Wednesday

November 25, 2015
Total # Posts: 35,789

**Geometry**

Which letter has rotational symmetry? I J K L IMy answer is I
*November 5, 2015*

**Calculus**

see related questions below.
*November 5, 2015*

**Geometry**

my pleasure, Steve
*November 5, 2015*

**Geometry**

different steves Thank you Steve
*November 5, 2015*

**Geometry**

looks good to me.
*November 5, 2015*

**Geometry**

The vertices of a triangle are P(-4,1), Q(-2,-8), R(8,-1). What are the vertices of the image reflected across the y-axis? my answer is P'(4,1),Q'(2,-8),R'(-8,-1)
*November 5, 2015*

**Geometry**

thank you
*November 5, 2015*

**Geometry**

right on
*November 5, 2015*

**Geometry**

Which rule describes the transformation that is a reflection across the x-axis? a- (x,y)>(x,-y) b- >(-x,y) c_ >(-x,-y) d- >(y,x) my answer is a
*November 5, 2015*

**math**

review your basic rules in this stuff. f = x^2/(x^2-1) f' = -2x/(x^2-1)^2 f" = 2(3x^2+1)/(x^2-1)^3 I expect you can find intercepts ok. Since f(x) is even, it's symmetric about the y-axis. vertical asymptotes where x^2-1 = 0 Since f = 1 + 1/(2(x^2-1)) horizontal ...
*November 5, 2015*

**Calculus**

in inches, v = (36-2x)(48-2x)x dv/dx = 12(x^2-28x+144) dv/dx=0 when x = 6.789" ≈ 0.5657 ft For (b), just plug in k, and you have v = x(k-2x)^2 dv/dx = 12x^2 - 8kx + k^2 dv/dx=0 when x = k(2±√3)/6 The max will occur at x = k(2-√3)/6, since (2+&#...
*November 5, 2015*

**quantitative reasoning**

needs x where x(1+.0725/4)^(4*5) = 16000
*November 5, 2015*

**Calculus 1-Optimization**

the volume v = x^2 z = 4000, so z = 4000/x^2 the area is a = x^2 + 4xz = x^2 + 16000/x da/dx = 2x - 16000/x^2 da/dx=0 when 2x - 16000/x^2 = 0 x^3 = 8000 x = 20 So the box is 20x20x10 cm
*November 5, 2015*

**Calculus 1 optimization**

That is correct. Good job. As usual in problems like this, maximum area or minimum fencing is achieved when the total fence is divided equally between lengths and widths.
*November 5, 2015*

**Mathematics**

The number n = 552k+53 = (23*24)k + 23*2 + 7 n/23 = 24k+2 R 7 Hmmm.
*November 5, 2015*

**programming ( qbasic)**

google is your friend. Use it. http://www.schoolfreeware.com/QBasic_Tutorial_38_-_Making_A_Function_-_QB64.html
*November 5, 2015*

**probability**

(a) p = 8/15 * 7/14 * 6/13 This is like choosing items without replacement, right?
*November 5, 2015*

**Calculus**

You are correct. It's just that at x=11, the linear approximation isn't very good when you get var away from 11. You were not asked to get an approximation which agrees with the true value to 3 places, just to get a value out that far. Extra credit: how far away from ...
*November 4, 2015*

**Pre algebra**

The first 7 are spot on. 8-10 you don't show.
*November 4, 2015*

**geometry**

the angles sum to 180. So, if the base is x, each of the other two sides is 2x-3. SO, now you have to find x when x + 2x-3 + 2x-3 = 44 Having found x, you can now determine the lengths of the sides.
*November 4, 2015*

**math**

well, just find the two derivatives: dR/dq = 600-2q dC/dq = 50 so, you want 600-2q = 50 q = 275 Note that this is the value of q at the vertex of the parabola, q = -b/2a = -550/-2. Note the typo in your final function. Should be +550q, not -550q
*November 4, 2015*

