Monday
March 30, 2015

Posts by steve


Total # Posts: 30,180

math
The base of the prism is an equilateral triangle of side 2, so its altitude is √3. The distance from thecenter of the triangle to a vertex is 2/3 of that, or 2/√3. Now, the distance from the base of the prism to the center of the sphere is one side of a right ...
March 17, 2015

Calculus
well, just plug and chug dy/dx = dy/du * du/dx = (1/4 - 4/u^2)(1 - 7x^6) = 1/4 (1-16/(x-x^7)^2)(1-7x^6) and you can massage that as you like
March 17, 2015

Math
I think your second model has a typo. Why not just say d(t) = 4.8t^2 ? At any rate, you can plot multiple curves on the same axes here http://www.wolframalpha.com/input/?i=plot+y%3D4.9t%5E2%2C+y%3D4.8t%5E2 If the second equation has to be tweaked, adjust it and fix the graphs.
March 17, 2015

math
1/4 did not wear spectacles, so (1/4)(1/3) = 1/12 were boys without spectacles.
March 17, 2015

maths
a right angle is π/2 radians I expect that by now you know how to handle fractions, and how the angles of a quadrilateral add up.
March 17, 2015

math
.9x-22 = .35x x = 40 check: 90% of 40 = 36 26 off, 4 on = 22 less, so we have 14 left 14 is 35% of 40 You got an answer; did you not check it?
March 17, 2015

math
the distance z from (x,y) to (11a,0) is z = √((x-11a)^2 + y^2) = √((x-11a)^2 + 4ax) = √(x^2-18ax+121a^2) dz/dx = (x-9a)/√(x^2-18ax+121a^2) dz/dx=0 when x = 9a So, P is (9a,6a)
March 17, 2015

math
you want (c-a)x(b-a) divided by its magnitude.
March 17, 2015

math
4 is the speed distance = speed * time
March 17, 2015

precalculus
actually, z1 = cos pi/4 +sin pi/4 i that is (1,π/4) z2 = (1,2π) = (1,0) no idea how you can say z1=√5, when you already said is is (1,π/4) z1*z2 = (1,π/4) z1+z2 = (1/√2 + 1/√2 i)+(1+0i) = (1+1/√2)+1/√2 i |z1+z2| = √((1+1...
March 17, 2015

Vectors
as your text no doubt shows, given the two lines L1 = a+bs L2 = c+dt the distance between the lines is given by (a-c).(bxd)/|bxd| In this case, that is (-1,2,-8).(-1,1,3)x(-3,2,5)/|(-1,1,3)x(-3,2,5)| = 15/3√2 = 5/√2 Hmmm. Better check my math.
March 17, 2015

precal
cos(2x) csc^2(x) = 2cos(2x) well, duh - divide by cos(2x), assuming cos(2x)≠0 csc^2(x) = 2 csc(x) = ±√2 x = all odd multiples of π/4 But, at those values of x, cos(2x)=0. So that set of roots is verboten. Naturally the equation is true if cos(2x) = 0, ...
March 17, 2015

Math
just divide the available flour by the amount required for each recipe. If I told you you had 10 cups and needed 2 for a recipe, you wouldn't have trouble finding how many batches you could make, would you? Same thing here. You just have to know how to deal with fractions...
March 17, 2015

Pre-Calculus
all appears correct.
March 16, 2015

Vectors
It helps if you show what you did. The two lines, in point-slope form are y-4 = 4/3 (x-3) y-4 = -7/2 (x-3) You don't always have to use y=mx+b. clearly, the two values for b are 0 and 29/2 With those, how could you not know what to do next? Knowing the slopes, you just ...
March 16, 2015

