Tuesday
March 31, 2015

Posts by Steve


Total # Posts: 30,212

math
An odd question. Since the vectors are independent, they span R^2, and the dimension is 2. Am I missing something here?
February 14, 2015

calc
does not matter. tan and arctan are inverse functions. tan(arctan(x)) = x As to how to find arctan(3) -- have you no calculator? There are gobs of them online if you do not.
February 14, 2015

Math
Naturally, that wold be f(w) = 0
February 14, 2015

Math
best convert to polar form z^4 = 46.87 cis 2.95 so, z = 2.62 cis 0.738 + k*pi/2 for k=0..3 then convert back to rectangular form.
February 14, 2015

Math
Hmmm. I can see that there could be two solutions -- one in front of the plane of the given points, and another behind it. But since the matrix has a linear determinant, I'm not sure how to get the other one. Need to think on that a bit.
February 14, 2015

Math
put the coordinates in columns of the matrix M: (2 6 3 x) (2 3 -1 0) (3 0 -1 0) (1 1 1 1) The volume of the tetrahedron is 1/3! |M| = 1/6 (13x-39) So, you want 1/6 (13x-39) = 26 13x-29 = 156 13x = 185 x = 14.23 google tetrahedron vertices volume and you can find several useful...
February 14, 2015

a sond wave is prouduced. 3seconds later its echo
the sound has to go out and back. SO, how far does sound go in 1.5 seconds?
February 13, 2015

math calculus
2^x is not the inverse of (1/2)^x log_2(x) is the inverse of 2^x log_1/2(x) is the inverse of (1/2)^x You can check this because if g(x) is the inverse of f(x), f(g(x)) = x and g(f(x)) = x (1/2)^x = 1/2^x they are reciprocals, not inverses.
February 13, 2015

math calculus
well, (1/2) = 2^-1 go to wolframalpha.com and enter plot y=2^x, y=(1/2)^x
February 13, 2015

math
do you actually read what I write? I explained k, and I used it. Don't make me do your thinking as well as your math!
February 13, 2015

math
so, if the dimensions are x and y, 50% increase of y is 1.5y. But, you want the new area to be the same. So, if x is multiplied by k, you want (k)(x)(3/2)(y) = xy (k)(3/2)(xy) = xy k(3/2) = 1 k = 2/3 So, if the new width is 2/3 of the old width, that is a decrease of 1/3, or ...
February 13, 2015

math
length is 3/2 so, width is 2/3
February 13, 2015

math
c-15 = (2/9)(c+15) + c/6
February 13, 2015

math
read what you wrote. There are no numbers given, yet you want a numeric answer? 42 is the answer to the Ultimate Question of Life, the Universe and Everything, so it surely must answer your puny question as well.
February 13, 2015

math
42
February 13, 2015

math
oh, please. If you divide by 4, the remainder cannot be 8 35 = 8*4 + 3 8 is the quotient 3 is the remainder
February 13, 2015

math
subtract multiples of 4 till you can't get any smaller. In other words, what is the remainder of 35/4 ?
February 13, 2015

math
Hmm. yes, good question. However, no rectangle with a diagonal of 20 inches can possibly have an area of 192 square meters!! I fear you have garbled the question.
February 13, 2015

math
400 is 20^2 looks like you need to review the Pythagorean theorem.
February 13, 2015

math
xy = 192 x^2+y^2 = 400 Now just find x and y
February 13, 2015

math
you must multiply everything by 4 to clear the fraction. Why did you continue on with another fraction? And your arithmetic is wrong, as well. 2x + [3x-(4x-5) ]=x/4-2 8x + 4[3x-(4x-5) ] = x-8 8x + 12x - 16x + 20 = x - 8 4x+20 = x-8 3x = -28 x = -28/3
February 13, 2015

math
OK. Now you show me yours, and I'll show you mine. Just clear the fraction and get rid of the parens. Then it's clear sailing.
February 13, 2015

