Sunday
December 21, 2014

Posts by steve


Total # Posts: 27,654

Calculus- Tangent Line
looks good to me. Of course, it would help to know just what the curve was ...
December 9, 2014

Math
x^2+4x = x(x+3) 2x^2+13x+15 = (2x+3)(x+5) x^2-16 = (x-4)(x+4) So, what you have is x(x+4)(x+5) ------------------ (2x+3)(x+5)(x+4)(x-4) That leaves you with x / (2x+3)(x-4)
December 9, 2014

Math
72x^7
December 9, 2014

Statistics
10P4 = 10*9*8*7
December 9, 2014

fuctions and statistics
you can always multiply by 1 without changing anything. You know that 1 ft = 0.3048 m That means that 1ft/0.3048m = 1 0.3048m/1ft = 1 Now, you want to convert feet to meters, so just multiply by the "correct" representation of 1, so that the units cancel out as you ...
December 9, 2014

English
They look ok to me. And yes, "according to" is ok, as well. I guess you are all "set" now, eh?
December 9, 2014

English
#2 is correct, except for the typo. I'd never use "the" in this case. However, it is correct to say He must have been late for the bus. A bus is a specific vehicle, but "school" is a more vague entity, implying education and other activities, and not ...
December 9, 2014

Physical Science
All oxygen boils at -183 C, but I have no idea what temperature your oxygen is at.
December 9, 2014

math(5th grade)
zero, if the school is north of his home.
December 9, 2014

Calculus
well, you remember that inflection is where y" = 0 concave up when y" > 0 For y" I get 2 times your answer, but that doesn't change its properties. y' = 2cosx(sinx+1) y" = -sinx + cos^2x - sin^2x = -sinx + 1 - 2sin^2x = -(2sinx-1)(sinx+1) Note ...
December 9, 2014

Calculus
the line has slope 2/3 So, the normal needs slope -3/2 3x^2-4y^2=8 6x - 8yy' = 0 y' = 3x/4y So, we need 3x/4y = -3/2 y = -x/2 3x^2-4(-x/2)^2 = 8 3x^2-x^2 = 8 x = ±2 y = ∓1 So, we want lines through (2,-1) and (-2,1) with slope -3/2 y-1 = -3/2 (x+2) y+1 = -...
December 9, 2014

Calculus
I suspect a typo. Why the ^1 ? At x=0, you have (1+0)^1/0 = 1/0 = +∞
December 9, 2014

Math
g(x) --> -6x^2/5x^2 = -6/5
December 9, 2014

Math (Word Problem into formula)
To start with, there is 1 kg of tin. After adding x kg of tin, then we have c(x) = (x+1)/(x+6)
December 8, 2014

algebra
the first thing is your sloppy typing. a/b - c/d is NOT (a-b)/(c-d)
December 8, 2014

geometry
18ft8in = 224in So, one side is 56in area = 56^2 in^2 Now convert that to ft^2
December 8, 2014

GEOMETRY
T(3+4),(5-4) = T7,1
December 8, 2014

Calculus
Hmmm. Not surprising, since you have not posed a question ...
December 8, 2014

geometry
you need to note that one pace is one yard. Now the instructions should make sense, since 15 paces is halfway from 3rd base to 2nd.
December 8, 2014

geometry
the stride is one yard. So, the bases are 30 paces apart. 15 paces is halfway between the bases, along the baseline. Then move back 3 paces from the baseline. Done.
December 8, 2014

Calculus
naturally, since that is the formula for the sum of a G.P.
December 8, 2014

Calculus
The sum is 1/(2^i) = 1/2^1 + 1/2^2 + 1/2^3 + ... = 1/2 + 1/4 + 1/8 + ... You will recognize that as a geometric series, with S = (1/2)/(1 - 1/2) = 1
December 8, 2014

Algebra 2
See the graph at http://www.wolframalpha.com/input/?i=solve+x^2+-+3x+%3D+1
December 8, 2014

