Thursday
November 26, 2015

# Posts by Steve

Total # Posts: 35,801

Math
If the tire has width w, then the inner radius is 2w, and the entire area has radius 3w. So, π(9w^2-4w^2)/π(9w^2) = 5/9 = .5555 or 56%
October 10, 2015

MATH
Not quite... The cost C is C = 8(2W+L)+15L since LW=400, = 8(2(400/L)+L) + 15L = 8(800/L + L) + 15L = 6400/L + 23L
October 10, 2015

Calculus
Looks like A&B to me. I mean, have you tried actually drawing a vector xi+yj, with its tail at (x,y)?
October 10, 2015

Calculus
using implicit differentiation, 2(x^2+y^2)(2x+2yy') = 16y' x(x^2+y^2) + y(x^2+y^2)y' - 4y' = 0 y' = -x(x^2+y^2)/(x^2y + y^3 - 4) So, the slope is vertical where x^2y-y^3 -4 = 0 y(x^2-y^2) = 4 Not easy to solve in general, but a little playing around gives x...
October 10, 2015

Physics i need hlp i have exams next weeks that is why i post the question that which i cannot do
c = av + b/v cv = av^2 + b av^2 - cv + b = 0 now just use the quadratic formula to find v. There will only be a maximum cost if a<0, since then the parabola will open downward.
October 10, 2015

Geometery i need help
well, let's assume the octagon is just a regular polygon. It consists of eight isosceles triangles, each with two sides of 12, and a vertex angle of θ=45°. So, if the base of each triangle (one side of the octagon) is s, (s/2) = 12 sin(θ/2) Now just plug in ...
October 10, 2015

Geometery i need help
clearly the band forms an octagon (with rounded corners) with a diameter of 3 oranges, or 24mm. Now play around a bit with the dimensions of an octagon.
October 10, 2015

trig
so, cotθ = (√7)/2, meaning x = √7 y = 2 since cotθ = x/y
October 10, 2015

trig
recall that sinθ = y/r cosθ = x/r tanθ = y/x r^2 = x^2+y^2 So, in QIII, where x and y are both negative, tanθ = √5 = √5/1, so y = -√5 x = -1 r = √6 cotθ = x/y = 1/√5 secθ = r/x = -√6 For #1, do you mean (1/2) &#...
October 10, 2015

maths
clearly, the bonuses are (2/3 * 105), 105, (4/3 * 105) So, the total is 3*105 = 315
October 10, 2015

Calculus
You are correct. I fear that the answer choices relate to a different problem, since with a simple power, no logs will arise.
October 10, 2015

How many of these number maths??
(a) 7!/(3!2!) = 420 (b) If 3,4 are used, that leaves 5!/3! = 20 (c) divisible by 5 means that 3,4,5 are used, leaving 4!/3! = 6 (2) divisible by 2 means that 2,3,4 are used, leaving 4!/2! = 12
October 10, 2015

precalculus
better review your trig functions sinθ = x/r cosθ = y/r r^2 = x^2+y^2 You have a 3-4-5 triangle. Draw the dang thing! x = -3, so cosθ = -3/5
October 10, 2015

precalculus
in QII, x is negative, so cosθ = -3/5 The rest is easy, right?
October 10, 2015

maths
as usual, draw a diagram. The tower's height is 20 + 20 cot30° * tan60° = 20(1+tan^2 60°) = 20 sec^2 60° = 20 * 4 = 80
October 10, 2015

geometry
Just knowing the four sides of a quadrilateral does not help find the area. As you know, if you build such a figure, you can squash it around, because the joints are not rigid. Unless you know some of the angles or something, you cannot determine the area.
October 10, 2015

MATH!
D is the best bet. It appears not to repeat.
October 10, 2015

Calculus i need help
x^2 y + sin(xy) + y^4 x^2 + 3xy = 5 Just use the product rule and the chain rule: d/dx(x^2 y) = 2xy + x^2 y' d/dx(sin(xy)) = cos(xy) (y + xy') d/dx(x^2 y^4) = 2xy^4 + 4x^2y^3 y' d/dx(3xy) = 3y + 3xy') So, add them all up, collect the y' stuff, and it's ...
October 10, 2015

Maths
well, how long does it take to go 200 miles, if you travel 100 miles each hour?
October 10, 2015

Pre-Calculus
you must have some ideas about some of these topics. At the very least, use a graphing utility to see what the graph looks like, and most of the answers should become clear immediately.
October 10, 2015

