Monday
September 1, 2014

Posts by Steve


Total # Posts: 24,522

Math
1. No - surely you have drawn pgrams which are not squares. 2. No - but 3. Yes 4. Yes 5. No - a rhombus has all sides equal Looks like you need to review your definitions some, and play around drawing some figures, with sides of various lengths and slants.
May 28, 2014

Mathamatics
you don't solve an identity -- you prove it. 1-cos^2θ = sinθ cosθ/cotθ since cotθ = cosθ/sinθ, now we have sin^2θ = sinθ sinθ QED (1-cos^2θ)(1-tan^2θ) = (sin^2θ-2sin^4θ/(1-sin^2θ) sin^2θ(1-tan^...
May 28, 2014

Harris
that would be 2(3x + 5 + x +7) = 8x+24
May 28, 2014

Math
these are all standard angles you should know by heart. It will save you a lot of trouble working them out all the time. -1 - 1 + 1 - 2 + 2 + 1 = 0 It also involves knowing the signs of the trig functions in the various quadrants, and how to figure the reference angle. Also, ...
May 28, 2014

Math
5{3a-2b(3a+6b)+6a} 15a-10b(3a+6b)+30a 15a-30ab-60b^2+30a 45a-30ab-60b^2
May 28, 2014

Geometry
I'm sure the question is correct. You probably want to know whether your answer is correct. I believe you are right in your choice.
May 28, 2014

Math
If you want to use vector notation, then if the vector to A is a, and to B is b, etc. Then AB = b-a BC = c-b CA = a-c AB+BC+CA = b-a+c-b+a-c = 0 AB is b-a because if there is a vector u such that a+u=b, then u=b-a.
May 28, 2014

Math
Looks to me like AB + BC + CA = 0 Similarly for the other one. Getting back to A, the sum is just 0 again. The vectors form a closed polygon, so the net result is zero.
May 28, 2014

math
54-24 = ?
May 28, 2014

math
30 <= 18+0.3(x-50) <= 45 12 <= .3(x-50) <= 27 40 <= x-50 <= 90 90 <= x <= 140
May 28, 2014

algebra
what's with the braces? Just use vertical bars: |8| = 8 |-9| = 9 and so on |x| = -x if x is negative otherwise, |x| = x
May 28, 2014

geometry
the scale Q'/Q = 2/3 2/3 * 15 = 10, the new length
May 28, 2014

Geometry
consecutive angles are supplementary opposite angles are equal So, what do you have here?
May 28, 2014

geometry
my first guess is you are allergic to that fruit.
May 28, 2014

geometry
2 - 3 = -1 Oops. If by difference, you mean the larger minus the smaller, the conclusion is true. Technically, though, the difference is    minuend - subtrahend ----------------- difference So it matters which is which.
May 28, 2014

math
MS Sue is trying to get you to figure out 8*(6ft+4in) = 8*6ft + 8*4in = 8*6*12in + 4in = ? in
May 28, 2014

7th grade math
(2/5 x) > 7 x > 7 * 5/2 x > 35/2 So, place a dot at 35/2 and shade to the right 2(x+7)-4 > 5(x-3) 2x+14-4 > 5x-15 2x+10 > 5x-15 25 > 3x 25/3 > x So, place an open circle at 25/3 and shade to the left
May 27, 2014

Calculus
This is indeed the MVT. The secant line through (1,1/3) and (4,2/3) has slope 1/9. The MVT says that in the interval (1,4), there is some c where f'(c) = 1/9. f'(x) = 2/(x+2)^2 So, we want c such that 2/(c+2)^2 = 1/9 (c+2)^2 = 18 c+2 = ±3√2 c = -2±3...
May 27, 2014

Calculus
use integration by parts u = x, du = dx dv = cos 15x dx, v = 1/15 sin 15x Now we have ∫x cos15x dx = 1/15 x sin15x - ∫1/15 sin15x dx And that's clear sailing. . . right?
May 27, 2014

algebra/geometry
no idea. However, what you have factors into (x-7)(x+4) = 0 Then the roots are clearly 7 and -4
May 27, 2014

