Tuesday
February 21, 2017

# Posts by steve

Total # Posts: 48,677

Math
215lb * 1kg/2.2lb = 97.727kg 97.727kg * (4.8mg/day)/kg = 445.091 mg/day 445.091 mg/day * 11ml/16mg = 306ml/24hr = 76.5 ml/(6hr)
January 23, 2017

math
square roots that end with a decimal?? square roots are called radicals, but so are cube roots, etc. 3?2 = ?18 = ?18.000 not sure where you're going with this.
January 23, 2017

Precalulus
I am assuming the usual carelessness with parentheses, and getting -2/(-3x-7) - 3/(2x-1) = 3/2 -2*2(2x-1) - 3*2(-3x-7) = 3(-3x-7)(2x-1) 4-8x + 18x+42 = -18x^2-33x+21 18x^2+43x+25 = 0 (x+1)(18x+25) = 0 x = -1 or -25/18 Assuming a little less sloppiness, I'd read (-2/-3)x - ...
January 23, 2017

just review the techniques of long division. You can see all the details if you play around here: http://calc101.com/webMathematica/long-divide.jsp It's just like regular numeric long division, as long as you line up the powers of x the way you do columns of digits in big ...
January 23, 2017

Math
you can play around with these things here, and see all the details. http://calc101.com/webMathematica/long-divide.jsp
January 23, 2017

Math
96/6 = 16 All we know is that the base has an area of 16 ft^2. I'm sure you can some up with two factors of 16 which could be the length and width.
January 23, 2017

MATH @Damon @ms. Sue
f(x) = 2*3^x on [0,1] the average rate is (f(1)-f(0)))/(1-0) = (2*3^1 - 2*3^0)/1 = 6-2 = 4 on [2,3] the average rate is (f(3)-f(2))/(3-2) = (2*3^3 - 2*3^2)/1 = 54-18 = 36 the ratio of the rates is 36/4 = 9. The reason the rate increases is that exponentials grow ever faster. ...
January 23, 2017

Science
is it a windy day? is it raining? is the street sloping? curving?
January 23, 2017

Math
12:01 12:29 12:46 I'm sure you can come up with others. Heck, use a clock if you need to.
January 23, 2017

Calculus
#1. Using horizontal shells of thickness dy, r = y h = y^2 - (3y^2-2) = 2-2y^2 v = ?[0,1] 2?rh dy = 2??[0,1] y(2-2y^2) dy = ? You got r and h reversed, but the product was luckily the same. Unfortunately, you added instead of subtracting. Using discs of radius y and thickness ...
January 23, 2017

Math
well, 9 is 3/4 dozen, so it will cost 3/4 of 20, or 15 Or, since the unit cost as the ratio of money:bananas is constant, x/9 = 20/12
January 23, 2017

the C balances as written, since there is one on each side. That leaves you with CH4 + ?O2 > CO2 + ?H2O you have 4H on the left, so you will need 2H2O on the right. That gives CH4 + ?O2 > CO2 + 2H2O That balances the C and H, so now you need 4O on the left, which is 2O2 ...
January 23, 2017

Math
correct, so now you can find the breadth, b.
January 23, 2017

Math
2(b + 2b-8) = 56
January 23, 2017

algebra
an equation has no coordinates. If you want the coordinates of the two lines' intersection, then just solve for x and y. The first equation tells you that y = 2x+11 so use that in the 2nd equation and you have x+4(2x+11) = 17 x+8x+44 = 17 9x = -27 x = -3 Now, y = 2x+11 = 2...
January 23, 2017

algebra
sorry. (a) we don't have the test in question (or even the class!) (b) we don't help students cheat we will help you learn how to solve the problems, though, if it's not already too late ...
January 23, 2017

Math
If those are logs to the same base, then 5(x-2)*8(x-4) = 6(x-1) x = (123+?2089)/40 If those are logs to different bases (5,8,6), it takes some more work. Changing all to natural logs, we have Log5(x-2) + log8(x-4)= log6(x-1) ln(x-2)/ln5 + ln(x-4)/ln8 = ln(x-1)/ln6 ln8*ln6*ln(x...
January 23, 2017

Pre-Calculus
the water surface has a constant area of 800 in^2. So, every inch of water adds a volume of 800 in^3. So, after t minutes, the tank holds v(t) = 7*800 + 800t in^3 You should probably restrict the domain of t so that the tank does not overflow.
January 23, 2017