Algebra 2
well, 5*2 = 8+2
December 8, 2014

Algebra 2
x^2-2x-35 = 0 Well, the factors of 35 are 5 and 7. They differ by 2, so ...
December 8, 2014

Math Help
all correct. good work.
December 8, 2014

Fraction
13 = 12 8/8 minus 7 5/8 equals 5 3/8
December 8, 2014

calculus
if the dimensions for metal and wood are m and w, then we know that cost = 2(10w+20m)=400 area = m*w = m(200-20m)/10 = 20m-2m^2 This is just a parabola with its vertex at m=5 So, the maximum area is with dimensions metal=5 ft wood=10 ft
December 8, 2014

12 Math
log_2(36)^3 = 3log_2(36) = 3(2+log_2(9)) = 6+6log_2(3) Not sure where you want to go from there. Now, if you meant log(32), that is 5, so log_2(32^3) would be 15.
December 8, 2014

College Algebra
DRS says there are 2 or 0 positive roots 1 negative root RZT says look for roots among ±1,5,7,35 Synthetic division using easy values first says f(x) = (x-1)(x^2-2x-35) I think you can probably take it from there, ok?
December 8, 2014

Linear Algebra
maximize r = 500x + 750y + 1000z subject to x+y+z <= 30 x/2 + y + 2z <= 3*8 The answer from the above constraints may in fact not allow for proper distribution among operating rooms, so watch out for that.
December 8, 2014

math
The bottom is +289
December 8, 2014

Math
what do you mean simplify? You can distribute the fraction, and you get -15/20.5 = 0.73 so you could write -.73x^2 - 2.20x - 1.65 but that's only approximate. SO, again, what do you mean by "simplify"? I will note that x^2+3x+2.25 = (x+1.5)^2 if that helps You ...
December 8, 2014

Math
12x^12/4x^3 = 3x^9 x^8/24x^6 = x^2/24 3x^9 * 24/x^2 = 72x^7
December 8, 2014

Homeschool
each 1.5 cm represents 3m So, how many times bigger is 8 than 1.5? There will be that many 3m lengths. So, the real length is 8/1.5 * 3
December 8, 2014

trig
you can't solve it. It's just a function definition. But, the graph is at http://www.wolframalpha.com/input/?i=r+%3D+3%281-sin%CE%B8%29 Now, if you want to see its equation in rectangular coordinates, r = 3 - 3sinθ r^2 = 3r - 3r sinθ x^2+y^2 = 3r - 3x x^2+y^2...
December 8, 2014

math
40*40 = 1600 So, the cost is (800/9)*25 + 800*2.50
December 8, 2014

math
if $x at 8%, then the rest (8000-x) is at 12%. So, .08x + .12(8000-x) = 650 Now do the math.
December 8, 2014

Algebra 2
clearly there are (2y^2+6)/(y^2-1) notebooks. So, plug in y=3 to find how many.
December 8, 2014

Math
you get the y-intercept when x=0 You get the x-intercept when y=0. So, 1/6 x^4 - 2x^2 + 4 = 0 x^4 - 12x^2 + 24 = 0 x^2 = (12±4√3)/2 = 6±2√3 So, take each of those values and get its ± square roots.
December 8, 2014

fundamental to programing
read x,y,z if (x<y & x<z) {print x} else if (y<x & y<z) {print y} else {print z}
December 8, 2014

Math (TRIG)
Review the equation for a hyperbola in polar coordinates. #2 Hint: sec^2 = 1 + tan^2 #3 y = 500 sin70° t - 16t^2 Solve for t when y=0 to find the time in flight The x-velocity is constant at 700 cos70° So using the time from step 1, distance = speed * time
December 8, 2014

