Posts by Steve
Total # Posts: 50,431
a(r^4-1)/(r-1) = 30 a + ar^3 = 18 (r^4-1)/((r-1)(1+r^3)) = 5/3 3r^4-3 = 5r^4-5r^3+5r-5 2r^4-5r^3+5r-2 = 0 (r-1)(r-2)(r+1)(2r-1) = 0 r = 1/2, 1, 2, -1 r=1,-1: extraneous solutions r=2: 2,4,8,16,... r=1/2: 16,8,4,2,...
ever think of using math notation instead of words? f(x) = 4x for x <= 3 7-x for x > 3 ?[1,7] f(x) dx = ?[1,3] 4x dx + ?[3,7] 7-x dx = 2x^2[1,3] + 7x - x^2/2 [3,7] = [(2*3^2)-(2*1^2)]+[(7*7-7^2/2)-(7*3-3^2/2)] = 16+8 = 24
3 log(u^2/v) 3(2logu - logv)
the lines intersect at (15,20) The new line has slope -3/5, so it is y-20 = -3/5 (x-15) now massage that into the form you want.
not 810, but vh=810*cos42 Read the information that was given to you.
With 90 cattle, he has 9/4 as many mouths, so 4/9 as long to eat: about 16 days
I cannot find a function of the form 80 + a*e^(-kx) which fits more than two of the points, since when x=0, you have 80+a=176, so a=96 and when x=1 you have 80+96e^-k = 169 e^-k = 89/96 k = ln(96/89) = 0.07571 80+96e^(-0.0757x) does not fit any of the other points.
Each inch has 8 1/8-inch parts. So, 3 1/2 inches is 28 times as long. so, ... or, each inch represents 8 feet. so, 3.5 inches is ? feet
terms are separated by + and - signs.
If you plug in your numbers here http://davidmlane.com/hyperstat/z_table.html You will see that it is the 87th %ile.
p+q = 150 3/4 p = 2/5 q I suspect a typo, as the solution is not an integer.
A delivery man pushes the button to ring the doorbell. Which of the following forms of energy is not involved in this process? electrical sound mechanical gravitational my answer is gravitational
You have 4 sides. Add 'em up and subtract from 30 to get the 5th side. Now, how many are equal?
a) which two factors of 6 add to 5? b) which two factors of 6 differ by 1? c) which two factors of 6 add to 1?
even integers differ by 2, so the three numbers are x, x+2 and x+4. Now you are told that x(x+2) = 11(x+4)-8 Now solve for x.
the range for an angled shot is R = v^2/g sin2? so, plug in your numbers. Remember to convert ft/s to mi/hr.
Math - Calculus
Recall that the vertical height h is h(t) = 6 + (810 sin42)t - 16t^2 so, just solve for t when h=0.
C = P if 0 < P <= 100 Now you can do the part where P > 100, right?
No. That is only the numbers between 0 and 15. You are not restricted to positive values.
real numbers that are less than 15 means s<15
see related questions below...
In the first 30 minutes you have walked 3 miles. Then, after a total of 40 minutes, you start walking again. So, D(t) = 3 + 1/60 (t-40) if 40 < t <= 65
Since the fraction is pointless as written, I assume you meant M = (log(E)-11.4)/1.5 1.5M = log(E)-11.4 log(E) = 1.5M+11.4 E = 10^(1.5M+11.4)
the ^ is used for exponents. I think he means 2e^x^2 + e^x = 4 sometimes they use ^x for ?x In either case, the equation seems unlikely. What do you say, Jason?
Just use the usual growth formula. It took 388 years, so 24e^(388r) = 4*10^12
correct. It can't get from -2 to 6 without going through 0 somewhere in between. You also need to mention that f(x) is continuous. That is necessary.
recall that x = r cos? y = r sin? now just plug in your numbers.
No way. I don't think you mean "permuted." Maybe a bit more explanation of the problem would make it clearer just what you have in mind.
7/12 as many stories -- 7/12 as long to type them.
You are correct
Number the pairs 11 22 33 44 55 66 Now, the left shoes can be arranged in 6! ways. For each of those ways, there are 6! ways to arrange the right shoes. Of those, there are 5! arrangements with one matching pair 4! with two matches, ... 1! with 6 matches. So, it seems to me ...
