area is s^2. The diagonal is s?2, so d^2 = 2s^2

English language
if the predicate contains two nouns, usually one will be a direct object, and other the indirect object. The indirect one answers the question: to whom? or for whom? so, what are your choices? Not all of the sentences contain both objects.

English language
usually, the first noun in the sentence is the subject. After that, the rest is predicate. What are your choices?

maths
YZ = 2(6 sin50°)

maths
how do the two figures relate? One diagonal of a rhombus does not tell you anything about its sides or angles.

maths
as with all triangles, the smallest angle is opposite the smallest side. So, it is opposite the side of 5cm, and tan? = 5/8

math
just plug it into the formula: 15000(1+.095/4)^(4*5)

Math. HELP!
#1. remember the slope-intercept form? y = mx+b #2. The slope is (1+3)/(3-1) = 2 So, the point-slope form is y-1 = 2(x-3) Now rearrange that into slope-intercept form. #3 -4y = 8x so, y = -2x for the equation y = kx, k is the constant of variation #4. y = kx, so y/x = k, a ...

math
S = a/(1-r) a = 2r, so 2r/(1-r) = 4 Now just solve for r, and you can then get A3 = ar^2

math
-48/6 = r^3 Now you can figure a, and then S11 = a(r^11-1)/(r-1)

math
a+39d = -54 S15 = 15/2 (2a+14d) S30 = 30/2 (2a+29d) So, 15/2 (2a+14d) + 30/2 (2a+29d) = 0 or, a+12d = 0 Now you have two equations, and you can find a and d, and then the sum S40.

math
no way for me to see. However, check your graph against this one: http://www.wolframalpha.com/input/?i=y%5E3+%3D+x-2

mathematics
but there are many online articles that show how to do it.

Mathematics Algebra
But (x^2 + 2x +4)/(x^2 - 2x - 4) does not always fit into the interval [1/3,3]. If x is very close to 1±?5 then the value is arbitrarily large f(3.2) = -129 plus, you have a typo. I think you mean [9.(3)^2x + 6.(3)^x + 4]/[ 9.(3)^2x - 6.(3)^x +4] using u = 3.3^x That ...

maths
huh?

Mathematics
"real"ize the denominator by multiplying top and bottom by 1-i sinx. Now you have [tan 2x - i(sinx+cosx)][1 - i sinx]/[(1-i sinx)(1+i sinx)] [tan2x - (sinx+cosx)(sinx) + i(junk)]/(1+sin^2 x) to get zero real part, we need tan2x = sin^2x + sinx cosx any multiple of ? ...

Math
For the code, something like count=0 for i=1..2000   with student[i] do {     read   name,sex,score     pct = score*5/2     sub45 = false     if pct < 45 then   &...

Math
If there are x cars and y yellow cars, clearly the new car is yellow, since 1/9 > 1/10 y = x/10 y+1 = (x+1)/9 There are now 81 cars, with 9 yellow.

trigonometry
draw the diagram, and it is clear that the distance x is x/100 = tan 50°11'10"

Math
c+d = 500 .75c + .50d = 275

math
so, you used 304 ft of fence.

Math, factoring
Divide by (x^2-x-6) and you get quotient: x^2+(a+1)x+(2a+7) remainder: (8a+24)x + b+6(2a+7) For the remainder to be zero, we need a = -3 b = -6 So, x^4-3x^3-3x^2+11x-6 = (x+2)(x-3)(x^2-2x+1) The other roots are 1,1

Algebra
multiply the 2nd equation by 12 and you have 12y = -3x+20 or 3x+12y = 20 so, the two equations are the same.

Math (Double checking trig identity)
Nope. my bad. Still you were also wrong (a^2sec?)^2 - (a^2)^2 = a^4 (sec^2?-1) = a^4 tan^2?

Math (Double checking trig identity)
not at all. (a^2sec?)^2 - (a^2)^2 = a^4 (sec^4? - 1) = a^4 (sec^2?-1)(sec^2?+1) = a^4 tan^2? (sec^2?+1)

Cornhole
if you want names, puntarelli pamela kathryn huckaby

Math
No, ?35 is a number like any other, so it has to be included Just as 20+10x is not 30x, 20 + 10?35 is not 30?35 20?35 + 10?35 = 30?35 20+10?35 = 10(2+?35)

math
c'mon -- just start plugging in values for n: n=1: 1(1-2)-3 = -4 n=2: 2(2-2)-3 = -3 n=3: 3(3-2)-3 = ... and so on

Science physics
work is in Joules 2.0kg * 9.8 m/s^2 * 4.5m = 88.2 kg-m/s^2 = 88.2N-m = 88.2J work = force * distance force = mass * acceleration

Science physics
The acceleration is due to gravity g = 9.8 m/s^2

Math
correct

Math
since the ratio of height:shadow is the same, h/5 = 2/3

math
draw the two circles, and a line through their centers. Label the radii, and it should be clear what the two distances are.

maths
not sure just what you want to do with this log 5 = 0.699 I guess you can take it from there.

Math
(3 3/4)/3 = 1 1/4 Just divide everything by 3

Algebra
If the ... indicates some set of repeating digits, the number is rational If not repeating, then it is irrational Either way, it is real

Math-age problem
f+g = 60 f+6 = 2(g+6)

Math
j = e+5 j-3 + e-3 = 17 now just find 21-j

Math
those numbers are all volumes. You need to find pairs of numbers. The sum of their products is the area. Better yet, study the net to see which vertices of the prism are represented; then use what you know about prisms to get the area.

algebra
nope. the area will be 1/13^2 as much.

algebra
correct

math
2/3 as many men, so 3/2 as much time.

algebra
no, it will grow by a factor of 4^2 = 16

Algebra
just divide term by term, using the distributive property: (4x³ + 10x² + 3a) ÷ 2x² = 4x³÷2x² + 10x²÷2x² + 3a÷2x² = 2x + 5 + 3a÷2x²

Math
since east is +x and south is -y (-10,6)+(3,-12) = (-7,-6)

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