Sunday
April 19, 2015

Posts by steve


Total # Posts: 30,637

algebra
R(x) = (8+x)(2000-100x) So, that is just a parabola, with its vertex (maximum revenue) at x=6 Now you can answer the other questions.
March 18, 2015

algebra
you might look at the many similar questions below. I'll give you the shortcut, which always works in this kind of situation. The maximum area is achieved when the fencing is divided equally among the lengths and the widths. In this case, we have one length and two widths...
March 18, 2015

algebra
150x300
March 18, 2015

algebra
x + 3y = 18 z = xy = (18-3y)(y) = 18y-3y^2 This is just a parabola with vertex (maximum value) at y=3 so, x=9, y=3
March 18, 2015

Math
the width and length are both reduced by 9.2cm on each side, so the new perimeter is 2((6.2-2*.092)+(5.6-2*0.92)) = 19.552 m
March 18, 2015

math
since y = -12x^2 has vertex at (0,0) and opens down, your function is reflected in the x-axis, shifted left 3 and up 2, so it is 12(x+3)^2 + 2
March 18, 2015

MATH
looks like output grows by 18 when input grows by 1. So, starting at f(2) = 30 = 36-6, f(x) = 18x-6
March 18, 2015

math
ns = k, a constant value. or, it is often written as n = k/s direct variation is n = ks
March 18, 2015

trig
assuming you mean line-of-sight distance, 300/x = sin 25° If you mean how far long the ground has he traveled, then 300/x = tan 25°
March 18, 2015

Algebra
As I said at 6:42 pm, check your signs. I get -3.125 or +1 Naturally, the negative answer may be disregarded.
March 18, 2015

math
ummm. hold the ruler next to the object and count the marks. Never done that?
March 18, 2015

Math
full price is 12*14 = 168 Since she bought 12 or more, she gets 1/4 off that amount, or 42 So, she pays 168-42 = 126 Or, you can say that with 1/4 off, each ticket costs $9 instead of $12. 14*9 = 126
March 18, 2015

Math
There were a total of 8000 seats for the two nights. The empties are therefore 8000-6109=1891 you got the right answer, but 6109-4000 is not 1891.
March 18, 2015

Math
5 * 7/8 = ?
March 18, 2015

Algebra
check your signs. I get -3.125 or +1 Naturally, the negative answer may be disregarded.
March 18, 2015

Science
1st step would be to read your textbook where it discusses the topic. You saying you've never done a web search? Hard to believe, but if that's so, just go to google.com and in the query box type process of filtering blood you will get many links. read some of the ...
March 18, 2015

Science
I can't imagine that any of us here could explain it any better than your course materials, or any of many google references.
March 18, 2015

Math
(4x+8)3 = 42 4x+8 = 14 4x = 6 x = 3/2
March 18, 2015

Math
the vertex is reached at t = -b/2a = 25/1.862 = 13.426 h(13.426) = 337.661 Your value is way high. To find time in flight, just find when h=0. Up till then, the ball is above the surface. 2 + 50t -1.862t^2 = 0 t = 26.89
March 18, 2015

Math
that is correct.
March 18, 2015

Math
#1 x = y+7, so 3(y+7)+2y = 6 now get y, then x = y+7 #2 multiply the equations by 5 and 4, and you have 10x-20y = 15 -12x+20y = 4 Now add them to get x, then find y.
March 18, 2015

math
-f(1/3 x+9)+8 -f(1/3 (x+3)) + 8 so, shift left 3, scale horizontally by 3, reflect through the x-axis, and shift up 8.
March 18, 2015

Algebra1414
If you're trying to find x, then just follow the normal rules of manipulation... 9.6 = 0.134^2 / 0.110x^3 9.6 * 0.110x^3 = 0.134^2 1.056x^3 = 0.002406 x^3 = 0.002279 x = 0.13159
March 18, 2015

algebra
the descriminant of ax^2+bx+c is always b^2-4ac So, what do you think now?
March 18, 2015

math
(3x+2y)/7 = (2x+3y)/8 8(3x+2y) = 7(2x+3y) 24x+16y = 14x+21y 10x = 5y 2x = y Using that, we have (xy^2-x^2y)/(x^3+y^3) = (x(2x)^2 - x^2(2x))/(x^3+(2x)^3) = (4x^3-2x^3)/(x^3+8x^3) = 2/9
March 18, 2015

physics
both hit the same time, all other conditions being equal. The coin's horizontal speed does not affect how fast it falls.
March 18, 2015

Algebra help please
16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4 = 2x^2y (8x^3y^3 + 3x - 1 - 12y^3) = -2x^2y (-8x^3y^3 - 3x + 1 + 12y^3) Naturally, if the divisor had only an x instead of x^2, all the terms in the quotient would have an extra x in them. 12y^3 + 1 - 3x - 8x^3y^3 is of degree 6, with ...
March 18, 2015

MATH
No, that was not the assignment. You pick any line. Then determine slope of a perpendicular line, and pick three other lines with that slope, but with different b values. Read things carefully.
March 18, 2015