math
Huh? I clearly showed the factors of each polynomial. When you divide by a fraction, it is the same as multiplying by its reciprocal. If you can't follow those steps, I fear you have a long road ahead... Sorry about the typo. 7 is near the y on the keyboard. I meant 1 + y...
February 13, 2015

math
1 + 7/(x+y) = (x+2y)/(x+y) 1 - 3y^2/(x^2-y^2) = (x^2-4y^2)/(x^2-y^2) so, the result is (x+2y)/(x+y) * (x+y)(x-y) / (x-2y)(x+2y) = (x-y)/(x-2y)
February 13, 2015

math
the only multiples of 6 nearby are 18,24 So, our number might be 16,22 Looks like 16 to me
February 13, 2015

Math Check
(a) and (b) seem to be ok I don't know what (2) is supposed to be, but that's d^2, not d.
February 13, 2015

math
well, since 12 is 3/4, 4 is 1/4, right?
February 13, 2015

Algebra 2
if the horse has speed h, and the motorbike has speed m, then since time = distance/speed, 60/m = 50/h - 2 m = h+10 60/(h+10) = 50/h - 2 60h = 50(h+10) - 2h(h+10) 2h^2 + 30h -500 = 0 Now you can find h, and then m=h+10
February 13, 2015

math
dS/dt = 3t^2-12t+9 for max/min, find t when dS/dt = 0
February 13, 2015

Math 20-1
neither. All you have to do is check the difference or ratio between the first two and the 2nd two terms. It is not constant.
February 13, 2015

GEOMETRY
the ratios given are equal because the angle involved is the same. opposite/hypotenuse is the same.
February 13, 2015

Geometry
a true b true c false d false (unless you consider r<0 as a reflection as well as a scaling. Then it could be true sometimes)
February 13, 2015

Calculus
Sorry about my half-angle formula hint. Got me nowhere. Instead, for F(x), let u^2 = 1+sinx 2u du = cosx dx and now you have ∫2u^2 du = 2/3 u^3 = 2/3 (1+sinx)^(3/2) + c Now you can find c, since you know F(0)
February 13, 2015

Pre-Calculus
You want the sum of the first 8 terms: S8 = a(1-r^8)/(1-r) = a(1-(2/3)^8)/(1/3) = 2.883a So, a = 258/2.883 = 89.49 Your answer is totally unreal. It would have turned 805.4 times in the 1st second, which is way more than the total turns after 8 seconds. I hope that is why you ...
February 13, 2015

Calculus
your expression is just 1/2 sin(14x) dx
February 13, 2015

Calculus
f(g(5x))/5
February 13, 2015

maths - ouch!
Thanks, Reiny. I'm glad someone around here can read!
February 13, 2015

maths
clearly, d=28 and the sequence is -44, -16, 12, 40, 68, 96, ... hint: 71*28 = 1988 but you didn't start at zero.
February 13, 2015

Calculus
Try using the half-angle formulas to re-express the integrands.
February 13, 2015

Calculus
a simple division turns this into ∫sec^2x - secx tanx dx how about that?
February 12, 2015

Geometry
Apparently PQ is not a bisector. It is just parallel to BC. So, AQ/QC = AP/PB 12/18 = 8/x x = 12
February 12, 2015

mathematics
since 10*19 = 190 and 10*20 = 200, what do you think?
February 12, 2015

Calculus
let u^2 = x+1 x = u^2-1 2u du = dx and we have ∫ (u^2-1)/u * 2u du = 2∫u^2-1 du and that's a cinch, right?
February 12, 2015

Geometry B
Draw a diagram. Using similar triangles, we know that h/9 = 17/√370
February 12, 2015

Math
or, you can reason that since her speed is 4/3 as great, the time required is 3/4 as much, or 15 minutes.
February 12, 2015

Math
20 minutes (1/3 hr) at 30 mi/hr is 10 miles. 10mi/(40 mi/hr) = 1/4 hr = 15 minutes
February 12, 2015