Grade 6: money and measures
1.50n + 10.00*floor(n/30) = 450 n = 246.7 Check: 246 games: 246*1.50 + 10*8 = 449.00 Add $1.50 for the 247th game, and that puts him over the top.
x/15 = cos75
(1 1/4)^2 = (5/4)^2 = 25/16 ft^2
Try reading this discussion. It is the same problem, different points. http://math.stackexchange.com/questions/1300484/distance-between-line-and-a-point
Vectors - Maths
since CD = CB, vector CD = v If we let AD be vector z, then u.z = (x-v).(x+v) = x.x-v.v Since |x| = |v|, that is zero. So, u and z are perpendicular.
Dependent and Independent variables
a. pick some values for x, and then calculate y. b. pick two of the (x,y) pairs and plot them on graph paper. Draw a line through the two points. All of the other points in your table will also lie on this line. If they do not, you have made a mistake. c. x is independent. You...
w(2w+4) = 48 w(w+2) = 24 4*6 = 24 4*12 = 48 or, you can solve the quadratic.
one way: determine where a perpendicular line intersects each, and find the distance between the two points of intersection. another way: determine the equation of one of the lines, then find the distance to it from a point on the other line, suing the formula d = |Ax+By+C|/?(...
c = 5.00 + 1.50t
distributive better go back and read up on both topics
well, 2?r^2+2?rh = 500 2?rh = 320 So, 2?r^2 = 180 ?r^2 = 90
You need to know the slope of the glider's descent. If he drops straight down, there is no triangle. That is, you need to know his horizontal speed. The vertical drop of 50 ft/s is no good by itself.
If the string covers the entire surface area, consider it a bunch of 3-inch circles. Now, you have to know the diameter of the string. If it is 1/20 inch, then there will be 16*20 = 320 loops. So, nail that down, and you can answer the question.
actually, the above solution applies if y is the position function. Since it is itself a rate, you need the average value of the function. That is ?[7,10] x^3+2x^2+3 dx ----------------------------- = 782.25 10-7
220+45h Note that when h=0, there is just the flat fee. Then add 45 each time h increases by 1.
into to algebra
add up the amount of alcohol in each part. It must equal the alcohol in the final mixture: .15*150 + .70x = .45(150+x)
Introduction to negative linear relationships
d = m Maybe you need to specify a bit more.
general equation x = a sin(b(t-c))+d Since equilibrium is x=0, d=0 x = a sin(b(t-c)) the period is 9, so b = 2?/9 x = a sin(2?/9 (t-c)) If it travels .4 m in a cycle, the amplitude is 0.1, so x = 0.1 sin(2?/9 (t-c)) Now we have a problem. If x(0) = -0.1, that is its minimum ...
.20x = 1
4x - 30 = -3x - 32 add 3x to both sides 7x - 30 = -32 add 30 to both sides 7x = -2 divide by 7 x = -2/7
1st step: lose the parentheses: 2(2x-7)-16=3(-x-7)-11 4x-14-16 = -3x-21-11 . . .
angle C = 85° (180-52-43) Labeling the sides a,b,c opposite angles A,B,C, you want side b, since angle B is the smallest angle. b/sinB = c/sinC b/sin43° = 50/sin85° Now just solve for b
it takes (50-30)/10 = 2 seconds to reach the final velocity. s = 30t + 1/2 t^2 Now just plug in t=2.
1. Just use the power rule recall that 1/x^2 = x^-2 2. product and chain rule: y = x^5 (1+x)^5 y' = 5x^4 (1+x)^5 + x^5 * 5(1+x)^4 = 5x^4(1+x)^4 (1+2x) 3. quotient rule. Assuming the usual carelessness with parentheses, y = (4-x^2)/(2x+3) y' = [(-2x)(2x+3) - (4-x^2)(2...
the slope-intercept rule is called that for a reason... Q2. y=kx, so y/x=k, a constant. You want y such that y/10 = 24/8
huh?? !! 13/16 = 0.8125 h(13/16) = -16(13/16)^2 + 26(13/16) + 5 = 249/16 = 15.5625 or, h(.8125) = -16*.8125^2 + 26*.8125 + 5 = -10.5625+21.125+5 = 15.5625 Too bad you couldn't be bothered to show your work ...
don't forget your Algebra I. h(t) is just a quadratic, and the vertex (maximum height) is at t = -b/2a = 26/32 = 13/16 Now use that to find h(13/16)
Sn = n/2 (A1+An) = 8/2 (6+46)
4rpm = 16 in/min, so 1 rev = 4in 2?r = 4, so r = 2/? for the 8" wheel, the ratio of radii is 8/(2/?) = 4? So, if its radius is 4? as big, its speed is 1/(4?) as fast, or 16/(4?) = 4/? in/min It makes 1/(4?) * 4 = 1/? rpm Your unknown radius is ok, but I don't see how ...
