Sunday
March 29, 2015

Posts by STEVE


Total # Posts: 30,154

mathematics
a+6d = 3 a+11d = -3 clearly, 5d = -6, so d = -6/5 that means a = 51/5
March 19, 2015

Algebra
Nope.
March 19, 2015

Math
always rearrange things into descending powers. Set equal to zero because after you factor it, you know that the product can be zero only if one of the factors is zero. f^2+7f-60 = 0 (f+12)(f-5) = 0 f = -12 or 5 6x^2-x-15 = 0 (2x+3)(3x-5) = 0 x = -3/2 or 5/3 6(y-3)^2 - (y-3...
March 19, 2015

math
each man can do 1/(20*24) = 1/480 of the job in a day. So, in 6 days, they have done 6*20/480 = 1/4 of the work. So, if the new men work at the same speed, you need to do 3/4 of the job in 15 days. m additional men can do 15m/480 = m/32 of the job in 15 days. So, we need m/32...
March 19, 2015

math
3-32 = -29 Divide that into two equal parts, and k has the same difference before and after: k = 32-29/2 = 35/2
March 19, 2015

electrical principles
the 4 240Ω resistors have a combined resistance of 60Ω Add that to the 40Ω in series, and the total is 100Ω P = E^2/R, so the parallel group dissipates 960W Now just figure the energy of the heater.
March 19, 2015

Math
1/6 + 1/3 + 1/(4/3*6) = 5/8 So, they will take 8/5 hr or 1 hr 36 min. Now just figure 1/3 - (1/6 + 1/8) = 1/24 so it takes 24 hrs to empty the pool
March 19, 2015

math
suppose y=0. That means x+z = 18 x-z = 26/5 x = 58/5 z = 32/5 So, the largest x can be is 58/5 Now, suppose we toss in y. If we subtract y/2 from both x and z, then the difference between x and z is still 26/5, and the sum is (x-y/2) + y + (z-y/2) = x+z = 18 For example, if y...
March 19, 2015

Quick math help
the one which includes the same variables and the same powers: A
March 19, 2015

algebra
as usual, just add exponents. 7^√3 * 7^√2 = 7^(√2+√3) Don't be spooked by radicals. They're just numbers.
March 19, 2015

Geometry
suppose you rotate around (0,0). That takes (x,y) -> (-y,x) Shifting the origin to (-8,3) changes the distance, and gives us (x+8,y-3). So, the shift takes (5,-9) -> (13,-12) Then the rotation takes (13,-12) -> (12,13) reflection through the line y=9 takes (x,y) ->...
March 19, 2015

Advanced Algebra
If you have the two points at the ends of the interval [a,b], then no matter how f(x) twists and turns in the interval, the average rate of change is the slope of the line joining (a,f(a)) and (b,f(b)). That is, (f(b)-f(a))/(b-a)
March 19, 2015

Math
clearly, 190 = 47*4 + 2 That means 47 whole cycles of digits 2,4,8,6 have been used, leaving 2 more: 2 and 4. 2^6 ends in the same digit as 2^2 and so on, till 2^190 = 2^(47*4) + 2
March 18, 2015

Math
Note that the powers of 2 end in digit that cycles: 2,4,8,6,2,4,8,6,... Since 190 = 47*4 + 2, 2^190 ends in 4 So, the remainder is 4 when divided by 5. If AC=32, the the hypotenuses AC and AD are in the ratio 2:1. So also are sides AD and AB. So, AB=12, making BC=24 And yes, ...
March 18, 2015

Math
I think you garbled your question, but since the cone and sphere share a radius, and the height of the cone is the same as the radius of the sphere, the volumes are hemisphere: 2/3 πr^3 = 2/3 π * 3^3 = 18π cone: 1/3 πr^2 h = 1/3 π * 3^2 * 3 = 9π
March 18, 2015

Math
the large triangle has base b and height h. So, its area is bh/2 The smaller triangle has base b/2 and height h/2, so its area is (b/2)(h/2)/2 = bh/8 = 1/4 (bh/2)
March 18, 2015

Math
This problem comes in many guises. One can be found here: http://math.stackexchange.com/questions/105084/a-line-which-bisects-two-sides-of-a-triangle-is-parallel-to-the-third Naturally, the area of the small triangle CBE is 1/4 the area of CAD, since it has half the base and ...
March 18, 2015

Math
You need to understand the concept of the slope of a line. It says how fast y changes as x changes by 1. That is, if the slope is 3, y increases by 3 whenever x increases by 1. If the slope is -2, y decreases by 2 when x increases by 1. So, given two points, the slope is the ...
March 18, 2015

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

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