Calculus
the average rate of change of f on [a,b] is just [f(b)-f(a)]/(b-a) f(x) = x^3-x^2+4x+c The c does not matter, so the average rate of change on [-1,4] is just [f(4)-f(-1))/3 = ((64-16+16+c)-(-1-1-4+c))/3 = 70/3 You want a c where f'(c) = 70/3 3c^2-2c+4 = 70/3 c = (1+√...
February 12, 2015

Trigonometry
This is a trick question. 2√3/5 = 0.69 but sec(x) is never less than 1.
February 12, 2015

Calculus
oh, please - just expand the square, and divide each term by √x
February 12, 2015

Pre-calculus
r = ±3
February 12, 2015

Math/Trig
check the related questions below. Looks like bobpursley did this one already.
February 12, 2015

math
(3/4)m = (1/2)w m/w = (1/2)/(3/4) = 2/3
February 12, 2015

math
3/8
February 12, 2015

Science
look them up in a table of hardness. Easy to find. I can't believe you would post such a question.
February 12, 2015

math
well, just plug in various values forn: 1(0)-4 = -4 2(1)-4 = -2 and so on...
February 12, 2015

physics
both are 9*0.7071 since sin = cos = 0.7071 at 45 degrees.
February 12, 2015

Math
when raising powers to powers, just multiply the exponents. That is because (3^4)^3 = (3^4)(3^4)(3^4) = 3^(4*3) So, you have (y^-5)^-10 = y^50 now multiply that by y^10
February 12, 2015

Math(Asap)
well, you should have caught my typo. I used 3.5% instead of 3%. Fix it and redo the calculation.
February 12, 2015

Math (Asap)
#1: 3500(1+.035/2)^(2*20) #2: 92000*0.85^10
February 12, 2015

Algebra 2 - eh?
umm, how many feet?
February 12, 2015

calculus
u = arcsin(x) x = sin(u) sqrt(1-x^2) = cos(u) dx = cos(u) du Now you have to integrate cos(u) * u * cos(u) du so integrate by parts.
February 12, 2015

calculus
u = arcsec(x) x = sec(u) dx = secu tanu du the integrand now becomes u secu tanu du Now use integration by parts and it's a cinch. If still stuck, just google it and I'm sure you can find lots of detailed solutions.
February 12, 2015

computer science
ok. It's pretty cool, believe me. Oh, yeah -- can't post it here.
February 12, 2015

math
since the plane is aimed basically SW, but its velocity is basically SE, I'd call it a tail wind, since its southward direction is increased. That's quite a side wind, though, as well. Does the vertical speed matter when considering this?
February 12, 2015

Trigonometry
the plane flies on a heading, not a bearing. the distance east is 200*sin(90-137) = 200cos(47) = 136.4 km
February 12, 2015

math
If the expensive side has length x, and the other is y, then the cost is 75x+30*2y = 1750 The area is a = xy Since y = (1750-75x)/60 = (350-15x)/12 a = x(350-15x)/12 = 1/12 (350x-15x^2) This is just a parabola with vertex at x = 35/3. That is x, so now you can figure y.
February 12, 2015

Geometry
sorry. I get a message saying I have to log in to view the page. Better describe the diagram.
February 12, 2015

Geometric progression
r = 1/2 try that to get started.
February 12, 2015

statitics
all probabilities must be positive.
February 12, 2015

math
Just add up all the powers of 7: 7^[(-1/5)-(-7/5)+(3/5)] = 7^((-1+7+3)/5) = 7^(9/5) The line in question is wrong. 1/7^(-7/5) is NOT 7^(5/7) it is 7^(7/5) 7^(-1/5) is NOT 7^5 it 1/7^(1/5) Reciprocals just cause the exponent to be minus what it was, not the reciprocal. Better ...
February 11, 2015

algebra
the two candles have height h and h+1 The shorter candle burns at the rate of h/4 in/hr The longer burns at the rate of (h+1)/6 in/hr So, h-(h/4)(2.5) = (h+1) - (h+1)/6 * 4 h = 8
February 11, 2015

physi<u>c</u>s
aaa
February 11, 2015

algebra
sorry - 2/3 of 135 = 90, as expected. single is 105/285 = 36.8%
February 11, 2015

algebra
the population has m men and w women. Assuming that each married person has a single spouse, 2/3 m = 3/5 w So, m = 9/10 w So, assume there are 9 men and 10 women. The given fractions don't give integer results, so we need to multiply the proposed population. LCM(3,5) = 15...
February 11, 2015

geometry
recall that the length of the altitude is the geometric mean of the two segments of the hypotenuse. That is, w+9 = √(8*18) = 12
February 11, 2015