**Calculus**

see related questions below
*November 4, 2015*

**Calc**

see related questions below
*November 4, 2015*

**Porportions (Pre-Algerbra)**

clearly not C, since 12/36 = 1/3 12 is about 1/2 of 22, so you' expect the answer to be about half of 55. So, not 45. In fact, doing the actual math 22/55 = 12/H 22H = 12*55 H = 12*55/22 = (2*6*11*5)/(2*11) = 6*5 = 30 6/11 = 84/x 6x = 11*84 x = 154
*November 4, 2015*

**science**

how long does it take to fall 10m? Then, using that value of t, solve for v in vt = 3 since the ball must travel horizontally for 3m in that amount of time.
*November 4, 2015*

**Calculus**

So, why is ∞ not a valid answer? Sometimes that is the limit. lHospital does not guarantee that the limit is defined. It just allows one to make sure that an indeterminate form is avoided. 1/0 is not indeterminate -- it is infinite. The only thing that bothers me is that...
*November 4, 2015*

**Precal**

fractions are just numbers. Why is it any easier to find θ if cosθ = 4/25 ?? You still have to evaluate cos^-1(x) using your calculator. Seems to me that using a decimal is even easier than using fractions. Now, if you have some problem like sin(arccos(.16)) then it ...
*November 4, 2015*

**Math**

Your alternate answer of 112° is not possible, since then 12 would not be the longest side. 68° is the only right choice. rather than saying 2nd function sin try saying sin^-1(.93) or arcsin(.93) calculator buttons vary from model to model. We are talking math here, ...
*November 4, 2015*

**Math**

You have weird notation. Using ^ for exponents, 3^2^3 = 3^8 so I guess (A)
*November 4, 2015*

**Math**

Looks good to me.
*November 4, 2015*

**math**

well, since T5-T1 = 4d, d=3/2 we know a=3, so Sn = n/2 (2*3+(n-1)(3/2)) 3/4 (n^2+3n) = 81 n^2+3n-108 = 0 (n+12)(n-9) = 0 n=9 and the sequence is 3 4.5 6 7.5 9 10.5 12 13.5 15 The sum is 81
*November 4, 2015*

**Calculus**

If the width is w, the length is 250000/w, so the perimeter is p = 2w + 250000/w dp/dw = 2 - 250000/w^2 dp/dw=0 when w = 500/√2 = 353.6 ft So, the least fencing needed is 1414.2 ft
*November 4, 2015*

**Math**

Just collect like terms (same radical): 5√7 + 12√6 - 10√7 - 5√6 Should be easy now, right? Can you simplify 5x+12y-10x-5y? Same idea here.
*November 4, 2015*

**maths**

If the sun is behind the building, and the building's height is h, then the longest shadow (s) cast by the fence is when the sun is just about to go down behind the building. s/3 = (s+10)/h If the sun is not directly behind the building, then all bets are off.
*November 4, 2015*

**trigonometry - oops**

rats - 1/2 * 250h = 43560 so, h=348.8 Adjust the other calculations accordingly. Good exercise for the student :-)
*November 4, 2015*

**trigonometry**

Draw a diagram. Let the 1-acre parcel be triangle ABC, with B=85° AB = 250 h is the altitude from AB to C x is the length of side BC y is side AC 250h = 43560 h = 174.24 h/x = sin85° x = 174.91 y^2 = 250^2 + x^2 - 500x cos85° y=292.36 x/sinθ = y/sin85° sin...
*November 4, 2015*

**maths**

cost: 20000 revenue: 10000*1.10 + 10000*0.90 = 20000
*November 4, 2015*

**Mathematics**

The numbers are x, x+1, x+2. So, x + 3(x+1) = 5(x+2)-18
*November 4, 2015*

**Trigonometry**

using the law of sines, the pole's height h can be found after determining all the angles involved. h/sin51° = 47/sin47°
*November 4, 2015*