IB Maths SL
The slope of the tangent to f(x) is f'(x) = (g'h-gh')/h^2 So, the normal has slope h^2/(gh'-g'h) At x=2, that is 6^2/(18*2-5*6) = 6 f(2) = g(2)/h(2) = 18/6 = 3 So, now you have a point and a slope, so the normal line at x=2 is y-3 = 6(x-2)
May 27, 2014

Cosine Law NEED HELP QUCIK
at 9:30 the hour hand has gone clockwise 9.5/12 * 360 = 285° from the top The minute hand is at 180° So, the angle between them is 105°. You want d where d^2 = 12^2 + 10^2 - 2*12*10*cos 105° d^2 = 306.1 d = 17.5 Just a straightforward application of the law of ...
May 27, 2014

Geometry
Just looking at the figure, angles AHM and TMH are congruent, so 3x+5 = 7x-27 x = 8 So, m<AHM = 29 If you answered #15, #17 should have been obvious.
May 27, 2014

Calculus
v = ∫[1,t] πr^2 dx where r=y=1/x. So, v = π∫[1,t] 1/x^2 dx = π(-1/x) [1,t] = π(1 - 1/t) as t→∞, v→π
May 27, 2014

Algebra 1--Please, help me! (Steve)
by now these should be getting easier. When multiplying/dividing powers, add/subtract the exponents. 3r^2t/6st^3 x 2r^2s^3t^2/8r^4s^2 = (3*2)/(6*8) r^(2+2-4) s^(-1+3-2) t^(-3+1+2) = 1/8 You gotta start using parentheses... x^2 + x/x^2 + 3x + 2 + 3/x + 2 = (x^2+x)/(x^2+3x+2) + ...
May 27, 2014

physics-force and pressure
well, geez - pressure is force/area, so that would be 300N/700cm^2 = 3/7 N/cm^2 Chances are you should convert that to N/m^2 so your answer could just be in Pa.
May 27, 2014

Algebra 1
you are correct
May 27, 2014

Algebra 1
You got (a) correct. So, for (b), just plug in x=5 and evaluate the fraction.
May 27, 2014

Algebra 1
yes, #1 = 2a^2b/c^2 #2 = 1/(3x-15)
May 27, 2014

Algebra 1
Hmmm. How about 2a^2b / c^2
May 27, 2014

Algebra 1
when dividing by a fraction, just invert and multiply. So, #1 3a^4b/2a^2c^3 * 8c^4/12a^2c = 3*8/12 a^4/a^2 b c/c^3 ... #2 x^2+4x-5 = (x+5)(x-1) x^2-25 = (x+5)(x-5) So, you just have (x+5)(x-1) / 3(x-1) * 1 / (x+5)(x-5) = (x+5)(x-1) / 3(x+5)(x-1)(x-5) = ...
May 27, 2014

Algebra 1--Please, help me!
#1 also t=0, since t^2-t = t(t-1) The original expression must be examined for excluded values. (t-1)/(t^2-t) = 1/t, so t≠0. But dividing top and bottom by t-1 to get there means that t≠1, because you cannot divide by zero. #2 huh? There is no x-2 in the ...
May 27, 2014

math
x(x-2) + y(x-2) (x+y)(x-2)
May 27, 2014

trig - incomplete
as usual, draw a diagram and recall your basic trig definitions. If the ledge is at height a, and at distance x from the tree (with height h), then we have (h-a)/x = tan25° a/x = tan10° Now eliminate a to get h-x tan25° = x tan10° h = x(tan25°+tan10°) ...
May 27, 2014

algebra
take a look at http://www.wolframalpha.com/input/?i=solve+z^5+%3D+i Note that the angles given are pi/2 + k*2pi/5
May 27, 2014