Trig (math)
#1 in polar form, -1+√3i = (2,2π/3) So, the two square roots of that are (√2,π/3) and (√2,4π/3) #2,#3 just plug in x = r cosθ y = r sinθ #4 8x - 7y = -10 7y - 8x = 10 7r sinθ - 8r cosθ = 10 r = 10/(7sinθ-8cosθ)
December 8, 2014

math
well, 2 2/3 = 2.66 2.75 = 2.75 5/2 = 2.50 So, which is least?
December 8, 2014

math
24 = 6*4 42 = 6*7 So, 6 people each clean 4 small and 7 large cages. No other larger number divides both 24 and 42, since 4 and 7 have no common factors.
December 8, 2014

Algebra
If there are n games, you want .40*.80n + p*.20n = .50n .32 + .20p = .50 .20p = .18 p = .18/.20 = .9, or 90% Check. If there are 100 games, you have won 32 already. So, there are 20 games left, and you need to win 18 of them, or 90%
December 7, 2014

Trig (math)
#1 You have y = 9 x = 9√3 So, tanθ = 1/√3 r = 18 You should be able to recognize a 30-60-90 right triangle... #2 (4*5)cis(30°+120°) #3 is just the same. #4 is the same, but divide r, and subtract angles.
December 7, 2014

calculus
Just plug in the numbers you have, and you get (20)(10)(5) + (20)(15)(3) + (10)(15)(8) = 3100 How did you come up with 265?
December 7, 2014

Math
the distance s = 1/2 at^2 So, 500 = 4.9t^2 Now you have the time. You need to say what the velocity's direction is. As you recall, s = vt + 1/2 at^2 It makes a big difference whether v is positive or negative. In 5 seconds it will fall 4.9*5^2 meters.
December 7, 2014

L'Hopitals Rule
sin(x^2-4)/(x-2) --> 2xcos(x^2-4)/1 --> 4 ln(x-3)/(x-5) --> (1/(x-3))/5 -> 0 (x-pi/4)tan(2x) = (x-pi/4)/cot(2x) --> 1/(-2csc^2(2x)) = -1/2 sin^2(2x) --> -1/2
December 7, 2014

linear approximation
f'(x) = -24x sin(3x^2) f'(0) = 0 So, you want the line with slope=0 through (0,4). Duh. y=4 Kind of a dumb place to approximate, eh? With a horizontal tangent, and all that.
December 7, 2014

Pre Calc Take 2
Hmmm. Let's try that again without the typo... log (x-6)*(x+3) = 1 x^2-3x-18 = 10 x^2-3x-28 = 0 x = (3±11)/2 x = -4 or 7 The only real solution is x=7 Check: log(1)+log(10) = 1 yes
December 7, 2014

Pre Calc
well, work it out... log(x-6)+log(x+3) = 1 log (x-6)*(x-3) = 1 (x-6)*(x-3) = 10 x^2-9x+18 = 10 x^2-9x+8 = 0 (x-1)(x-8) = 0 x = 1 or 8 x=1 does not work, because then x-6 < 0 and the log is not defined. So, the only real solution is x=8 Check: log(2)+log(5) = 1 log(10) = 1 ...
December 7, 2014

Algebra 1
Describe how the graphs of y =IXI nand ym = IXI -15 are related. 1- the graphs have the same shape,. The y intercept of the 2nd graph is -15 2-the graphs have the same y intercept. The 2nd graph is steeper than y= absolute x 3- the 2 graphs are the same 4- the graphs have the ...
December 7, 2014

Algebra 1
Graph y= absolute x -2
December 7, 2014

solve
since time = distance/speed, if the speed was x, 168/(2x) = 168/x - 3 x = 28
December 7, 2014