Grrr.
Oops. I thought we were doing serious math homework here. My bad :-( Like 16/64 = 1/4 because you can just cancel the 6's.
October 10, 2015

Prove also need help
this is nonsense. Of course 13/12 is not 2 You want to fix up your question a bit?
October 10, 2015

Trigonometry prove need help
tan 45-b = (tan45-tanb)/(1+tan45 tanb) = (1-tanb)/(1+tanb) square that, and you have (1-2tanb+tan^2b)/(1+2tanb+tan^2b) = (sec^2b-2tanb)/(sec^2b+2tanb) = (1/cos^2b - 2sinb/cosb)(1/cos^2b + 2sinb/cosb) = (1-2sinb cosb)/(1+2sinb cosb) = (1-sin2b)/(1+sin2b) I think you have a typo...
October 10, 2015

pre calc
Tough to describe the function, when it not given...
October 10, 2015

pre calc
first, put the words into algebra. If there is x at 5.5% and y at 11%, you have: x+y <= 130000 x >= 40000 y <= 60000 maximize p = .055x + .11y Now just use your favorite linear programming tool.
October 10, 2015

pre calc
You've posted a bunch of these. Some have been done for you. No ideas yet?
October 10, 2015

calculus
that is the definition of an inverse function. For any f(x), f(f^-1(x)) = x f^-1(f(x)) = x if f is single-valued, which sinh(x) is. If you take sinh^-1 of both sides, you have sinh^-1(sinh(sinh^-1(x))) = sinh^-1(x) but that only helps if you already know that sinh^-1(sinh(u...
October 10, 2015

Math
for the short diagonal x, x^2 = 5^2+10^2-2*5*10 cos50° for the long diagonal y, y^2 = 5^2+10^2-2*5*10 cos130°
October 10, 2015

calculus
y' = (x^2-10x+16)/(x-5)^2 y" = 18/(x-5)^3 So, max/min if y'=0 max if y" < 0, min if y" > 0 The rest is just algebra.
October 10, 2015

calculus
Assuming the two walls meet at a right angle, x+y = 30 a = xy = x(30-x) this is just a parabola, with vertex at x=15. As usual, the area is a square. You can take the derivative if you want, but no calculus needed here...
October 9, 2015

math
just multiply both elements by the same nonzero value. Think of fractions.
October 9, 2015

Maths
why take the derivative to find t? It won't help here. Just expand and solve: 0.2t^3 - 2.84t^2 + 9.282t = 2.4 + 0.75t 0.2t^3 - 2.84t^2 + 8.532t - 2.4 = 0 Now you can fall back on graphical methods, or Newton's method or something you have in your bag of tricks.
October 9, 2015

math
sin = y/r cos = x/r tan = y/x r is always positive In QIV, x is positive and y is negative In QII, x is negative and y is positive So, in QII, cos,tan,cot,sec are negative in QIV, sin,tan,cot,csc are negative only tan,cot are negative in both.
October 9, 2015

pre calc
S1: 2 is a factor of 1^2+7*1 and so on. Clearly, since if n is odd, n^2 and 7n are both odd, so their sum is even if n is even. n^2 and 7n are both even, so their sum is even. Or, if n is odd (2k+1)^2+7(2k+1) = 4k^2+4k+1+14k+7 = 2(2k^2+9k+4) and similarly for even n=2k
October 9, 2015

math
4x+5y=10 2x+3y=8 x = -5 y = 6 Now just find 3x+4y
October 9, 2015

Pre-calculus
9^(2x-6)=6^(8x-5) (2x-6) log9 = (8x-5)log6 (2log9)x - 6log9 = (8log6)x - 5log6 x = (6log9 - 5log6)/(2log9 - 8log6) you can massage that a few ways, but that's the idea
October 9, 2015

Math
see http://www.jiskha.com/display.cgi?id=1444227515
October 9, 2015

Trig
after t seconds, Michael has gone 2t ft and Alyssa has gone 3t feet. So, the distance z between them using the law of cosines, is found using z^2 = (2t)^2 + (3t)^2 - 2(2t)(3t)cos60° so, plug in your time (in seconds!) and find z.
October 9, 2015

precalc
looks like our calculator agree!
October 9, 2015

precalc
Draw triangle LBM where the ball is at B; angle B is 158°. Using the law of sines, if the ball's distance from M is x, then x/sin9° = 23/sin158°
October 9, 2015