Math
if y = u^v, where u and v are functions of x, y' = v u^(v-1) u' + ln(u) u^v v' If you look carefully, you will see that y=u^n and y=a^v are just special cases, where u' or v' = 0. Anyway, just plug in u = x^2 v = sinx and you get (2x sinx)*(x^2)(sinx-1) + ...
May 27, 2014

maths - still bogus
1983 is not a leap year. After you fix that, just divide the number of years involved by 4, but watch for remainders. Then post your work, so we can see how you solved it...
May 27, 2014

misc stuff
If you're planning to attend a school where English is the language of choice, I suggest you improve your language and writing skills first.
May 27, 2014

maths
First, there was no 29th of Feb in 1983; that was not a leap year Second, you give no date to end the calculation.
May 27, 2014

maths
98-14 (also, the verb is "lose," not "loose." Unless she deliberately threw them away.)
May 27, 2014

math
I assume you know how to find the volumes of such solids. Just subtract the volume of the sphere from that of the cylinder. The leftover space holds the water: π(2x)^2*(2x) - 4/3 πx^3
May 27, 2014

algebra 2 and Trigeonomerty
(a) You have to multiply for the three draws, and allow for the changing population of blues and the total: 12/30 * 11/29 * 10/28 (b) That would be 18/30 * 17/29
May 27, 2014

math - incomplete
no table provided
May 27, 2014

algebra
just multiply each event by its probability. The sum is the expected value of income. Then subtract the costs involved: (395000)(1/40)+(125000)(1/20)-25000 Technically, we need all the probabilities to add to 1, so we should include the term for a dry well: (0)(37/40) but that...
May 27, 2014

Algebra 1--How Am I Supposed to Solve This?!
just divide the two, as you would do with any ratio: (πrl + πr^2) / (2πrh + 2πr^2) πr(l+r) / 2πr(h+r) = (l+r) / 2(h+r)
May 27, 2014

Algebra 1--how am I suppose to graph this?!
plot it the way you plot any function! Pick some values of x and calculate y. Then plot the point at (x,y). The curve will be smooth, but the only poi9nts that make sense in the real world are where x is a divisor of 75. Your graph should look like this: http://www....
May 27, 2014

math
mixed numbers are useless for calculation. Convert them to fractions and things get easy. 21/10 * 15/7 = ?
May 26, 2014

Precal, please help asap!
You need to clarify the diagram. Label the airplane A, the tower T and the post P. The plane is at altitude h, with AP=t and AT=p. Point Q is directly below the plane. The distance PQ=q and thus TQ = 2-q. If the plane is between the tower and the post, then h/q = tanα h/(...
May 26, 2014

Algebra, Need help with last part.Thank you
you are correct on the first two. The last should also be no sweat. There is only 1 2-hearts in the deck of 52 There are 4 twos in the deck. So, how many hearts are there? Also, just as advice, usually you will need to reduce your fractions for your final answers. 4/52 = 1/13 ...
May 26, 2014

algebra 1
since xy = k is constant, k = (1/2)(-10)
May 26, 2014

maths
If you mean x = √(y+3) then x^2 = y+3 y = x^2-3 If you mean x = √y + 3 then x-3 = √y y = (x-3)^2 If you mean √x = y+3 then y = √x - 3 It sure helps if you proofread your posts to make it quite clear what's going on. Use parentheses if there is...
May 26, 2014

math
you know the volume is x*y*z = 12x So, y*z = 12 y cannot be less than 1, so z cannot be more than 12
May 26, 2014

math
You know that if the remainder is zero, x is a multiple of 3. But, there is a remainder of z, so add that in. Only one of the choices is a multiple of 3, with an extra z
May 26, 2014

algebra/Did I do this right
correct.
May 26, 2014

Math
correct
May 26, 2014

math
correct
May 26, 2014

algebra
(x^5+x^2-3)(x^3-1) = x^8-3x^3-x^2+3 Now subtract -3x^3+x^2-4x and you get x^8-2x^2+4x+3 Now subtract 2x^2-4x and you get x^8+3 So, the whole thing is just (x^5+x^2-3)(x^3-1)-(-3x^3+x^2-4x)-(2x^2-4x)
May 26, 2014

Math
x is the total amount added. Since you get x=10, that means that 5m was added on each side. I'm interested in how you made this calculation: (10+x)(20+x)=600 200+10x+20x+4x^2=600 Where did the 4x^2 come from? looks like answer analysis to me. In addition, you did not solve...
May 26, 2014