Algebra 1
A box shaped like a rectangle prism has a height of 17 inches and a volume of 2,720 in^2. The length is 4 inches greater than twice the width. What is the width of the box?
February 11, 2015

Algebra 1
Find the solution of x^2+14x+112=0 I don't think that there is a solution
February 11, 2015

Algebra 1
What is a solution of x^2 +6x=-5? my answer is -1
February 11, 2015

Algebra 1
What is the value of n so that the expression x^2+11x+n is a perfect square trinomial?
February 11, 2015

Algebra 1
thank you
February 11, 2015

Algebra 1
The area of a rectangle is 30 ft^2. The length is 1 less then 3 times the width. How wide is is the rectangle?
February 11, 2015

Algebra 1
my answer is 42 feet
February 11, 2015

Algebra 1
A ball is thrown into the air with the in initial upward velocity of 60 ft/s. It's height (h) in feet after t seconds is given by the function h=- -16t^2+60t+6. What will the height be at t=3 seconds?
February 11, 2015

Algebra 1
my answer is 3 seconds
February 11, 2015

Algebra 1
A ball is thrown into the air with the in initial upward velocity of 45 ft/s. It's height (h) in feet after t seconds is given by the function h=- -16t^2+45t+6. After about how many seconds will the ball hit the ground?
February 11, 2015

Algebra
the acceleration is (41m/s)/(.28s) = 146.43 m/s^2 F = ma
February 11, 2015

math
for the horizontal asymptote, as x gets large, only the highest powers matter. So, what is x^2/9x^2 ? For vertical asymptotes, they can only occur where the denominator is zero. 9x^2-44x-5 = (9x+1)(x-5) so, when is that zero?
February 11, 2015

Icp
F = ma
February 11, 2015

math
Seems like you'd have to know the various amounts of debt and interest, doncha think?
February 11, 2015

math
see the 1st related question below
February 11, 2015

Geometry
42° = 1/2 (large-small) so, large-small=84° but, large = 7/3 * small 7/3 * small = small+84 4/3 * small = 84 small = 63 large = 147 So, since the three arcs add up to 360°, 63+147+x = 360 x = 150° A nice discussion of the topic is found at http://www....
February 11, 2015

Maths
Hmmm. Looks like 20 to me, too. There aren't any fractional laps to worry about.
February 11, 2015

Geometry
Suppose the sides were exactly 3,10,12. The perimeter would be 25. But, the actual perimeter is 400 = 16*25 So, the sides are 16*3,16*10,16*12 = 48,160,192
February 11, 2015

math
blue beads are 3,6,9,12,15,18 green ones are 7,14 so, what do you think?
February 11, 2015

math
a = pi r^2 = 38.5 r^2 = 38.5/pi r = 3.50 c = 2pi r = 22.06 Now, for the square: s = 22.06/4 = 5.515 a = 30.42
February 10, 2015

math
(.05*540 + .80*(720-540))/720 = 23.75%
February 10, 2015

9th Grade Math
(4πx^2)/(3x^2) = 4π/3 = 4.19
February 10, 2015

math
2(q^2-3q) = 2q^2-6q So, you want to add up 2q^2-6q+q+10+q^2 Keep like powers together, and you end up with (2+1)q^2 + (=6+1)q + 10 3q^2-5q+10
February 10, 2015

Math
7/15 - 6/15 = ?
February 10, 2015

Math
you are correct
February 10, 2015

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