Tuesday
July 22, 2014

Posts by steve


Total # Posts: 23,914

math
I assume a typo, and that g(x) = -(x-1)^2 + 3 if -2 < x <= 2 just look at the data: since -2 < 1 <= 2, g(1) = -(1-1)^2 + 3 = 0+3 = 3 since -2 < 2 <= 2, g(2) = -(2-1)^2 + 3 = -1+3 = 2 since 5>2, g(5) = 3 Don't let all the symbols confuse you. Each just ...

Math
(8-4x)/(x+5) > 1-x If x+5 > 0, 8-4x > (x+5)(1-x) 8-4x > -x^2-4x+5 x^2+3 > 0 This is true for all x, but the initial condition was that x > -5. So, that is the domain: x > -5 If x+5 < 0, 8-4x < (x+5)(1-x) 8-4x < -x^2-4x+5 x^2 < √3 But, we ...

math
look at the amount of tar: 1.0*6 + .05*120 = x(126) x = 0.095, or 9.5% Or, consider that 5% of 120g = 6g So, now you have 12/126 = .095

Algebra/Steve
You're not sure about the zero? I'm not sure about the equation!

algebra
just do what you did with 13 and 6: wherever you see an x, substitute in p: f(p) = p-7 Not a numeric answer, because you haven't specified what value p has. f(bozo) = bozo-7 f(40) = 40-7 and so forth.

math
if the first term is 456, then the 17th term is 456+7*16 Tn = 456 + 7(n-1)

programming oop
sum12 = n1 + n2 diffs3 = sum12-n3 prodd4 = diffs3*n4 quotp5 = prodd4/n5 I think you can write the code to gather n1-n5 and display the values calculated above.

Algebra
Think of a number between 1 and 10: n Add 1; n+1 double the result; 2(n+1) = 2n+2 add 3; 2n+2+3 = 2n+5 subtract 4; 2n+1 add 5; 2n+6 halve the result; (2n+6)/2 = n+3 add 6; subtract 7; add 8; subtract 9; n+1 subtract the number you first thought of: 1 Don't see any inductio...

geometry
Using only reflections in vertical lines, then horizontal lines, you can get B by reflecting through x = -1/2: (-2,-1) -> (-1,-1) through y = -7/2: (-1,-1) -> (-1,-6) No idea what your operations were. Just move your coordinates an equal distance on the other side of the...

calculus - unclear
Man, there's a lot of missing information here. That leads me to conclude that the hammer spins in a counterclockwise direction, then flies in a straight, horizontal line from the circle to the screen. Apparently the screen is a circle of radius 50. Now, your solution of (...

math
If the current's speed is x, then 10+x is the downstream speed of the boat 10-x is the upstream speed. the downstream time is 90 minutes (3/2 hours) less than the upstream time. Hence, the given equation. 36/(10+x) = 36/(10-x) - 3/2 36(10-x) = 36(10+x) - 3/2 (10-x)(10+x) n...

math
since time = distance/speed, 36/(10+x) = 36/(10-x) - 3/2 x = 2 check: 36/12 = 3 36/8 = 4.5 ok

math
if his rowing speed is x and the stream's speed is y, then we have 4/(x+y) = 3/(x-y) 48/(x+y) + 48/(x-y) = 14 x=7 and y=1 check: x-y=6 x+y=8 It is clear these values fit the conditions.

Math
assuming you mean integers, 501 - 1499 will both round to 1000 any number can be rounded to the nearest thousand. You will have to be a bit more specific.

math
as written, I'd say $189.95 Now, if you mean that each phone costs $189.95, then 100 of them cost $18995.00

math
6 is the same as 5 8/8 So, 5 8/8 - 3 5/8 = 2 3/8

mathematics
can you see how little context you have provided?

algebra
c'mon. You know that 99 = 9*11 So, what might the two consecutive odd integers be? ...

algebra
Note that the terms come in repeating groups of 5. 38 = 7*5 + 3 So, S38 = 7(4+8+2+6+2) +4+8+2 = 168

math
4/7 * 3/8 = 12/56 or 3/14 Good luck finding that measuring cup!