Math
what is h when d=0? As you know the vertex of a parabola is where d = -b/2a = -4.4/-.88 So, figure h for that value of d. What is h when d=14? Or, how far away is the ball when h=0 (it hits the floor)?
May 26, 2014

Precal
(a) x(t) = 0 (since it went straight up) y(t) = 75 + 76t - 16t^2 (b) Just plug in t=2
May 26, 2014

Precal
(a) If you got the equations, answering the last 4 questions should be no sweat. (b) the ball is in the air while y(t)>0.That is, solve for t when y=0. (c) Knowing how long it took to hit, plug that into x(t). (d) y(t) is just a parabola. As usual, the vertex (where the ...
May 26, 2014

Precal
boarding at t=0, the height y at time t minutes is y = -60cos(pi/6 t) + 6 Now just start plugging in your numbers.
May 26, 2014

Precal
since the horizontal speed does not change, we have the usual x(t) = 150 cos 30° t y(t) = 150 sin 30° t - 16 t^2 The rest is downhill from here
May 26, 2014

Math, grade 10
except, don't make my typo. Better say x+y = 17
May 26, 2014

Math, grade 10
follow the same logic I used in your previous post: x+y = 18 x^2+y^2 = 185 go for it
May 26, 2014

Math, grade 10
x+y = 18 x^2 + 6y = 163 now substitute for y: x^2 + 6(18-x) = 163 x^2 - 6x + 108 = 163 x^2 - 6x - 55 = 0 (x-11)(x+5) = 0 x=11 and y=7
May 26, 2014

math
slope = rise/run, so 1.9 = 4/run run = 4/1.9
May 26, 2014

math
slope = rise/run = 5/15
May 26, 2014

math
No, x=5 is not correct. The solution set to an inequality is an interval, not just a single point. Your logic should have been: -5(x-7) < 15 -5x+35 < 15 -5x < -20 x > 4 You could have checked your answer to see that x=5 works, but it is not the only number which ...
May 26, 2014

Algebra
Not sure what a 2x3 matrix has to do with coordinates. Can you splain a bit, please?
May 26, 2014

Math
7s/1320ft * 1313ft = 6.96 s assuming instant change in velocity. Assuming a constant acceleration, 1/2 a*49 = 1320, so a = 53.877 ft/s^2 Now, to get 1313 ft using the same acceleration, we have 53.877/2 t^2 = 1313 t = 6.98 s
May 26, 2014

algebra
3 21 (3,21) -3 0 (-3,0) I think. Hard to say just what you are after.
May 26, 2014

math
h/100 = tan 24
May 26, 2014

Algebra 1--Please, help me!
#1 we have n calculators that cost c each. Since nc = k is constant, 24*60 = 80n #2 Actually, the cost must be a positive integer divisor of 75, since the number of packages must be an integer. #3 well, you have the formulas, and you want the ratio scone/scyl = (πrl + &#...
May 26, 2014

geometry math help
(a) two layers means 24 cans per layer. The cans are 10 cm across, so the 46x60 dimensions of the box allow for that many cans. The height of the box will accommodate the two layers. (b) You know the way to compute the volume of the box. Now, just subtract 48 times the volume ...
May 26, 2014

math
no idea. what does the pattern represent? How many more terms are to be considered? Ans why the ?? marks around the 20?
May 26, 2014

trigonometry
the angle is x, where sin x = 50/120
May 26, 2014

business math
just askin', but did you complete the table?
May 25, 2014

business math
just solve 2.903 t - 1.98 = 18 when you get t, add that to 2000 such bogus wordage. 4 <= t <= 9 is the condition.
May 25, 2014

Cosine Law
At 12:00 the hands are together After h hours, the hour hand has gone h/12 * 360 degrees After m minutes, minute hand has gone m/60 * 360 degrees 9:30 = 9.5 hours :30 = 30 minutes So, the hour hand has gone 9.5/12*360 = 285° and the minute hand is at 180° So, the angle...
May 25, 2014

Cosine Law
sinB/b = sinC/c that will get you B Then A+B+C=180 gets you A a^2 = b^2+c^2 - 2bc cosA gets you A. Then, b/sinB = c/sinC = a/sinA gets you A and B
May 25, 2014