Study School (Math)
t+u = 9 10t+u+9 = 10u+t Now just find t and u, then answer the question.
January 23, 2017

college algebra
try writing it without the words. This is a math problem, not an English essay ... -4/(2x+3) + 1/(x-1) = 1/((2x+3)(x-1)) -4(x-1) + 1(2x+3) = 1 -4x+4 + 2x+3 = 1 -2x+7 = 1 2x = 6 x = 3
January 23, 2017

college algebra
Put the words into math. You are told that: s+g = 10000 g = s-3000 Now just solve for s and g.
January 23, 2017

Math
(48ft*48ft) * (1can/192ft^2) = (2304ft^2) * (1can/192ft^2) = 12 cans
January 23, 2017

maths
This one is long, but not overly complicated. I expect that u=x^2 is a good substitution to start with. Then I expect a trig or hyperbolic trig substitution will come in handy. I suggest you enter your integrand at this URL and it will show all the steps involved. http://www....
January 23, 2017

Math
no, since the discriminant (b^2-4ac) is negative. The roots are complex.
January 22, 2017

math question
distance=speed*time So, if it flew at 800km/hr for x hours, then it flew at some unknown speed s for 2x hours: 800x + s*2x = 700*3x 800+2s = 2100 2s = 1300 s = 650
January 22, 2017

Precalculus
oops. the cubes factor as (x + (x+1))(x^2-x(x+1)+(x+1)^2)
January 22, 2017

Precalculus
For the complex solutions, note that you want x^6 - (x+1)^6 = 0 This is just the difference of two squares, so it factors as (x^3 - (x+1)^3)(x^3 + (x+1)^3) = 0 The left factor becomes just a simple quadratic when expanded, as the x^3 terms go away. The right factor is the sum ...
January 22, 2017

Algebra2
f(x)=3x-7 and g(x) = -2x-6 find (fog)(4)
January 21, 2017

Algebra2
let f(x) = -2x+4 and g(x) = -6x-7 find f(x)-g(x)
January 21, 2017

Math
w = 4m m + w = 150
January 18, 2017

math
assuming the cost is 63/m^2, it will come to (5-2*.5)(4-2*.5)(63)
January 18, 2017

science - eh?
huh? If it keeps accelerating, will it come to rest at all? I cannot parse the language to come up with a question.
January 18, 2017

math
the height:shadow ratio is the same, so x/42 = 6/7
January 18, 2017

math
1/5 = 0.2 = 20% think you can handle that now?
January 18, 2017

Math
Nope. y2 = -5, not 5 (-5-3)/(1 - -3) = -8/4 = -2
January 18, 2017

physics
speed is m/s v = at it accelerated for 15/.1 = 150 seconds after another 150 seconds, until t=150 s = 5 min. Then it decelerated for the remaining 3 minutes, or 180 seconds. That means it decelerated at 15/180 = 1/12 m/s^2 v(t) = t/10 for 0 <= t <= 150 15 for 150 < t...
January 18, 2017

English Grammar
January 18, 2017

physics
at max height, v=0 sin 30 = 1/2, so the velocity is given by 39.2/2 - 9.8t = 0 t = 4 So, it rose for 4 seconds to max height. Now recall that the height is given by h = 39.2t - 4.9t^2 Just plug in t=4
January 18, 2017

Math
b = (27+5)x
January 18, 2017

Algebra
You can play around with polynomial division here: http://calc101.com/webMathematica/long-divide.jsp
January 18, 2017

Math- Inequalities
the easy way is to use what you know about the graphs of parabolas. Since the coefficient of x^2 is positive, you know that the parabola open upward. Since the graph crosses the x-axis at the roots, the function is negative between the two roots, and positive below and above ...
January 17, 2017

math
taxes: .22*240 = ? after taxes: 0.78 * 240 = ? left to spend: .60 * (0.78 * 240) = ? savings: .40 * (0.78 * 240) = ?
January 17, 2017

Basic Algebra
7.25h >= 125
January 17, 2017

Just checking Math-Absolute Value
nope. That is the distance from x to 4. Try marking a number line. The distance from x to h is |x - h|.
January 17, 2017

Math (Semicircle)(Pre-calc)
a circle with center at (4,0) and radius 4 is (x-4)^2 + y^2 = 16 or, y = ?(16-(x-4)^2) The left semicircle has center at (-4,0) and radius 4, but lies below the x-axis, so So, f(x) = -?(16-(x+4)^2) for -4 <= x <= 0 ?(16-(x-4)^2) for 0 <= x <= 4
January 17, 2017

Math
If the meet after x hours, then 1.5 + 4.5x = 10x
January 17, 2017

Recursive Sequence and its Limit
A little work shows that the nth term a<n> = 3/(2^(n+1)-1) Now, do you want the limit of the terms, or the limit of the sums? a<?> = 0 S<?> = 3(sum 1/(2^(n+1)-1) I thought that would be relatively simple, but you can see below that it is not: http://www....
January 17, 2017

