Saturday
April 25, 2015

Posts by Steve


Total # Posts: 30,777

Calculus Chain rule
not 6. It's -5 - 1 = -6
February 17, 2015

math - relations and functions
(x,y): (1,2),(2,4),(3,9) are 3 ordered pairs. It is a function because no single value of x maps to more than one value of y. Looks like time to review the discussion of functions in your text.
February 17, 2015

calculus 3
the vertical speed of the ball is 55 sin 25° = 23.24 m/s So, the height y is y = 23.24t - 16t^2 The horizontal speed is a constant 49.85 m/s (b,a) find when y=0 x = 49.85t (c) max height at the vertex of the parabola (d) assuming the same 55 m/s initial speed, find t when ...
February 17, 2015

maths
7^x + 4*7^x = 245 5*7^x = 245 7^x = 49 since 49 = 7^2, x=2 x-√x+20 = 0 think of this as (√x)^2 - √x + 20 = 0 I think you must have a typo. It is much better if you have (√x)^2 - √x - 20 = 0 (√x-5)(√x+4) = 0 √x = 5 or √x = -...
February 17, 2015

calculus
This is just like the last one, but oriented the other way. The graphs intersect at x = -3 and 4. So, the area is just ∫[-3,4] f(x)-g(x) dx where f(x) = (16-x^2)/2 g(x) = (4-x)/2
February 17, 2015

Calculus
the curves intersect at y = (-1-√13)/2 and (-1+√13)/2 area is thus ∫[(-1-√13)/2,(-1+√13)/2] (-y+3)-(y^2) dy
February 17, 2015

Calculus
3y = -3y + 9 ??? Fix that. Then, find where the two graphs intersect. Since the parabola opens to the right, it's easier to integrate along dy. The area is just a bunch of thin strips of height dy and length the distance between the two curves. Express that and integrate ...
February 17, 2015

math
If a book has 10 pages, and there are 6 books, can you find the total number of pages? I expect so. You just multiply the number of pages by the number of books. Same here. Just multiply the number of apples by the number of containers. So, what is 1/3 times 6?
February 17, 2015

imp
If you want to dig up the dirt on someone, then it becomes just information, a more abstract quantity. Many nouns in English have several meanings, some concrete, others more abstract, or metaphorical.
February 17, 2015

kayli
maybe it was a cold day, but the sun was shining on the table. The drink shaded a spot on the table, so sunlight no longer warmed the spot. The drink was in an insulated cup, so it did not absorb any heat.
February 17, 2015

maths
Hmmm. OK. In that case, the two circles must be orthogonal to each other. That is, if you draw triangle acb and adb, each is a 3-4-5 right triangle. The common chord is just twice the altitude to the hypotenuse, which I'm sure you can find.
February 17, 2015

maths
how can a line though the center (ac) be a tangent to the circle?
February 17, 2015

Math
you are correct. A dilation might be around some other point, in which case distances to that point are scaled, and things get much more complicated.
February 17, 2015

Math
Let the boxes be E,O,M. Draw a ball from E. If it is even, then the box marked O must contain the even balls, because otherwise the M box would contain the evens, leaving O containing the odds. But O is mislabeled, so it must contain the evens. So, drawing an even ball from ...
February 17, 2015

Calculus
well, where is cosx a maximum? At x=0. So, at x=0, the slope of 2sinx = 2. 2sin(0) = 0, so, at (0,0) the slope is 2. The line is y=2x. By now you should know that sin(x) has its maximum slope where it crosses the x-axis. That's what we have calculated here.
February 17, 2015

Science
I agree with D
February 16, 2015

calculus
s= [b]*[d]+64t-16t^2 what is the greatest height above the ground the rock will go
February 16, 2015

Precalc
Are you confusing k and θ? I see no k in the function. It also appears you are missing some information. Ought we not to know S?
February 16, 2015

calculus
well, you should start out by solving the DE: P = 10/(1+c*e^(-t/5)) (A) P(0) = 3, so 10/(1+c) = 3 c = 7/3 P(t) = 10/(1 + 7/3 e^-t/5) Now it's clear that P->10 Now try the rest.
February 16, 2015

Pre calculus
Draw a diagram. Label the angles in the drawing, and you will see that the angle you must use is 180-38-35 = 107° Be sure to note that the current is coming from the direction of 125°. That means the current's flow is in the direction 305°.
February 16, 2015

Algebra 1
the differences are constant, so the function is linear. The slope is 50/2 = 25 I don't see any likely choice. I suspect a typo.
February 16, 2015

Algebra 1
The attendances at a high school basketball games seems to be affected by the success of the team. Look at the table and decide what function would represent the data shown. attendance 150 200 250 300 350 wins 2 4 6 8 10 a) a=2(3)^g b) a=-25g+100 c) a=25g^2+100 d) a=-25g^2+100
February 16, 2015

GEOMETRY
the legs and hypotenuse of a 30-60-90 triangle are in the ratio 1:√3:2 so, depending on whether the 7√3 leg is the short one or the long one, w could be 14 or 14√3
February 16, 2015

math
sin 30° = cos 60°, so x=30.
February 16, 2015

ALGEBRA
looks like (b) to me. 1/2 x would leave extra 1/2's at all the odd values of x.
February 16, 2015

Physics
conserve momentum 3.5*24 = m*320
February 16, 2015

maths
If I understand you to mean that AB┴AD and BC, then BC-AD=12 and h=AB=√(19^2-12^2)=√217 so, the area is (42+54)/2 √217
February 16, 2015