3D Shapes & Scale
a 2m cube occupies 8 times the volume of a 1m cube. I assume the trailer is enclosed, so the volume makes a difference. So, what's 128/8?
May 25, 2014

trig
h/65 = sin 32
May 25, 2014

Earth Science Regents!!!
It is clearly #2. Since both observations were made at the same time, the orbit traveled by the planet can have nothing to do with it. Only separate observations at different times could indicate how the earth has moved. If the earth were flat, the star is so distant that all ...
May 25, 2014

math
well, that's 2(1/2) + 2/5 = 1 + 2/5 = 7/5
May 25, 2014

more logarithms help!
just plug in your values: 24000(1-0.15)^n = 2500 Now solve for n. First step is .85^n = 2500/24000
May 25, 2014

logarithm math help
log(x^n) = n*log(x) log(u/v0 = log(u) - log(v) Now go for it.
May 25, 2014

Math binomial formula and sequence
Almost: C(8,4)(2x)^4(-3)^4 90720x^4 ar^3 = 16 ar^6 = -128 r^3 = -8 r = -2 so, a = -2 a_n = -2*(-2)^(n-1) = -(-2)^n S15 = 15/2 (2*8+14*4) = 540
May 25, 2014

Math - Ratio
(a) 2.5km/10^4 = 2.5*10^5cm/10^4 = 25 cm .5cm:2.5km = .5:2.5*10^5 = 1:5*10^5 = 1:500,000 Just as a check, the 1:10,000 scale used 25cm, and .5cm is 1/50 of that, so the scale should be 1:500,000
May 25, 2014

Calculus
If you are assuming a parabola, then a little work will show that the equation is y = ax^2+bx+c 2500a-50b+c = 50 2500a+50b+c = 70 a(-b/2a)^2 + b(-b/2a) + c = 47 y = 1/200 x^2 - 1/5 x + 47 and the vertex is at (20,47) Now, the length of cable is thus s = ∫[-50,50] √...
May 25, 2014

Math - Logarithms
(a) x^5 = 100, so x = 100^(1/5) (b) I assume you mean 3^(x+5) = 81 we know that 3^4 = 81, so x+5 = 4 (c) log (4x+2)/2 = log 6x the logs are equal, so we just have (4x+2)/2 = 6 I guess you can probably handle that one, eh?
May 25, 2014

Geometry
review the description of a circle with center at (h,k) and radius r: (x-h)^2 + (y-k)^2 = r^2
May 25, 2014

Precalculus
4x^2-y^2-24x-10y+11=0 4(x^2-6x) - (y^2+10y) = -11 4(x^2-6x+9) - (y^2+10y+25) = -11 + 4(9) + 25 4(x-3)^2 - (y+5)^2 = 50 Better check to see what you lost while completing those squares.
May 24, 2014

Algebra 2
a = -2 r = -2 so, T20 = -2*(-2)^19
May 24, 2014

Math
I also get 1/2 * 1/2 = 1/4 since the two events are independent.
May 24, 2014

Algebra 2
If the box originally had side s, then the new box has side s-6, since 3" was cut off each corner. The height of the box is just the 3" that was cut off. So, s(s-6)^2 = 675 Now, just by inspection, 675 = 3*225 = 3*15^2 So, the box now has sides of 15, and height=3 ...
May 24, 2014

Math - eh?
since T3 = T1 * r^2, r = 3 No idea what "124 of the fifth" means
May 24, 2014

Math - Linear Equations
T = k√L so, T/√L is constant. (a) .63/√9 = T/√25 (b) .63/√9 = 1.5/√L
May 24, 2014

Algebra
since time = distance/speed, d/(12-5) + d/(12+5) = 3 now just solve for d. Assuming the round trip takes 3 hours.
May 24, 2014

Algebra
Assuming they both work the same time, Alma works 4/3 as fast as Kevin, so she does 4/7 of the work, or 57% Or, you can find how long it takes to do the whole job together: 1/x = 1/4 + 1/3 x = 12/7 So, in 12/7 hours, Alma does 1/3 * 12/7 = 4/7 of the work.
May 24, 2014

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