**trigo**

draw a diagram. extend the chimney downward to where it meets a horizontal line drawn from the point Q 10'8" down the roof. Label T = top of chimney B = bottom of chimney PQ = base of right triangle TPQ. using the law of sines, 6/sin17°40' = 10'8"/...
*November 4, 2015*

**Calculus I**

Why thanks, young fan... But seriously though, i'm just here to help Mjeed in his homework so, yeah have a nice day gentlemen :)
*November 4, 2015*

**Calculus I**

f = x - arctan(x) f' = 1 - 1/(1+x^2) = x^2/(1+x^2) f'=0 only at x=0 f" = 2x/(1+x^2)^2 f"(0) = 0, so x=0 is not a min or a max, but a point of inflection. See the graph at http://www.wolframalpha.com/input/?i=x+-+arctan%28x%29
*November 4, 2015*

**algebra or algebra1**

the slope is 3, so if x changes by 2, y changes by 6.
*November 4, 2015*

**MATH**

yes
*November 4, 2015*

**Math**

3√5 - 2√7 + √45 - √28 since 45=9*5 and 28=4*7, that is = 3√5 - 2√7 + 3√5 - 2√7 = 6√5 - 4√7
*November 4, 2015*

**Math**

2√3 - 2√3 = 0
*November 4, 2015*

**precalculus**

clearly the line must intersect the circle in only one point. x^2 + (2x+b)^2 = 9 5x^2 + 4bx + b^2-9 = 0 The discriminant of this quadratic is (4b)^2 - 4(5)(b^2-9) = -4b^2+180 For the quadratic to have a single solution, the discriminant must be zero, so b^2 = 45 b = ±3...
*November 3, 2015*

**algebra - incomplete**

no idea. when did they start? How fast does the bus go?
*November 3, 2015*

**math**

√2 = 2^(1/2) so you have 3√2^7 = 3*2^(7/2)
*November 3, 2015*

**Calculus**

recall that (1 + 1/x)^x --> e and now let x=8u to get (1+1/u)^8u = [(1+1/u)^u]^8 = e^8
*November 3, 2015*

**Finance**

Abby previously owned 200 shares of a NEWAGE stock at $25 per share. Today the company split the stock in a 3:1 split. Now what is the value of Abby's stock?
*November 3, 2015*

**geometry**

the post's shadow is 6 times as long as the hydrant's. So, the post is 6 times as tall. or, using ratios, x/15 = 1.5/2.5
*November 3, 2015*

**Math**

slope-intercept form is y = mx+b So, you want to get y all alone on the left side: 3x+4y = 12 4y = -3x + 12 y = -3/4 x + 3
*November 3, 2015*

**maths**

9:00 to 3:00 is 6 hours. So, what is 2/3 of 6? Add that to 9:00
*November 3, 2015*

**Math**

Draw a diagram, and you can see that the desired length x is x^2 = 48^2 + 20^2
*November 3, 2015*

**math again helpp**

0.6x + 0.8 = 1.4 subtraction property of equality: subtract 0.8 from both sides 0.6x = 0.6 now use the division property, and divide both sides by 0.6: x = 1
*November 3, 2015*

**math**

draw a picture, as always. You will have a right triangle representing the speeds involved. The hypotenuse will be the boat's actual speed (8) and direction (θ). The vertical leg will be 2.5 So, the angle θ, measured upriver from the east-to-west direction, will ...
*November 3, 2015*

**Geometry**

× is the multiplication operator x is a variable name Since BD bisects ABC, the angles ABD and DBC are equal. So, 5x = 3x+10 Now you can easily find x and ABC.
*November 3, 2015*

**Math**

looks good to me
*November 3, 2015*

**math**

looks good to me, though the question is rather poorly worded.
*November 3, 2015*