Math
I believe A is indeed correct.
March 16, 2015

science
only A
March 16, 2015

math
since g'=0 when x = ±4, those are the only two possibilities. g' does not exist when x=2, but that does not matter here. Since g" > 0 at both points, both are minima. See the graph at http://www.wolframalpha.com/input/?i=integral+%28x%5E2%E2%80%9316%29%...
March 16, 2015

algebra
by definition, (f◦f^-1)(x) = x So, B is correct. Similarly, (f^-1 ◦ f)(x) = x
March 16, 2015

Algebra help please
(gof)(x) = g(f) = f^2 = (x+2)^2 (gof)(-5) = (-5+2)^2 = (-3)^2 = 9 B is correct. Good work.
March 16, 2015

Algebra help please
f/g = (3x-6)/(x-2) = 3 B is correct
March 16, 2015

Algebra help please
f+g = (-5x-4)+(6x-7) = (-5+6)x + (-4-7) = x-11 Bzzzt. Looks like B
March 16, 2015

physical
the acceleration is constant, meaning that the mass of the ball does not matter.
March 16, 2015

MATH
grade is the slope of the road. That is, the change in height divided by the change in horizontal distance. In this case, descending 20 feet means you have moved horizontally 200 feet. Doesn't sound like much, but even the steepest roads seldom exceed a 6% grade.
March 16, 2015

Math
you can draw any rectangle and label it so it conforms to the scale. I think you need to reword the question.
March 16, 2015

math
since both A and B are at the same longitude, they are separated by 60° latitude = π/3 the distance s = Rθ where R is the radius of the earth. If the plane flies to C along the 30° latitude line, it flies along a circle with radius Rcos30°, through an ...
March 16, 2015

Math
(-3)^2 = (-3)(-3) = +9 -3^2 = -(3^2) = -9 Review the order of operations. -23 subtracted from 17 is 17-(-23) = 17+23 = 40 -23-17 is 17 subtracted from -23 = -40 Get out your number line and review how to do subtractions and negative values.
March 16, 2015

calculus
I assume I will find it where it landed. That would be where the height is zero. y = tanθ x - g/(2(vcosθ)^2) x^2 In this case, that's y = 0.4877x - 0.0012088x^2 y=0 at x=403.5 So, I'd start looking at 403.5 feet from where it was shot. Did you have something ...
March 16, 2015

algebra
|-4-5| = |-9| = 9 |7+3| = |10| = 10 9-10 = -1
March 16, 2015

chemistry
0.178 * 300/1000
March 16, 2015

chemistry
2H2 + O2 = 2H2O 2Na + 2H2O = 2NaOH + H2
March 16, 2015

Science
line up 4 AA cells, end to end, + to -. That is an example of 4 cells in series. Your 12V car batter is another good example of cells in series. I think each cell can charge up to 2.4V, so there are 5 or 6 cells. See http://hyperphysics.phy-astr.gsu.edu/hbase/electric/leadacid...
March 16, 2015

Geometry
If the altitude h from A divides a into two parts, x and y, then since any side of a triangle is less than the sum of the other two sides, h < b+x h < c+y 2h < b+c+x+y but, x+y = a, so 2h < b+c+a h < (a+b+c)/2
March 16, 2015

math
I think this is answered in the related questions below.
March 16, 2015

math
There are 24C5 = 42,504 ways to pick 5 people. Only one of those ways includes the 5 youngest.
March 16, 2015

Trigonometry
(tanx-8)(tanx+1) = 0 tanx = 8 or -1 arctan(8) = 1.446 or 4.588 arctan(-1) = 3π/4 or 7π/4
March 16, 2015

consumer math
start off with the gross. 12 hrs @ 7.45/hr = 89.40 I will assume that you deduct your expenses before taxes. In that case, the taxable income is 89.40 - 3*5.70 = 72.30 Now for the tax bite. Total tax rate is .0765 + .1065 + .057 = .24 tax is thus .24*72.30 = 17.35 Subtract ...
March 16, 2015

Math
you can convert all to decimals, then it's easy to order them: .20,.375,.40,.45,.60 As you can see, they're already in order Or, you can convert all to fractions with a common denominator. In this case, that would be 40: 8/40, 15/40, 16/40, 18/40, 24/40
March 16, 2015