Calculus for Business Administration and social s
?(432x^12) = ?(8*27*2 x^12) = 6x^4 ?2
Let the length AM=1. Let C be the midpoint of AM. Draw the line CO. It has radius 1/2 + r. Draw the line MO. It has length 1-r. So, in the right triangle CMO, 1/2^2 + (1-r)^2 = (1/2 + r)^2
you know that the length is between 19.5 and 20.5 meters the width is between 2.5 and 3.5 meters So, use the largest and smallest values to get the range of perimeters.
I'll do one: C(t) = 45 - (45-27)/4 * 4 - (27-18)/2 * (t-6) = 27 - 9/2 (t-6) = 54 - 9/2 t if 6 < t <= 8 This should give a clue to the other parts...
average value is integral divided by the interval width.
I'm guessing you meant ?[4,7] (1+x^2) sinx dx or something. Try reposting with better notation. You can also use my notation above at wolframalpha.com to evaluate integrals.
not quite clear on your notation, but the distance is the integral of the velocity over the interval.
recall that KE = 1/2 mv^2 PE = mgh Now just plug in your numbers.
visit this site for Z table stuff: http://davidmlane.com/hyperstat/z_table.html
Good work, but I interpret the wheel size as the diameter. If so, same steps apply, just adjusted for the smaller radius.
you can play around with Z table stuff here: http://davidmlane.com/hyperstat/z_table.html For this problem, you find that 99.7% of the area lies less than 2.748 ? above the mean.
12r+11s = 228 6r+5s = 108 ...
I don't know what you mean by it "didn't work." It just shows that the expression is never positive. (x-2)^2 is a square, so it is always positive So, -(x-2)^2 is never positive. Trying to plug a formula into a request for a proof will never work. The logic ...
= -(x^2-4x+4) = -(x-2)^2
x+y = 900 .05x + .08y = 64.50
12a+2c = 122 7a+8c = 160 ...
Ca comprises 2/3 of the 1.28g CaCO3, or 0.853g So, assuming that all of the calcium is contained in the CaCO3, the 0.853g is 31.37% of the 2.72g pill
The maximum area occurs when the fencing is divided equally among lengths and widths. For all 4 sides fenced, that is a square. In this case, with the length parallel to the wall, we have length=500/2 = 250 and width = 500/2/2 = 125 so the area is 250*125 = 31,250 This is ...
try typing the equations yourself; copy/paste does not do well here. You can copy and paste the ? symbol as you go.
.13x + .09(x+700) = 239 x = 800 as above.
Draw diagonals AC and DF. The hexagon is now divided into a parallelogram (rectangle?) and two congruent triangles. AC and DF can be found using the law of cosines, since all the interior angles are 120 degrees.
what you mean is 2 <= x <= 5 This is just a parabola, with vertex at (2,-1). So, clearly, f(2) = -1 is the minimum value. The axis of symmetry is at x = 2, so f(5) will be the max on the interval [2,5], since it is away from the axis.
So, why not use a 1? |3y+4|-1 = 0 |3y+4| = 1 3y+4 = 1 3y = -3 y = -1 3y+4 = -1 3y = -5 y = -5/3
for i=1 to 5 prompt for marks read marks[i] next i
number base help plz
1234 = 4^2 + 2*4 + 3 = 2*8 + 8 + 3 = 338
x = u/(1 + u^3) y = u^2/(1 + u^3) dy/dx = dy/du / dx/du dy/du = u(2-u^3)/(1+u^3)^2 dx/du = (1-2u^3)/(1+u^3)^2 dy/dx = u(2-u^3)/(1-2u^3)
Mathematics of finance 1
see related questions below
bricks: 180*6*50 * 8 = ? tank: Assuming a square base, v = 150*150*40/1000 L
the principal (not principle) can be found by solving P*1.04^2 - P = 1632 P(1.04^2-1) = 1632 ...
If x is at 3%, then the rest (12000-x) is at 5%. So, add up the interest: .03x + .05(12000-x) = 460
If he traveled x miles by bus, then he went 1900-x by plane. Since time = distance/speed, x/60 + (1900-x)/700 = 5
w = width 54/w = height The page area is thus a = (w+1)(54/w + 2) Assuming you want minimum page area, da/dw = 0 at w = 3?3
The amount of bacteria after n seconds is A = Q*3^(n/15)
1W = 1J/s = 1N-m/s so, 3500 kg * 9.8N/kg * 9.50m /(9000N-m/s) = 36.2 s
PV=kT, so PV/T is constant You want T such that 2*25/(T+273) = 1*20/(120+273)