Math
7P3 = 210
January 17, 2017

Math
the vertical distance moved is 12 sin25° = 5.07 ft Work = PE lost = 5.07 * 180 ft-lb
January 17, 2017

math
37A-A = 36A 36A/4A = 9 36A is the 10th term.
January 17, 2017

Math
100 coffee a 50% solution ???
January 17, 2017

math
42 is the answer to The Ultimate Question of Life, the Universe, and Everything. So it is surely the answer to whatever puny question you have in mine.
January 17, 2017

Maths factorise
note that the fits two terms are 3p(x-y) and then use grouping.
January 17, 2017

Science
well, 1 mole fills 22.4L 28cm^3 = 0.028L So, you have .028/22.4 = 0.00125 moles (1/800 moles) Thus, if the mol wt is x grams, x/800 = 0.4 x = 320
January 17, 2017

Algebra
I assume the usual sloppiness with parentheses, and that your original equation was x/(x-2) + (x-1)/x + 1 = 0 If you found x=0 as one solutions, you need to exclude it. (x-1)/x is undefined when x=0 So, while it may appear that x=0 is a solution, it is not acceptable as a ...
January 17, 2017

Algebra 2
What you have is already in recursive form. Each An depends on the previous term. Now, if you want an explicit formula, An = 5*3^(n-1) + 2
January 17, 2017

Algebra 2
If you meant (2?(3x^5) - 2?y)^2 = 4(3x^5) - 8?(3x^5y) + 4y Not sure how that's any simpler, though...
January 17, 2017

Maths
Huh? If ABCD is a parallelogram. AB∥CD and has the same length.
January 17, 2017

Maths
recall that the area of a rhombus is 1/2 the product of its diagonals.
January 17, 2017

Mathematical Induction
you need to show that a<n+1> > a<n> (increasing) or a<n+1> < a<n> (decreasing) If you expand the expression from the recursion, you can clearly see that it is. Once you can show that each term is greater (or less) than the previous one, then you ...
January 17, 2017

riddle
Guys! This is easy! The answer is NEW MOON! The new moon is old and also 'new' at the same time!
January 17, 2017

math;);)
draw a side view. Draw a circle Mark a vertical diameter Draw a horizontal radius from the center O The radius has length 3 Draw another vertical line 1 unit away from the center. On that vertical line, mark its intersections with the horizontal radius (A) and the circle (B). ...
January 16, 2017

Calculus
Looks good to me.
January 16, 2017

calculus
f(x+3) = 2^(x+3) = 2^x * 2^3 = 8*2^x f(x-1) = 1/2 * 2^x PI, not PIE! G(0) = sin(2*0) = sin(0) = 0 similarly, just plug in the other values for x. These are some of your standard angles, whose trig functions you should know. They come up so often, it's better if you just ...
January 16, 2017

calculus
just look at the graph of sin(x). Clearly, it is defined everywhere, so its domain is all real numbers. sin(2x) gets to each x value twice as fast, but has exactly the same domain: all real numbers.
January 16, 2017

maths
make the two colors anything except black.
January 16, 2017

Math
tan(x) = 45/60 x = 36.87° As for the time of day, since you don't give any information on location, assume sunrise is at 6:00 am and sunset is at 6:00 pm. In that case, 180° of arc covers 12 hours. Use that to find how many hours after 6 am (or before 6 pm) it is.
January 16, 2017

If you have an explicit formula, coming up with a particular term is easy. If not, you have to use the recursion several times. #1. try (-2)^(n-1) #2. You can use the explicit formula, but showing how to handle it as a general arithmetic sequence is also nice. Naturally, any ...
January 16, 2017

Math
what, you can't solve 4x+8 = 0 ??
January 16, 2017

Math
momentum is not measured in kg.
January 16, 2017

Algebra
(0.8-3.4)/(2007-1972) = -2.6/35 = -0.074 (hc/mile)/year if you want a % yearly rate, then that would be -0.77%/year
January 16, 2017

Math
Not quite sure what the "at 50m" means. Also, knowing the other stake is 65m from the end of the pond does no good. Now, if the two stakes are at the ends of the pond, and the given distances are as measured from the observation point, then the distance between the ...
January 16, 2017

Algebra
use the number of tickets, and the total income: s = 2a 10a+6s = 3300
January 16, 2017

math
because there was no bounce at first - just a drop. When it hits the ground for the 5th time, it has made a single 3-foot drop, and then 4 round-trip bounces.
January 16, 2017

maths trigonometry
you have the formulae. What do you get?
January 16, 2017

Math
yes, except 30*100 = 3000
January 16, 2017

math
n = k/(y^2-1) So, n(y^2-1) = k, a constant. You want n such that n(5^2-1) = 24(10^2-1) 24n = 24*99 n = 99
January 16, 2017