Math Help
as you know a^2 + b^2 = c^2 so, plug in your numbers 7^2 + b^2 = 11^2 49+b^2 = 121 b^2 = 72 b = √72 = 8.5
March 16, 2015

math
the real world has dimensions 1000 times as large as the map, so 4cm -> 4000cm = 40m 3cm -> 3000cm = 30m the map area is 3cm * 4cm = 12 cm^2 the actual area is 40m * 30m = 1200 m^2 or, you can use the scale factor to figure the real area. Since area is length * width, ...
March 16, 2015

Math
pick 4 numbers (bottles) multiply each by the unit cost, 1.50 Now plot the pairs: (bottles, cost)
March 16, 2015

Math
come on. which numbers are between 4 and 6? as you may have noticed, I forgot 5x12=60 One you have the height, the other factor is the width.
March 16, 2015

Math
the factors of 60 are 1x60 2x30 3x20 4x15 6x10 Now pick the pairs that meet your requirements.
March 16, 2015

maths
30*20cm = 600 cm
March 16, 2015

MATH
the heading is now 135° period. All headings are measured clockwise from due North. This can also be expressed as relative headings, such that the angle is at most 90°, as in E 45° S S 45° E These are both abbreviated as just SE.
March 16, 2015

math
(8/9) * ((64/243)/(8/9))^(1/3) = 16/27
March 16, 2015

Math
so, how many diagrams have you seen here?
March 16, 2015

Math
in 27 days they will double 3 times. So, what is 2550*2*2*2 ?
March 16, 2015

maths
I assume you mean the angle of the sun's rays. The altitude of the sun is 93 million miles. tanθ = 1/2
March 16, 2015

math
Q2. points with equal y-coordinate are all in the same horizontal line: y = 1.3 Q3. slope = -1/3, so it slopes down. the other line has slope -1/2 So, is -1/3 greater or less than -1/2? Q4. y-intercept is at x=0 x-intercept is at y=0 check the points to see whether they fit ...
March 16, 2015

Calc
well, of course. (it is kind of a silly question) You know after 5 seconds the balloon has gone up 5*50 = 250 feet. Now you know x and you can get z.
March 16, 2015

Calc
as you say, tanθ = x/50 so, sec^2 θ dθ/dt = 1/50 dx/dt You know x at t=5, and you know dx/dt=20, so you can find θ. The distance z is given by z^2 = 50^2 + x^2 z dz/dt = x dx/dt so, find z at t=5 and plug in the numbers.
March 16, 2015

math
ok. now what?
March 16, 2015

Calculus
well, f' = 5e^x - 4e^(2x) so, plug in x=1
March 16, 2015

math(5th grade)
steps area perimeter 1 1 4 2 3 8 3 6 12 4 10 16 ... n n(n+1)/2 4n so, 10 steps will have area 55 and perimeter 40
March 16, 2015

math
There are 5C2 = 10 ways to select the weights. However, there are some duplicates, such as 1+5 and 2+4 I suppose you can find how many, and subtract them from 10.
March 15, 2015

algebra
C = 5/9 (F-32) = 5/9 (45) = 25
March 15, 2015

algebra
clearly not C. 3 < 7, so √3 < √7
March 15, 2015

algebra
-(-3)^2 - 4(-3) -9+12 3 you are correct
March 15, 2015

business math
1460(1+.039/12)^(12t) = 1552.84 t = 1.583 years, or 19 months
March 15, 2015

Statistics
as always in a normal distribution, 50% are above the mean, regardless of std.
March 15, 2015

math
If the number doubles every 17 minutes, then that means it doubles 1440/17 times in 24 hours. That means there will be 100*2^(1440/17) = 3.15x10^27 zombies I guess that's not reasonable. So, assume that the number grows by 100 every 17 minutes. That means there will be 100...
March 15, 2015

trig
since the arc length is radius * angle, arc speed (linear speed) is radius times angular speed: 32 * pi/9 cm/s
March 15, 2015

precal
-1+i = √2 cis 3π/4 raise that to the 7th power and you have (√2)^7 cis 7*3π/4 (√2)^7 cis 21π/4 = 8√2 cis 5π/4 = -8-8i
March 15, 2015