**math**

2w + 2(w+3) = 24 Now find w, and thus w+3
*November 3, 2015*

**mathematics**

T6=T4+2d, so 2d=12 Now you can find T1=a, and then T7
*November 3, 2015*

**Calculus**

y = (x^3)(e^−x) y' = -x^2 e^-x (x-3) so, y'(1) = 2/e Now you have a point and a slope, so the line is y - 1/e = 2/e (x-1) see http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x^3%29%28e^%E2%88%92x%29%2C+y%3D2%2Fe+%28x-1%29%2B1%2Fe+for+0.5+%3C%3Dx+%3C%3D+1.5
*November 3, 2015*

**Physics**

well v increased by 2 m/s every second, so it wound up at 50+2*6 = 62 m/s since the position is s(t) = 50t + t^2 just figure s(6)
*November 3, 2015*

**Math**

see related questions below
*November 3, 2015*

**math**

Recall that the average score is the sum of the scores, divided by the number of tests. So, you need to have 80 <= (78+93+x)/3 <= 90 240 <= 171+x <= 270 Now can you determine the needed range of scores?
*November 3, 2015*

**math**

oh yeah - I see an x hiding in there. -(((P/L)*(l-x)^2)/2) / (E*I) = -(PE/2IL)(1-x)^2 so, call all that junk k. Then you have d^2/dx^2 = k(1-x)^2 dv/dx = -k/3 (1-x)^3 + c1 v = k/12 (1-x)^4 + c1*x + c2 Not sure what else you want to do with this.
*November 3, 2015*

**math**

looks like it already is, except for the q part. I = dq/dt
*November 3, 2015*

**Algebra**

draw the number line. place a small open circle at x=3. Shade everything to the left of the circle. ta-daa!
*November 3, 2015*

**math**

the path's area is the total area minus the flower bed's area: π(65/2 + 5)^2 - π(65/2)^2 ≈ 1100m^2
*November 3, 2015*

**math**

you have a point and a slope, so start with that form: y-5 = (2/3)(x+3) Now just rearrange things to wind up with the slope-intercept form. y-5 = (2/3)x + 2 ...
*November 3, 2015*

**Algebra help fast**

correct
*November 3, 2015*

**maths**

so, the 6th term is midway between the 4th and the 8th: 14 I guess that's not what you wanted to know. Note that T8 = T4 + 4d Now you can find d, then a.
*November 3, 2015*

**English 9**

one place to start would be to read some items about surviving in the wilderness, since you seem to have no experience that relates. Then, after thinking about what you have read, write a narrative about how you would use those skills.
*November 3, 2015*

**Mathematics**

draw a diagram. The distance between centers is the sum of the radii, so if the circles have radii a,b,c we have a+b=11 a+c=15 b+c=19 Now it's easy to figure out a,b,c.
*November 3, 2015*

**Mathematics**

use the distance formula and you have PQ^2 = (-2+3)^2 + (3-7)^2 = 17
*November 3, 2015*

**algebra or algebra1**

plot the points. You have an isosceles triangle with base 6 and height 6. Area = 1/2 bh = 18
*November 3, 2015*

**algebra**

If the rates are a and b, then we are told a+b = 175 15a+5b = 1525 Now just solve for a and b.
*November 3, 2015*

**Calculus**

There is no exponential growth here. The population and volume are not growing by a fixed percentage, but just as a linear amount. the concentration is measured in molecules/μm^3, so at t minutes later, c = (10^6 + 10^4t)/(1000+5t) = 2000(100+t)/(200+t) = 2000(1 - 100/(...
*November 3, 2015*

**algebra**

Close. You do need to specify that c is not negative, so the domain is 0 <= c <= 16, or the interval [0,16]. The range would then be [0,1568]. There is no equation, just a couple of expressions.
*November 3, 2015*

**Algebra**

since the perimeter is the sum of the sides, the missing side x must be found using (4z-2)+(3z+2)+x = 112 Now just solve that for x. Since you have not assigned a value to z, the answer for x will still involve z.
*November 3, 2015*

**math**

no way. Different liquids have different weights. A pound of liquid silver will be much smaller than a pound of water.
*November 3, 2015*