Algebra
(x+3)/(x+8)-(x-8)/(x-3) =[(x+3)(x-3) - (x-8)(x+8)]/[(x+8)(x-3)] =[(x^2-9)-(x^2-64)]/[(x+8)(x-3)] = (-9+64)/[(x+8)(x-3)] = 55/[(x+8)(x-3)] You probably forgot to use parentheses to keep track of quantities. But aside from that, what did you do with your denominator?
October 9, 2015

geometry
since DB bisects the angle ABC, the two smaller angles are equal. So, 12x+24 = 20x+16 So, find x, and you can figure the angles.
October 9, 2015

4718(1+.05/4)^(4n) = 5323 (1.0125)^(4n) = 1.1282 4n = log(1.1282)/log(1.0125) n = 2.4 or, roughly 2 1/2 years
October 9, 2015

Math
-2+5x-7=3x-9+2x collect constants and x's on each side: 5x-9 = 5x-9 Since both sides are the same, it will be true for any value of x at all!
October 9, 2015

Calculus
using shells, v = ∫[0,1] 2πrh dy where r = 1-y and h = √y - y^2 v = 2π∫[0,1] (1-y)(√y - y^2) dy = 11π/30 using washers, v = ∫[0,1] π(R^2-r^2) dx where R = 1-x^2 and r = 1-√x v = π∫[0,1] ((1-x^2)^2-(1-√x)^...
October 9, 2015

Maths
|a|-3/4=-5/8 |a| = -5/8 + 3/4 = 1/8 clearly, a = 1/8 or -1/8
October 9, 2015

math
As always, draw a diagram. The parabola has vertex at (1,0) and opens to the right. The line x=2 intersects the parabola at (2,1) and (2,-1). So, you will be revolving the sort-of-semicircular chink around the line y=-2, which is below the curve. So, as you say, v = ∫2&#...
October 9, 2015

Maths
|a|-3/4=-5/8 |a| = -5/8 + 3/4 = 1/8 clearly, a = 1/8 or -1/8
October 9, 2015

Maths
L1 has intercepts at A:(-6,0) and B:(0,4) L2 has gradient -3/2 and passes through (0,4), so L2 is y-4 = (-3/2)(x-0) 3x+2y-8 = 0 L2 passes through B:(0,4) and C:(8/3,0) So, if you plot the points, you can see that you have a triangle with base along the x-axis, and its third ...
October 9, 2015

Maths
why plug in 3 for x? Why change the polynomial? x^2 + 2kx - 3k = 0 the discriminant is (2k)^2 - 4(1)(-3k) = 4k^2 + 12k For two equal roots, the discriminant must be zero. 4k^2+12k = 4k(k+3) = 0 k = 0 or -3 k=0: clearly x^2=0 has two equal roots k = -3: x^2-6x+9 = (x-3)^2 has ...
October 9, 2015

Algebra
(8+12)/(4*5)=1
October 9, 2015

Algebra
24000(1+.0685/12)^(12*18) = 82,067.98
October 9, 2015

math
It's a little easier to check if you mark your answers with the questions. Saves a lot of scrolling back and forth. However, the wily teacher opens a 2nd window to avoid that, too! #1: 20/2 – 32 – (-2)2 = 10 - 32 - (-4) = 10 - 32 + 4 = -22+4 = -18 Since that'...
October 9, 2015

Algebra
in 2 hours, Molly was 54 miles ahead. Mark was going 18 mi/hr faster, so it took him 54/18 = 3 hours to catch up. But 3 is not the answer to the question ...
October 9, 2015

Physics/trig
as you recall, the equation of motion is y = tanθ x - g/(2(v cosθ)^2) x^2 So, plugging in your numbers, y = 0.664x - 0.00806x^2 That's a parabola with vertex at x=41.2
October 9, 2015

pre calculus
This is just a standard linear programming problem. For x breakfast packages and y afternoon packages, you want to maximize p=1.50x+2.00y subject to x/3 + y/2 <= 45 2x/3 + y/2 <= 70 Now just use your favorite linear programming tools.
October 9, 2015

pre calculos
Just substitute k for n and you have Sk. Same for k+1. Sk+1: 1∙2+2∙3+...+k(k+1)+(k+1)(k+2) = [(k+1)(k+2)(k+3)]/3 Can't get much simpler than that.
October 9, 2015

math
shift 3 left scale by 2 vertically reflect in x-axis In this case, the order does not really matter. Try them and see.
October 9, 2015

prasanna high school
been done. http://www.jiskha.com/display.cgi?id=1444216542
October 9, 2015

math - eh?
Not sure what you are saying here. When you say the building and the pole are at equal angles, do you mean the top of the building, or the bottom? The top of the pole, or the bottom?
October 9, 2015