Algebra
kinda weird, but if you've written it correctly, log(4/x) (x^2 - 6) = 2 raise 4/x to both sides and you have x^2-6 = (4/x)^2 x^2 - 6 = 16/x^2 x^4 - 6x^2 - 16 = 0 (x^2+2)(x^2-8) = 0 x = ±√2 i or ±2√2 (x+√(x^2-5))/5 = (x+√(x^2-5))(x-&#...
March 15, 2015

math
(800000*r^5)(.96) = 480000 r = .91 So, the car depreciated at 9% per year
March 15, 2015

Calculus 2 Trigonometric Substitution
I think your 2nd line is bogus, and the brackets are unbalanced. (1-tan^2)/sec^2 = 1/sec^2 - tan^2/sec^2 = cos^2 - sin^2 = cos(2x) integral of cos(2x) = 1/2 sin(2x)
March 15, 2015

Algebra
-2(2x + 9) > -4x + 9 -4x - 18 > -4x + 9 -18 > 9 Never
March 15, 2015

Calculus
we want the slopes to be equal 4cosx = x That occurs only 3 places. See http://www.wolframalpha.com/input/?i=x+%3D+4cosx
March 15, 2015

Calculus check
D Consider the function y = |sin(x-1)|
March 15, 2015

Programming in Java
check out MATH.sin and MATH.cos If you have the hypotenuse and an angle, these will help. If all you have is the hypotenuse, you're stuck. There is no way to figure the legs with just that.
March 15, 2015

Please check my calculus
since h = 3r, v = 1/3 pi r^2 h = pi/27 h^3 dv/dt = pi/9 h^2 dh/dt -50 = pi/9 * 9 dh/dt dh/dt = -50/pi C is correct
March 15, 2015

calculus check
siny = cosx cosy y' = -sinx -y' = -1 C is correct
March 15, 2015

calculus
#2 since lnx is not defined for x<0, I'd say False #3 since ln 7x = ln7 + lnx, I'd say True #4 7 (why?)
March 15, 2015

calculus
y = ((x+3)/e^x)^lnx wow! lny = lnx(ln(x+3)-ln(e^x)) = lnx(ln(x+3)-1) 1/y y' = 1/x (ln(x+3)-1) + lnx*1/(x+3) y' = y(ln(x+3)/x - 1/x + lnx/(x+3)) Now you can massage that in many ways.
March 15, 2015

math
If the scale factor is r, then the area grows by r^2 the volume grows by r^3 So, if the area scales by 20/45, the volume scales by (20/45)^(3/2). The smaller cylinder has cross-section area of .945*(20/45)^(3/2) = 0.28 cm^3 If x cm is transferred to the smaller container, then...
March 15, 2015

Calc
do you mean y = x ln(ln x)? if so, then y' = ln(lnx)) + x * 1/lnx * 1/x = ln(lnx) + 1/lnx y = log_x(7) = ln7/lnx if u = lnx, then y = ln7 u^-1 y' = -ln7 u^-2 u' ... since cosh^2 = 1+sinh^2, sinh^2-cosh^2 = -1 so the derivative is zero
March 15, 2015

Math Geometry - Please check my answers!
C is not correct. The point (16,0) clearly indicates that 16 is in the domain. It has to be A.
March 15, 2015

Math Geometry - Please check my answers!
#1 ok #2 ok #3 The only points we can use are those given. That would make the domain {10,13,16}. But, they have said line is a parabola, so the function is continuous. The domain is thus [10,16]. I guess you could consider that they started counting at t=0, when the dolphins ...
March 15, 2015

precal
√2/2^2 = √2/(√2*√2*2) = 1/(2√2) If that is what you meant... I suspect it is not. In that case, use some parentheses so we know just what the expression is. (√2/2)^2 √(2/2)^2 ...
March 15, 2015