MATH
the slope has to be the same, so just choose other values for b. The problem is, a line with slope -2/3 is not perpendicular to a line with slope 2/3.
March 18, 2015

math
well, you can find the exact interval: it's where g" < 0 Since g" = (x^2-4x+16)/(x-2)^2 g" < 0 where x^2-4x+16 < 0 Since that is never negative, there is no interval where g(x) is concave down. g(x) = (x^2+4x-13)/2 - 12log(x-2) See that this is so ...
March 18, 2015

Calculus AB: Area Between Curves
your first task is to find the tangent line at (-1,4). Since that is y = -x+3, you need to find where else the line and the curve intersect. That will be at (2,1). See the curves at http://www.wolframalpha.com/input/?i=x%5E3-4x%2B1%3D3-x So, now just add up all the little ...
March 18, 2015

precap
kewl!
March 18, 2015

Math
see related questions below
March 18, 2015

Algebra
well, you add 50 each hour, starting at 25, so ...
March 18, 2015

Mathematics
(3x-1)(x-5) = -11 3x^2 - 16x + 5 = -11 3x^2 - 16x - 16 = 0 (3x-4)(x-4) = 0 Now you can find x. If two numbers multiply to zero, one or the other must be zero! So, x = 4/3 or x = 4
March 18, 2015

math
well, how many minutes in a day? Multiply that by 75.
March 18, 2015

Math
(x+√(x^2-5))/5 multiply top and bottom by (x-√(x^2-5)) and you have (x+√(x^2-5))(x-√(x^2-5)) --------------------------------- 5(x-√(x^2-5)) since (a+b)(a-b) = a^2-b^2, that is x^2-(x^2-5) ----------------- 5(x-√(x^2-5)) 5 --------------- 5(...
March 18, 2015

Math
log_m(m/n) = 1 - log_m(n) log_n(n/m) = 1 - log_n(m) adding things up, we have 2 - log_m(n) - log_n(m) = 2 - 1/log_n(m) - log_n(m) if m>=n, log_n(m) >= 1 so, if you call log_n(m), that gives you 2 - 1/x - x This achieves a maximum value of 0 at x=1, which is when m=n.
March 18, 2015

math
26.25 * 2^5 = 840.00
March 18, 2015

math
Take a look at this site https://ca.answers.yahoo.com/question/index?qid=20101128113606AAYRwSF and you should be able to see why the limit is e^-3
March 18, 2015

math
there are two 2's and 6 possible stopping places. So, P(2) = 2/6
March 18, 2015

Pre-Calculus
given the x-intercepts, y = a(x-2)(x-7) The vertex is midway between the roots, at x = 9/2 y(9/2) = a(5/2)(-5/2) = -25/4 a Since we want y(9/2) = 25, a = -4 y = -4(x-2)(x-7) See http://www.wolframalpha.com/input/?i=-4%28x-2%29%28x-7%29
March 17, 2015

Math
do parens first, separately. Within them, multiplication first: (100-7x2+3) (100-14+3) Now add/subtract, left to right (86+3) (89) Now you have 89/10 = 8.9
March 17, 2015

Math
350/(375+275+350)*360 = 126
March 17, 2015

math
Kibet rode from 8:00 to 9:30 Akinyi rode for 20/80 = 1/4 hr, so the car arrived at 8:45 Now figure the time difference.
March 17, 2015

Math
since half the teams are out after n rounds, you want 64 * 2^-n = 1
March 17, 2015

Math
just add up the values of the coins: 25x + 10(30-x) = 585 Now find x, and go from there.
March 17, 2015

math
you want cost = revenue 2x+10 = -5x^2+21x 5x^2 - 19x + 10 = 0 I think that R(x) is bogus, since it starts to decline as more shorts are sold. http://www.wolframalpha.com/input/?i=2x%2B10+%3C+-5x%5E2%2B21x
March 17, 2015

Math
what does 2_3 mean? 2/3? 2.3?
March 17, 2015

Math (ASAP)
the answer to the first one is not 2. What does that even mean? 3x + 2y < 6 means that 2y < 6-3x y < 3 - 3/2 x o, you graph the line y = 3 - 3/2 x and everything below that line is where y < 3 - 3/2 x. It's a region, not a number. 2x^2 + y > 2 y > 2 - 2x^...
March 17, 2015

algebra
shifting down 2 means you subtract 2 from the y values. So, what do you think?
March 17, 2015

Vectors
in (c) the two s- and t-vectors are collinear.
March 17, 2015

Algebra II
yes. lne is redundant. ln means log_e. SO, things are a bit clearer if you do it 2lnx = 2 lnx = 1 x = e^1 = e
March 17, 2015

Vectors
clearly (b) why was there any question?
March 17, 2015

Integral Calculus
This is discussed clearly at http://www.ltcconline.net/greenl/courses/202/multipleIntegration/MassMoments.htm Where do you get stuck?
March 17, 2015

algebra
can't seem to see the diagram . . .
March 17, 2015

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

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