**MATH**

2(x+4)(x-2p) = 2(x^2 + (4-2p)x - 8p) Completing the square, we have 2(x + (2-p))^2 - 8p - (2-p)^2) So, at x = p-2, the value is 2(-8p-(2-p)^2) = -2(p+2)^2 If that is -18, (p+2)^2 = 9 p+2 = ±3 p = -5 or 1 check: 2(x+4)(x+10) = 2(x+7)^2 - 18 2(x+4)(x-2) = 2(x+1)^2 - 18 ...
*November 3, 2015*

**MATH**

Find all values of p such that 2(x+4)(x-2p) has a minimum value of -18. (AoPS, Please show steps)
*November 3, 2015*

**Math**

2*75
*November 2, 2015*

**Math**

so, you have (assuming the real world) d = 16t^2, so t = √(d/16) That's how long it takes to fall a distance d. The sound takes another d/1100 seconds to get back. Thus, you have √d/4 + d/1100 = 4 That's just a quadratic equation, so finding √d is easy
*November 2, 2015*

**math**

and the question is ...?
*November 2, 2015*

**Math**

If the single issue price is x, then 29.99/12 = .70x Now just find x, and you can answer part B.
*November 2, 2015*

**Geometry**

looks good to me.
*November 2, 2015*

**Business Calculus**

yes. you know that 2(2l+w)+6w = 600 4l+8w = 600 l+2w = 150 so, l = 150-2w The area is a = lw = (150-2w)w = 150w - 2w^2 So, find w which makes a the maximum. That will be at the vertex of the parabola.
*November 2, 2015*

**math**

The worst case is when all six chairs are sold at the lowest acceptable price, which is 270/6 = $45 each. So, you want w where 80*0.85^w = 45 w = 3.54 So, the 3rd week is the last possible week to make a profit. 80*.85^3 = $49.13 80*.85^4 = $41.76 - too low
*November 2, 2015*

**9th grade**

Fractions are always messy. Since the LCD of 1/3 and 1/4 is 12, try multiplying everything by 12. Then you have 96 = 12b + 16 Now you can find b, right?
*November 2, 2015*

**Math**

that's the way I'd do it. Of course, the reverse ordering would also be a way to do it. Your way gives you the European size for a given US size.
*November 2, 2015*

**bearing**

As always, draw a diagram. The x- and y- components of the distances are PQ:<5cos60°,-5sin60°> QR:<3cos30°,3sin30°> add them up to get PR. The find its magnitude and direction.
*November 2, 2015*

**Algebra**

Draw a diagram. You can see that x^2 = 80^2 + 30^2 assuming he tried to swim straight across. Although the question is worded poorly. He swam 80m, regardless of how far the river took him.
*November 2, 2015*

**math**

odd definition, but try just substituting in for y: y = x/(2x^2-x+8) (x-1+y)^2/4y =(x-1+(x/(2x^2-x+8)))^2/(4(x/(2x^2-x+8))) = (2x^3-3x^2+10x-8)^2 / 4x(2x^2-x+8) (x-1+y)^2/4y=(1+2y-63y^2)/16y^2 =(1+2(x/(2x^2-x+8))-63(x/(2x^2-x+8))^2)/(16(x/(2x^2-x+8))^2) = (x^2-4)^2 / 4x^2 I ...
*November 2, 2015*

**trig**

x = |v| cos 45° y = |v| sin 45° surely you can sketch the vector.
*November 2, 2015*

**trig**

if the wind's vector is w, then u+w = v <487,-780> + <x,y> = <527,-628> So, now you can figure x and y, then get the speed and direction.
*November 2, 2015*

**Math**

3/4 x = 4 2/3 x = (4 2/3)/(3/4) = 14/3 * 4/3 ...
*November 2, 2015*

**Math**

Nothing to solve. If you mean to simplify it, then 4m(-2mn^2)^3 / 4m^-6n4 = 4m(-8m^3n^6) / 4m^-6n^4 = -32m^4n^6 / 4m^-6n^4 = -8m^10n^2
*November 2, 2015*