Math 11 - Rational Expressions
the only restrictions are because you cannot divide by zero. So, check the denominator of any rational expression. Wherever it is zero, those values must be omitted from the domain. Otherwise, all real numbers are allowed. So, for #3 above, since 2x^2+5x+2 = (2x+1)(x+2) the va...

math
so, just fix the typo and solve -16t^2-32t+320 = 48 t = 3.24

alegbra
(3x-1)(x+2)

Math
Add up all the numbers: 632 There are 12 numbers, so the mean is 52.666 Now, you want to remove one value so that the remaining 11 have a mean of 56.09. Well, 11*56.09 = 617 So, if you remove one of the 15's, the remaining 11 numbers add up to 617, giving the desired mean.

Pre-Calculus
You show that it is true for n=1. Then you show that if it is true for n=k, then it must also be true for n=k+1. That means that the assertion is true for all values of n, starting with n=1, and thus for n=2,3,4,... For instance, a common proof is that the sum of the first n o...

Math
to lower the mean, remove the highest scores. To raise the mean, remove the lowest scores.

finite Math
17000 * 1.04^5

physics
same seat assuming that the windows are closed...

math
63 divided by (10-3) + 2 x 4 = 63/7 + 8 = 9+8 = 17 However, (63/7 + 2)x4 = (9+2)x4 = 11x4 = 44 Normally multiplication is done before addition

math
8*600 = 4800 radios produced. That leaves 2800 more to be done in 4 days. I think probably you can take it from there.

Math
I generally don't think of circles as having ends, so maybe the fence is rectangular or square. However, since you talk about using pi=22/7, I'll assume you want a circular fence, and the diameter is 10 ft. So, C = 10pi = 31.4 ft $440/31.4ft = $14.01/ft

algebra
first place is to check your text for some kind of distance formula. Next, get out some graph paper and plot the two points, then draw a line between them. Call them A and B, respectively. Now draw a horizontal line from A and a vertical line from B. Where the two lines inters...

physics
if the velocity changes from 25m/s to 0 in 5 seconds, that's an acceleration of -5m/s^2. So, the distance covered till the full stop is 25*5 + 25t + 1/2 (-5)t^2 with t=5, that's 25*5 + 25*5 - 125/2 = 187.5 m

Math
when (1/2)^(t/60) = .05 t/60 = log.05/log.5 t = 259.3 days

chemistry
HCl + NaOH -> NaCl + H2O each mole of NaOH reacts with one mole of HCl. so, how many moles of NaOH in 40g? How many grams of HCl in that many moles?

Math
25x^2 - 30x = -9 25x^2 - 30x + 9 = 0 (5x-3)(5x-3) = 0 ...

Algebra
mathematically, |b| ≠ 2 or b^2 ≠ 4

physics
on the ground, the weight is mg = 100*9.8 = 980N Now, g=9.8 because F = GMm/r^2 = mg, so g = GM/r^2 If we say that r=6371km, then at 1000km altitude, we will have 9.8 * (6371/7371)^2 = 7.32, so the 100kg mass will weigh only 732N

Algebra direction how to do it
As you know, y = 4x-4 is just a line. All the points on the line satisfy the equation. > means "greater than". So, if (2,4) is on the line, (2,5),(2,6),... are above the line, where y > 4x-4. So, the solution to an inequality is a whole region of the plane, not...