Advanced Algebra
Since we have a geometric series, Sn = A * (e^knt - 1)/(e^kt - 1) So, plug in the numbers and we have S5 = 0.5 (e^(-0.853*4*5)-1)/(e^(-0.853*4)-1) = 0.517
December 7, 2014

math
23 min * 100/3 rev/min = 766.666 rev So, divide the distance between the 1st and last grooves into 767 grooves, and you get 4/766.666 = 0.0052 inches between grooves So, you have an arithmetic sequence with a = 5.75*2π d = 0.0052*2π and you want S767 Just plug and chug
December 7, 2014

problem solving
If there were n bricks at price p, then we know that 1.05np = 315 (n+6)p = 315 Now just eliminate p and solve for n.
December 7, 2014

Maths
There is a lot of missing information here. I can easily devise a scenario where the assertion is false. Suppose A is 1 cm above L and B is 10 cm above L. If D and E are on L, clearly CD < CE.
December 7, 2014

AP CALC. AB
#2 (a) is correct #3 f' = lnx + 1 The only extremum is at x = 1/e f" = 1/x, which is positive at 1/e, so f(1/e) is a minimum. Looks like (c) is the answer See the graph at http://www.wolframalpha.com/input/?i=x*lnx Ignore tha part where x<0, since lnx is not real ...
December 6, 2014

Pre calculus
look up the half-life of C-14. If it is k years, then the amount left after t years is (1/2)^(t/k) So, you want to solve for t in (1/2)^(t/k) = 0.289
December 6, 2014

math
a + c = 8 3.5a + 2.5c = 23 Now just solve for a and c.
December 6, 2014

math
the LCD(2,3) is 6. So, multiply the whole equation by 6: 3x-30 = 2
December 6, 2014

Algebra
Heck, they gave you an example, so that makes it easy. Just pick any values for a,b,c: 9-3=6 ==> 9*6<+>-3*6=9*-3 or 54<+>-18=-27 Who cares what <+> really means?
December 6, 2014

programming urgent
just loop on the indexes. If the arrays x and y have m rows and n columns, then for (i=1..m) for(j=1..n) z(i,j) = x(i,j)*y(i,j) next j next i
December 6, 2014

Physics: need detailed answer
It means there is a horizontal force of 100N applied to the mower.
December 6, 2014

trig
well, you know that x = -2029 y = 2129 so, r = 2941 So, now you just have to review your basic trig functions for angles in standard position. I was a bit confused by the double minus sign, but if I have it right, you're ready to move along.
December 6, 2014

Algebra 1
Which equation is the equation of a line that passes through (-10,3) and is perpendicular to y=5x-7? 1- y=5x+53 2- y=-1/5x -7 3- y= -1/5x +1 4- y= 1/5x +5
December 6, 2014

Math
correct
December 6, 2014

Math
the easiest way is indeed to use the slope-intercept form. It saves having to memorize another formula. If ax+by=c, then by = -ax+c y = -a/b x + c/b and you can see that the slope is -a/b
December 6, 2014

Math
as in any scenario, it is rise/run. More precisely, it is the change in the dependent variable -------------------------------------- the change in the independent variable
December 6, 2014

MATH
not at all. x(t)=3t+5 You have to write the function using the independent variable as the parameter. In this case, t is the independent variable. However, referring to your previous posts, if you are using x and y, yes, x is usually the independent variable. Try reading your ...
December 6, 2014

MATH
no way to tell. However, it is usually x, given the choice between x and y.
December 6, 2014

MATH
plug in y=0 10x+0=500
December 6, 2014

Math
(1.4*2.5)x10^(3-6) 3.5x10^-3 multiply the numbers, add the exponents
December 6, 2014

Math
given the vertex, you know that y = a(x-2)^2 - 1 Now plug in the point to find a: a(4-2)^2 - 1 = -3
December 6, 2014

MATH
the intercept in slope-intercept is the y-intercept; what you get when x=0. I just told you how to find the x-intercept: set y=0 and solve for x.
December 6, 2014

