# 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)