Calculus check
clearly (3,3) is no kind of intercept!! Since f'=0 and f"<0, it is a relative max.
March 15, 2015

precal
r^2 = (2√3)^2 + 2^2 = 16, so r=4 (2√3 + 2i) = (4,π/6) (2√3 + 2i)^5 = (4^5,5π/6) = (-512√3,512)
March 15, 2015

math
the plate has a volume of (1050g)/(8.4 g/cm^3) = 125 cm^3 Since v = s^2 * h, .2s^2 = 125 s^2 = 625 s = 25 cm
March 15, 2015

Please check my calculus
looks good to me.
March 15, 2015

math
θ = 5/3, so a = 1/2 r^2 θ = 1/2 * 3^2 * 5/3 = ?
March 15, 2015

Calculus check
looks good to me.
March 15, 2015

math
for the smaller segment, sin θ/2 = 2/3.3 the larger segment's angle is thus 2π-θ for each segment, a = 1/2 r^2 θ
March 15, 2015

AP CALC
the average value of f' on the interval is ∫ f' dx = (f(4)-f(2))/(4-2) = -3/2 Since II and III say the same thing, I pick (D) we know nothing about the average value of f.
March 15, 2015

calculus
well, y" = 20x^3 - 2 - sinx where does y" = 0?
March 15, 2015

Calculus
f(-2) and f(2) do not exist. Thus, the theorem's conditions are not satisfied -- f must be continuous on the closed interval. This should have been clear, since none of the choices for c is in (-2,-2), except 0, and f(0) = 0. However, D and E both give the wrong reason. So...
March 15, 2015

Calculus check
y' = cosx - 2sinx y'(pi/2) = 0 - 2 y-1 = -2(x-pi/2) or 2x+y = 1+pi I get B. http://www.wolframalpha.com/input/?i=plot+y%3Dsinx%2B2cosx%2C+y+%3D+1%2Bpi-2x+for+x+%3D+0+to+3
March 15, 2015

Calculus
the value given is the definition of f'(5). So, II and III are true, making E the correct choice.
March 15, 2015

math
can you not look up the formulas? a = 1/2 r^2 θ, so 1/2 (36^2) θ = 54 pi (not pie!) θ = 108π/1296 = 0.2618 now for the arc length, s = rθ = 36 * 0.2618 = 9.42
March 15, 2015

math
40/x = tan 60°
March 15, 2015

math
geez, what's the problem? Just plug and chug: A(1 + e^kt + e^2kt + ... + e^(n-1)kt) is just a geometric series where a = 1 r = e^kt and there are n terms. So, Just before the 5th dose, there have been for doses, so n=4, and Sn = A(1-r^n)/(1-r) = 0.3 (1-e^(-.862*4*4))/(1-e...
March 15, 2015

Calculus
clearly, f"=0 at {0,1/2,-1/3} However, for an inflection point, f' must not change sign. (Think of the graph of x^3) The function for f'(x) is a nasty polynomial, so I assume that (A) is correct. If you actually do the calculations, you will see that f'(x) >...
March 15, 2015

Calculus
√x(√x+1) = x + √x surely you can do that...
March 15, 2015

maths
since the medians intersect 2/3 of the way from vertex to opposite side, and each median is also an altitude, the altitude is 60, making the sides 40√3
March 15, 2015

Calculus
assuming you can interpret the garbled text, did you follow the tip?
March 15, 2015

math
we have x^2 + y^2 = 25 x^2 + (x+1)^2 = 25 2x^2 + 2x - 24 = 0 x^2+x-12 = 0 (x+4)(x-3) = 0 So, the points are (-4,-3) and (3,4)
March 15, 2015

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