MATH
well, what is x when y=0? 30x+20 = 0
December 6, 2014

Math
well, think about it. Every 15 ft of the field is 1/2 in in your drawing. So, if the field is 150ft long, that is (1/2)*10 = 5in in the drawing. So, find out how big the field is, divide both dimensions by 15, and use that many 1/2-inches in the drawing.
December 6, 2014

Maths
correct. So, what is n?
December 5, 2014

Algebra 1
you want slope = -1/5 So, the point-slope form of the line is y-3 = -1/5 (x+10) Now massage that into one of the choices.
December 5, 2014

Algebra 1
Which equation is the equation of a line that passes through (-10,3) and is perpendicular to y=5x-7? 1- y=5x+53 2- y=-1/5x -7 3- y= -1/5x +1 4- y= 1/5x +5
December 5, 2014

Calculus
f'(x) = (1-x)e^-x f is increasing when f' > 0 e^-x is always positive, so f is increasing when 1-x > 0 See the graph at http://www.wolframalpha.com/input/?i=x+e^-x%2C+0%3C%3Dx%3C%3D2
December 5, 2014

Calculus
e^e^2 is a constant. Fix the typo and try again. f is increasing when f' > 0 f is concave up when f" > 0
December 5, 2014

Algebra 2/Trigonometry
f(x) has 3 sign changes, so 3 or 1 positive roots f(-x) has no sign changes, so no negative roots There might be two complex roots.
December 5, 2014

Calculus
I think we can assume arccos. If so, then recall that d/dx (arccos(u)) = -1/√(1-u^2) du/dx Now just plug and chug.
December 5, 2014

Calculus
and you would be wrong. You have it exactly backwards. f is increasing where f' > 0. Better double-check your derivative.
December 5, 2014

Calculus
If f = √u, f' = u' / 2√u. You have u=3x, so f'(x) = 3 / 2√(3x) f'(3) = 3 / 2√9 = 1/2
December 5, 2014

Intermediate Algebra
√(40x^3) = √(4x^2)√(10x) = 2x√(10x) √(3/4) * √(4/7) = √(3*4 / 4*7) = √(3/7) √6 + √20 = √6 + 2√5
December 5, 2014

Algebra 1
What equation has a graph parallel to the graph of 9x + 3y = -22? 1- y = 3x -22 2- y = -3x + 8 3- y = 1/3 x + 12 4- y = - 1/3 x - 2
December 5, 2014

maths
Don't give much away on the line and point, do you? For the other, just draw a 3-circle Venn diagram, and start filling in the pieces.
December 5, 2014

Math
Good idea, but you don't need x. There are n sides and n angles. Since you already have 4 angles, there are n-4 remaining. So, (n-2)180 = 125+220+40+295+20(n-4) n=6
December 5, 2014

Math
Doesn't matter. I'm full!
December 5, 2014

math
(2/3)/3 * 36 = 2/9 * 36 = 8
December 5, 2014

Algebra
height=39 length = height+21 = 39+21 = 60
December 5, 2014

Algebra
review your equation of motion. the distance is s = 1/2 at^2 You know s=435 and a=-9.8 So, just find t.
December 5, 2014

Math
If he borrowed $x from his friend at 8%, then the rest (170000-x) is at 4%. So, now you have .08x + .04(170000-x) = 9800 x = 75,000
December 5, 2014

Calculus
The graphs intersect at (-4,20) and (5,25) So, consider the area as a bunch of thin strips, each of width dx, and height equal to the distance between the curves. The area is thus ∫[-4,5] (x+20)-x^2 dx = 1/2 x^2 + 20x - 1/3 x^3 [-4,5] = 243/2
December 5, 2014

Math
Grrr! It's pi, not pie! ∫[0,π/2] cos^2(3x) dx Now, you know that cos(2u) = 2cos^2(u)-1, so cos^2(u) = (1+cos(2u))/2 and the integral becomes ∫[0,π/2] (1+cos6x)/2 dx = x/2 + 1/12 sin6x [0,π/2] = π/4
December 5, 2014

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