Maths
-(x^2+3x)+7 3 = 2 * 3/2, so -(x^2 + 3x + 9/4) + 7 - 9/4 -(x + 3/2)^2 + 19/4
October 9, 2015

Math
Not to mention gazillions of others, like 99/100 87/150 1234124/2468247 and so on. I didn't see anything about having a single digit in the bottom or top.
October 9, 2015

Math
well, it has to double three time to be full, right?
October 9, 2015

math
well, 20 = 4*5 25 = 5*5 So, what do you think?
October 9, 2015

Math
not quite. 6 pizzas makes 48 slices 3 1/4 pizzas are 26 slices. So now, how many slices were left over? How would you interpret Janet's suggestion?
October 9, 2015

pre calculus
well, just plug in k and k+1 for n. You need to prove that if Sk is true, then Sk+1 is also true. Then, if you can show that S1 is true, then S2,S3,... are all true as well. 1+4+...+(3k-2)+(3(k+1)-2) = Sk+3(k+1)-2 = k(3k-1)/2 + 3(k+1)-2 = (k(3k-1) + 6(k+1)-4)/2 = (3k^2-k+6k+6-...
October 8, 2015

math
how much did each eat? Heck, they told you that. Convert each fraction to decimal to compare. 0.5 is 1/2. 2/3 = 0.666 and so on
October 8, 2015

Math
The one-digit factors of 54 are 1,2,3,6,9 so, which three of those add to 14?
October 8, 2015

Science
All the energy ultimately comes from the sun.
October 8, 2015

trig
nice formulas. Is there a question in there somewhere?
October 8, 2015

math
you want to add some parentheses, or at least some spaces, so we can work with that? As written, using the normal order of operations, you have 4-x^2/x^2+7x+12/2x-4/x+3 4-1+7x+6/x-4/x+3 3+7x+2/x+3 6 + 7x + 2/x I doubt that is what you had in mind.
October 8, 2015

algebra
enter your polynomials at http://calc101.com/webMathematica/long-divide.jsp and see all the details
October 8, 2015

geometry
assuming RST are collinear points, in that order, RS+ST=RT, so hmmm. If R bisects ST, and 5x=7 is a typo for 5x+7, then since SR=RT, 5x+7 = 15x-1 10x = 8 x = 4/5 But you may have had other things in mind. Remember, we cannot see what diagram you have in front of you. Nor can ...
October 8, 2015

Pre Calculus
(a) if you mean (3f+2g)(1) then that is 3f(1)+2g(1) = 3*50 + 2(-5) = 140 (f◦g)(-1) = f(g(-1)) = f(-3) = 10 f(x) = x^2 g(x) = x/(x+4) h(x) = g◦f = f/(f+4) = x^2/(x^2+4)
October 8, 2015

math
see related questions below
October 8, 2015

math
pick any five values for x. Multiply each by 18. Plot those points. Can you see what a useless exercise it is for you to ask us to plot a graph and verify it? Sheesh.
October 8, 2015

Math
one-digit factors of 54 are 1,2,3,6,9
October 8, 2015

Math
Let 2x be the least. Then the next 3 even integers are 2x+2, 2x+4, 2x+6 So, add them up: 2x + 2x+2 + 2x+4 + 2x+6 = 2x Now solve for x, and ... Extra credit: We used 2x to make sure it was an even number. What would have happened if we had just used x instead?
October 8, 2015

Pre-Calc
the same way you would simplify 2/3 + 3/2. Put it all over a common denominator: tan/(1+sec) + (1+sec)/tan = [tan^2 + (1+sec)^2]/(tan(1+sec)) = (tan^2 + 1+2sec+sec^2)/(tan(1+sec)) = (sec^2-1+1+2sec+sec^2)/(tan(1+sec)) = (2sec^2+2sec)/(tan(1+sec)) = 2sec(1+sec)/(tan(1+sec)) = ...
October 8, 2015