Algebra
1 - x^2/x = 1-x (1-x^2)/x = 1/x - x (2b-2)/(2b^2-8) = (b-1)/(b^2-4) = (b-1) / (b-2)(b+2) Not sure just what you're after

math
since a = bh/2, we have a = 14x/2 = 7x so, 7x <= 112 x <= 16

College Alegbra
(a) d(j(x)) = .75(j(x)) = .75(x-5) (b) j(d(x)) = d(x)-5 = .75x - 5 (c) go for it

algerbra
the difference between three-fifths and five is equal to the product of x and the sum of y and seven. Seems kinda dumb. Why all the nonsense with 3/5 - 5?

math
55+25-15 = ?

geometry
time to draw a diagram and review your basic trig functions: DE/10 = tan 25° It also helps to recall the alternate interior angles between parallel lines are equal.

algebra
well, you need a 1, so that would be 3/3 Now you need 30 more, using three 3's. Looks like 3^3 + 3 + 3/3

Math
a.bc a > 0 b = a+1 c = a+b 1.23, 2.35, 3.47, 4.59 Unless there are further conditions, just pick one.

math
Well, the roots are -1/2 and 1, so I hope some of the choices were near those values.

math
each of 5 people plays 4 others. That's 5*4 But, that counts each person twice, so you really have 5*4/2 = 10 games

math
all correct good work

algebra
If you mean 2y/3 + 2y - 6/15 then that is just 2y/3 + 6y/3 - 6/15 = 8y/3 - 2/5 = (40y-6)/15 If that's not it, then use some parentheses and show your own work.

Math
well, you have ax^2 = -h ax^2 = h In either case, a and h must have the same sign, since x^2 is always positive. Unless x=0, in which case, h=0. x = ±√|h/a| Naturally, if a=0, there is no solution unless h is also zero.

math
looks like you need to review your basic triangles: sin 60°/cos^2 45° - cot 30° + 15cos 90° √3/2 / 1/2 - √3 + 15*0 √3 - √3 0

Math
You have calculated the number of feet in 26 miles. Now divide that by (32/12), the number of feet in one stride. Or, you can multiply 137280 by 12 to get the number of inches in 26 miles, and then divide that by 32, the number of inches in one stride. Same difference.

Trigonometry
secx - √2 = 0 secx = √2 x = π/4 If this gave you trouble, it looks like you need to review your basic trig functions and common triangles.

algebra
x+y = 15000 .08x + .07y = 1100 Now just solve for x at 8% and y at 7%

Physics
(30,0) + (9.64,-11.50) = (39.64,-11.50) √(39.64^2 + 11.50^2) = 41.27 tanθ = -11.50/39.64

Math
750000 * 0.8^3 at the start of the 4th year. 750000 * 0.8^4 at the end of the 4th year you will have to decide when "during" the year you want its value.

Math
sinθ = 10/15

Math
(1*1 + 5*2 + 3*5 + 1*10 + 1*100) ------------------------------------ (1+5+3+1+1)

finite math
(# left field) / (# hits) = 6/59

math
Clearly, attendance on M-W is 33,34,35 So, attendance on Th-Sat is 36,37,38 with average=37

algebra
think 3-4-5 right triangle. or, do the math: √(50^2 - 30^2)

Math
481,924,821,947,217,481,274,832,748,971,298

math - ouch
Dang. Don't know what I was thinking.

math
what's the trouble? Just start working in the clues. The number is 2.abcdefg... c = a+b b = c-a (well, duh) b = c-1 It appears that the number is just 2.abc c = a+c-1 a = 2c+1 Now, since a < 10, c < 5 So, if a = 0,1,2,3,4 then c = 1,3,5,7,9 and b = 1,2,3,4,5 So, we c...

Algebra 1
the slope of the line is positive, so maximum y will occur where the maximum x occurs. So, y <= 5 Since lines extend to infinity, the range is thus (-∞,5]

math
The 48 is just noise. The cost (c) of the tickets for p pupils is c = 150p 150*43 = 6,450 So, the figure of 6,350 is incorrect. Whether or not it is wrong for the teacher to say otherwise is a moral question ...

math
1/(1+√2+√3) * 1/(1-(√2+√3))/(1-(√2+√3)) = (1-√2-√3)/(1 - (√2+√3)^2) = (1-√2-√3)/(-4-2√6) = (1-√2-√3)/(-2(2+√6)) = (1-√2-√3)/(-2(2+√6)) * (2-√6)/(2-√6) ...

Math
yes each value of x produces a distinct value of y.