MAth
clearly, tax was included . . .
February 16, 2015

math
The room was measured to be 20 by 30 m. So, just multiply each dimension by 0.95 to find the true area. Or, just do it in one step: 600 * 0.95^2
February 16, 2015

maths
the difference in height is 30. So, draw a diagram. The rope is the hypotenuse of a 30-40-50 right triangle.
February 16, 2015

College Algebra
x(x-2)(x-9) = 0
February 16, 2015

Calculus
wow! what a lot of work. juat factor out the cosx and expand the (1-sin^2 x)^3
February 16, 2015

Calculas
what you have is cosx (1-sin^2 x)^3 dx Now expand the polynomial, and each power is sinx is accompanied by cosx, which is just d(sinx).
February 16, 2015

Algebra 1
me too.
February 15, 2015

Algebra 1
Which kind of function best models the set of data points: -1,22 0,6 1,-10 2,-26 and 3,-42? linear quadratic exponential non e of the above my answer is linear
February 15, 2015

math analysis
how about a few parentheses, so we can see just what is divided where... I mean, secs/secx = 1
February 15, 2015

math
R is 3/7 of the way along S is 5/7 of the way along RS is the difference: 2/7 * 8 = 16/7 cm
February 15, 2015

Calculus
well, you have calculated where the extrema occur, so just plug in the values for x and calculate f(x). or, you can easily see the values because sinx-cosx = √2(sinx/√2 - cosx/√2) = √2(sinx cos π/4 - sin π/4 cosx) = √2 sin(x-π/4) ...
February 15, 2015

Algebra 1
How many solutions are there form 5x^2+7x-4=0? my answer is 3
February 15, 2015

Algebra 1
thank you
February 15, 2015

Algebra 1
Which method is the best method for solving the equation 8x^2-123x+3=0 square roots factoring graphing quadratic formula my answer is quadratic formula
February 15, 2015

Math
enter your functions here and see the steps: http://maccery.com/maths/#newton-raphson
February 15, 2015

math
3-2x < x <= 2x+5 3-2x < x 3 < 3x 1 < x x <= 2x+5 -x <= 5 -5 <= x combine them and you are left with x > 1
February 15, 2015

algebra
5/(6x-1) = -1/(x+1) Just clear denominators as usual. Suppose you had 3/8 + 2/3 You multiply by 3/3 and 8/8 so you have 3*3/24 + 2*8/24 So, for your equation, multiply to use the common denominator (6x-1)(x+1) 5/(6x-1) = -1/(x+1) 5(x+1)/[(6x-1)(x+1)] = -1(6x-1)/[(6x-1)(x+1)] ...
February 15, 2015

multivariable calculus
just review your spherical coordinates. I'm sure the relevant section justifies the claim.
February 15, 2015

Pre-Calculus
sequence converges series diverges (unless a=0)
February 15, 2015

Computer Science
if the original price is $100, the final cost is $91.
February 15, 2015

maths
#1 for n odd, Tn = 3n-2 For n even, Tn = 1/2^n #2 r^3 = T7/T4 = √81/√3 = √27 r = √3 Now you can find a
February 15, 2015

maths(urgent answer pls)
n ∑ (2k-1)/[k(k+1)(k+2) = k=1 n(3n+1) -------------- 4(n+1)(n+2)
February 15, 2015

math help
where is P?
February 15, 2015

Math
use both equations. e^.04t < 6 for t < 45 http://www.wolframalpha.com/input/?i=plot+15%2Be^%280.04t%29+sin%28pi*t%2F3%29%2C+15%2B6*sin%28pi*t%2F3%29
February 15, 2015

math
calculate f(2) and f(3) If the value changes sign, then the graph must cross the w axis somewhere in the interval, since f(w) is continuous there.
February 15, 2015

maths
the area of metal is the area of the small circle plus the area of the sides. The small circle has area 49π Now for the sides. Consider the entire cone with base radius 28 and height 4h. Chop off the top 1/4 of the height, and the missing volume is (1/3)π*7^2*h The ...
February 15, 2015

maths
h/35 = tan 57°40'
February 15, 2015

mathematics
Sn = 5/2 n^2 + 7/2 n = n/2 (5n+7) Sn = n/2 (2a+(n-1)d) 5(n-1)+5+7 = 5(n-1)+12 a=6 d=5 T10 = 12+9*5 = 57 check: 6 = 1/2 (12+0) 6+11 = 17 = 2/2 (12+5) 6+11+16 = 33 = 3/2 (12+10) looking good.
February 15, 2015

mathematics
Better clarify just what 3/5/9 means.
February 15, 2015

mathematics
ar = a+4 ar^2 = ar+9 r = 9/4 a = 16/5 so, now figure the first 3 terms.
February 15, 2015

math
the volume of the liquid of height h is v = πr^2*h also, v = (384g)/(0.6g/cm^3) So, equate the two, plug in r, and solve for h.
February 15, 2015

Pre-Algebra
As always, draw a diagram. Using similar triangles, it is clear to see that 4/5 = (x+4)/15
February 15, 2015

math
you are apparently using logs base 10, so log 0.096 = log(96*10^-3) = log96 - 3 = log(16*6)-3 = 2log4 + log6 - 3 ...
February 15, 2015

math
assuming the rectangle is long enough to wrap around the cylinder, a = πr^2 + πr^2 + 2πrh = 2πr(r+h) Now just plug in r and h.
February 14, 2015

Calculus
y = 3x 3^x - 1 y' = 3*3^x + 3x(ln3)3^x = 3*3^x * (1+x ln3) So, y'=0 when x = -1/ln3 That is the only extremum. Now find whether y" is positive or negative there to determine which kind.
February 14, 2015

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

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