Math Help
October 8, 2015

You'll need to use the quadratic formula on that one. Or, completing the square, 8x^2+2x-4 = 0 8(x^2 + x/4) = 4 8(x^2 + x/4 + 1/64) = 4 + 8/64 8(x + 1/8)^2 = 4 + 1/8 (x + 1/8)^2 = 33/64 x + 1/8 = ±√33 / 8 x = -1/8 ±√33/8 x = (-1±√33)/8
October 8, 2015

Algebra i need serious help
Sorry, I only give jocose help. Since 3-x = -(x-3) |x-3| = |3-x| for all values of x
October 8, 2015

Division need help urgently plz
all you want is the last digit. So, look at the powers of 7: 7^1 = 7 7^2 = 49 7^3 ends in 3 7^4 ends in 1 since 3*7=21 913 = 4*228 + 1 So, 7^913 = 7^4^228 * 7 thus, it ends in 7
October 8, 2015

Algebra 2
try using ^ for powers. That is y^3 means y cubed. The formatting has messed things up to where they are incomprehensible.
October 8, 2015

Physics
220 km/hr = 2.20 * 10^5 m/hr So, there must be a headwind of 2.8-2.2 = 0.6 * 10^5 m/hr. That is, a wind blowing north at 60 km/hr
October 8, 2015

Math
paycheck: x food: 1/6 x, leaving 5/6 x house: 3/5 of 5/6 x = 1/2 x, leaving 1/3 x bills: 1/3 of 1/3 x = 1/9 x, leaving 2/9 x entertainment: 1/4 * 2/9 x = 1/18 x, leaving 1/6 x so, 150 = 1/6 x x = 900
October 8, 2015

the graph is concave down where 16e^-x^2 (2x^2-1) < 0 that is where 2x^2-1 < 0 x^2 < 1/2 so, f is concave down on the interval (-1/√2,1/√2)
October 8, 2015

Math 125
It appears that the number of calculators sold, as a function of the amount of discount (x) is p(x) = 10000+400x so, just plug in x=20 for the demand at \$75.
October 8, 2015

Calculus
∫[0,8] 8x-x^2 dx = 4x^2 - 1/3 x^3 [0,8] = 4*8^2 - 1/3 * 8^3 = 256 - 512/3 = (768-512)/3 = 256/3 Maybe you should have shown your work.
October 8, 2015

Mathematics(XI)
October 8, 2015

math
since √y = 7-x, √x + (7-x)^2 = 11 √x = -x^2+14x-38 x = x^4-28x^3+272x^2-1064x+1444 x^4-28x^3+272x^2-1065x+1444 = 0 (x-4)(x^3-24x^2+176x-361) = 0 good luck with the cubic. But, if x=4, y=9
October 8, 2015

Find x algebra help
no easy algebraic way to do this. However, with a little thought, you should be able to come up with 3^2-1 = 2^3
October 8, 2015

Pre-Calculus
well, just plug in the values: f(x)-f(1) = (-3x+2)-(-3*1+2) = -3x+3 Now divide by x-1 and you have (-3x+3)/(x-1) = -3(x-1)/(x-1) = -3 For the other, the same thing: f(x+∆x)-f(x) = 2(x+∆x)-2x = 2x+2∆x-2x = 2∆x Now divide by ∆x and you have 2∆...
October 8, 2015

math
a < b x >= y etc. If you have some specific questions, it would be a bit more useful to see how they can be answered.
October 8, 2015

Algebra
Looks like 9!-1 to me. Now, if you want (9!-6!)/(9-3)! that's 503. What is that supposed to model?
October 8, 2015

Math
If the faster person takes x hours, then the slower person takes (x+1) hours. So, how much of the job gets done in an hour? 1/x + 1/(x+1) = 1/5 Now just find x.
October 8, 2015

Calculus 1
the light turns through angle θ where dθ/dt = 4π. If the light hits x km away from P, then x = 4tanθ So, knowing that tanθ = 1/4, plug in the numbers and find dx/dt: dx/dt = 4 sec^2(θ) dθ/dt
October 8, 2015

calculus
I'll let you do the discussion. You just need to recall that f' = x^3 - 3x f" = 3x^2 - 3 f is increasing where f' > 0 f is concave up where f" > 0 f has max/min where f'=0 f has inflection where f" = 0
October 8, 2015

Geometry
as with the supplementary angles problem, 4x = (90-x)+10
October 8, 2015

Geometry
two angles are supplementary if they add to 180. So, if one angle is x, the other is (180-x), and you have 2x = (180-x)-36 2x = 133-x 3x = 144 x = 48
October 8, 2015

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