Sunday

December 21, 2014

December 21, 2014

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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