Math
yes no maybe

math
If those "x" signs mean multiplication, then you surely know that 0x anything is zero.

math
n(n-1)/2 = 171 Since 342 = 18*19, there were 19 teachers.

physics
g = GM/r^2 at r+h, g1 = GM/(r+h)^2 at r-x, g2 = GM/(r-x)62 ∆g = GM(1/(r-x)^2 - 1/(r+h)^2) = GM/((r-x)^2(r+h)^2) ((r+h)^2-(r-x)^2) = GM/((r-x)^2(r+h)^2) (2rh+h^2 - 2rx+x^2) Since r-x and r+h are both approximately r, we have ∆g = GM/r^4 (2r(h-x) + h^2+r^2) = 2GM/r^3...

finite mate
anythingP0 = 1 There is only 1 way to choose nothing.

Algebra
You can factor out a^2 b, giving a^2 b (a^2 + b^2) Not sure that's any simpler.

Math
multiply RS top and bottom by cos2x and you have 2/(1-cos2x) = 2/(1-(cos^2 x - sin^2 x)) = 2/(1-cos^2 x + sin^2x) = 2/(2sin^2 x) = 1/sin^2 x = csc^2 x

Algebra
you want two factors of 45 which add to 18. Since 45 = 15*3, you get (x+15)(z+3)

math
y = 6x+4 Since you know the number of games, and the cost depends on that, x is the independent variable.

math
Arrange the coefficients into a 3x3 matrix, filling in zeros for missing values. A matrix is in row echelon form if (1) All nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (if any). (2) The leading coefficient of a nonzero row is always s...

Algebra/please can some one help I forgot
Just look up the formula for monthly payment of loan amortization, and plug in your numbers.

MATH
no problem. Literally -- no problem. All you have done is give us the definition of some set of BOYs.

geometry
C = 3.14 * 60 = 188.4 cm 33.3 rpm means the bicycle travels 33.3 * 188.4 cm in one minute.

geometry
360 degrees is just one revolution. So, in 48 minutes, it turns 48 times. By the way, most LPs rotate at 33 1/3 rpm, not just 1 rpm. Also, they don't play for any 48 minutes either. Stupid question.

geometry - oops
I misread 1008 as 1080. Go with Reiny.

geometry
720 = 2^4 * 3^2 * 5 1080 = 2^3 * 3^3 * 5 672 = 2^5 * 3 * 7 So, the largest number that evenly divides all of those is 2^3 * 3 = 24

algebra
x+y=15 8x+5y=96 now just solve for x and y

Math
150 is less than the mean for Natalia's class. So, if that score is removed, the mean rises. Similarly, since 150 is greater than the mean for Eric's class, if that score is added, the mean rises.

Math
y = x^2 + 3x + 1/4 = x^2 + 3x + (3/2)^2 + 1/4 - (3/2)^2 = (x + 3/2)^2 - 2 That should answer most of your questions.

Math
30x+20y+10z = 800000 x+y+z = 40000 x = y/2 x=10,000 y=20,000 z=10,000

algebra 1
If we model the situation as y = mx+b then we have 120m+b = 18 300m+b = 6 Subtract to get -180m = 12 m = -1/15 So, b = 26 y = -1/15 x + 26 y=0 when x = 390

finite math
Hmm. Looks like 0.438

finite math - PS
That's the experimental probability. The theoretical probability is still 1/2.

finite math (probability
I'd say 57/100

math
400m+b = 2150 300m+b = 1650 subtract to get 100m = 500 m = 5 so, b = 150 y = 5x+150

physics
given the drawing as shown below, I calculate 3.62 km at 46°

geometry
Assuming the chords are parallel, think of 8-15-17 right triangles.

Science
Seems to me that the only possible reason can be that ice provides less friction, whatever the underlying properties. Friction translates into a restraining force, reducing the speed.

science
F = ma, so 20 = 4m m = 5 kg

math
what a lot of noise. Distance traveled: 128100 ft = 24.26 mi Average speed: 335.92 mi/hr so, time falling is 24.26mi / 335.92mi/hr = 0.0722hr = 4.3 minutes

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