Monday

April 20, 2015

April 20, 2015

Total # Posts: 30,680

**math104**

it's not a cross-product. It's just times. 10log(2.64*10^-5/10^-12) = 10log(2.64*10^7) = 10(7+.4) = 74 dB
*March 20, 2015*

**Math**

just use your formula for the FV of an annuity.
*March 20, 2015*

**Trigonometry - Oops**

My bad - switched x and y: (y/x + 1/√3)/(1 - y/x√3) = (y+35)/x x^2+y^2 = 25^2 x = 19.408, y=15.759 so, z = 54.343 not very far off, really, eh?
*March 20, 2015*

**Trigonometry**

as usual, draw a diagram. Let T be the top of the pole B be the bottom of the pole P be the point where the wire meets the ground. Draw a horizontal line from P, and extend TB into the ground, so that Q is the intersection of the horizontal from P and the vertical from T Then ...
*March 20, 2015*

**math**

so far so good. The complete solution turns out to be, as I'm sure you have worked out: y = c1 e^-x + c2 e^-2x + 1/4 (2x^2-6x+7)
*March 20, 2015*

**math(Discrete)**

As I recall, ∃! means "there exists exactly one" So, I guess the negation would be There exists at least one or there is none (∃ ∨ ∄) or, maybe ~∃!
*March 19, 2015*

**trig**

since cos(x+pi) = -cos(x), y = -3cos(x) - 3 Not sure what you want to know about it. -3cos(x)-3 is 3cos(x+pi)-3 shifted left or right by pi, and then flipped over. Since cosx has a period of 2pi, you can see why this would result in an identical graph.
*March 19, 2015*

**Geometry**

see the 1st related question below.
*March 19, 2015*

**Geometry**

since the circumference is 3π feet, it makes 45/3π = 15/π turns per second. That is π/15 seconds per turn. So, it takes 100π/15 = 20π/3 seconds to do the job.
*March 19, 2015*

**Math**

50m is the total length of the paths, but that was not the question. 30m*20m = 600m^2 you don't say which path runs the length and which the width. If the wider path is the longer, then the area used up by the paths is .8*30 + .7*20 - .8*.7 = 37.44 So, that leaves 600-37....
*March 19, 2015*

**Geometry**

12 turns/5s = 2.4 turns/s each turn of a wheel of diameter d is πd inches, so (225in/s)(1s/2.4rev) = 225/2.4 = 93.75 in/rev so, πd = 93.75 d = 29.84 in
*March 19, 2015*

**Geometry**

actually, that's not quite right. If the circumference is c, and the tire width is w (both in feet), the area of track made by one turn is cw. So, the tire makes 250/cw turns. Pick your own c and w.
*March 19, 2015*

**Geometry**

if the tire has width w and diameter d, then w*πd = 250 ft^2 wd = 250/π ft^2 so, pick any width and diameter (both in feet) that multiply to 250/π
*March 19, 2015*

**Math**

2.5 min = 150 sec, so A. 150+4*10 B. S10 = 10/2 (2*150 + 9*10)
*March 19, 2015*

**Math**

A: 1.6 * 0.8^5 B: 1.6 * (1 - 0.8^7)/(1-0.8)
*March 19, 2015*

**algebra**

I assume you mean y = -2√(3x-12)-5 = -2√(3(x-4)) - 5 so, the function √x has been shifted right by 4, scaled horizontally by a factor of 1/3, reflected over the x-axis, stretched vertically by a factor of 2, and shifted down 5.
*March 19, 2015*

**Calculus**

see the 2nd related question below. Just change the numbers.
*March 19, 2015*

**Algebra**

#1: √(11^2 - 7^2) #2: √((5+3)^2 + (6-1)^2) #3: ((-6+8)/2,(-2+4)/2) Better review your text for these topics.
*March 19, 2015*

**Alegbra 1**

just plug in the values for t, using the formula 25000 * 1.08^t For example, after 2 years, the salary is 25000 * 1.08^2 = 29160
*March 19, 2015*

**Math**

what's the trouble? Just plug in the values for t. For example, Q(800) = 300 e^(-0.000324*800) = 231.5006
*March 19, 2015*

**Math**

#1 False, if you meant (5x+1)/(x+2)(x-1) Do partial fractions just the way you add fraction of unlike denominators. 2/3 + 3/4 = (2*4 + 3*3)/(3*4) Now, you are given the result, and you want to find the parts. So, we are looking for (5x+1)/(x+2)(x-1) = A/(x+2) + B/(x-1) = (A(x-...
*March 19, 2015*

**Math**

oops. i gave the price per book. So, 60 books would cost p(60) = 60(86.45 - .055*60) = $4989.00
*March 19, 2015*

**Math**

No idea. Maybe there's a price break from $86.45/book to $80.95/book if you buy more than 100 books. In that case, 60 books cost 60*86.45 = $5187.00 There are many different functions that pass through those two points. I assume you are looking for a linear relationship. ...
*March 19, 2015*

**math**

x/25 = cos 63°
*March 19, 2015*

**math**

3500 * 1.04^6
*March 19, 2015*

**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*