Math
Newton's method converges rapidly. If you don't have calculus, then there are other methods, such a bisection. f(x) = 6x + 12 + 2cosx Start off with the interval (-3,-1) and find f at the midpoint: -2 f(-2) = 6(-2)+12+2cos(-2) = -0.832 So, f=0 occurs in (-2,-1). f(-1.5...
January 16, 2017

Math
As I recall, (a) ?x P(x) means "there exists an x such that P)x) is true. So, in this case, that wold be P(-2) V P(-1) V P(0) V P(1) V P(2) Hmmm. Not sure what (c) ? ¬P(x) means. There exists "not P(x)"? Is that the same as ?x ¬P(x), that is there exist ...
January 16, 2017

Vector Calculus
Take a look at your previous post. See whether my solution makes any sense, and whether I interpreted things correctly.
January 16, 2017

Calculus
Just a note on #3 even though ?x^2 dx = x^3/3 ?cos^2(x) dx is NOT cos^3(x)/3 cos^2(x) = 1/2 (1+cos(2x)) since cos(2x) = 2cos^2(x) - 1 Thus, ?cos^2(x) dx = x/2 + 1/4 sin(2x)
January 16, 2017

Calculus
using discs of thickness dx, v = ?[0,2] ?r^2 dx where r=y=x^3 v = ?[0,2] ?(x^3)^2 dx = ?[0,2] ?x^6 dx = 128?/7 using shells of thickness dy, v = ?[0,8] 2?rh dy where r=y and h=2-x = 2-?y v = ?[0,8] 2?y(2-?y) dy = 128?/7
January 16, 2017

Calculus
#3 3. Use the washer method to find the volume of the solid that is generated by rotating the region in the first quadrant bounded above by y = cosx and on the right x = pi/2 about the line y=2 My work: pi((4(pi/2) - ((2-(cos(pi/2))^3)/3) My Answer: 11.36 v = ?[0,?/2] ?(R^2-r^...
January 16, 2017

Calculus
#2 This time, our discs are of thickness dy, so v = ?[0,2] ?r^2 dy where r=x = 3y/2 v = ??[0,2] (3y/2)^2 dy = 6? checking with shells, v = ?[0,3] 2?rh dx where r=x and h=2-y = 2 - 2x/3 v = ?[0,3] 2?x(2 - 2x/3) dx = 4?/3 ?[0,3] 3x-x^2 dx = 6? Your answer, 72?/12 = 6? is correct.
January 16, 2017

Calculus
#1 Zero? Really? That did not see strange to you? Too bad you didn't show your original integral. The graphs intersect at (-1,1) and (1,1). Since the area of a disc is ?r^2, the volume of a disc of thickness dx is ?r^2 dx. So, your integral should be v = ?[-1,1] ?(R^2-r^2...
January 16, 2017

Algebra
Nice work. I'd have changed things a bit here: Your system become: a * ( r ^ 2 - 1 ) = 12 a * r * ( r ^ 2 - 1 ) = 36 Divide the bottom by the top to get r = 36/12 = 3 a*8 = 12 a = 3/2
January 15, 2017

Algebra
ar^2 = a+12 ar^3 = ar+36
January 15, 2017

calculas
well, (a)(i) 4/(6-6.9) = 4/-.9 = -4.44 mPQ = (-4-(-4.444))/(7-6.9) = .444/.1 = 4.444 similarly for the other points (b) I expect you will guess m=4 (c) now you have a point and a slope, so the line is y+4 = 4(x-7)
January 15, 2017

vector calculus
The unit vectors are just the vectors perpendicular to the cylindrical surface. r^ points radially outward ?^ points tangent to the planar circle z^ points upward To convert to Cartesian vectors, r^ = cos? i + sin? j ?^ = -sin? i + cos? j z^ = z^ You have V = rrˆ + r^3 ...
January 15, 2017

vector calculus
Not sure what the R 3 means, but the transformation is just the usual polar-Cartesian we all know and love: x = r cos? y = r sin? z = z
January 15, 2017

Math
Hmmm. The statements are an exercise to see whether you can correctly evaluate and compare the expressions. Note that once a true condition has been found, the value of x changes, and the following statement works with a new value. There is no positive number such that x^2 = 5...
January 15, 2017

Math
Just work them. For example (a) is 3^2 = 5^3? No Some of the conditions will match, and then you can do the assignment. The last assignment done will be the new value for x.
January 15, 2017

Math
no idea. what was his cost? But, 2000/3600 = 5/9 So, he would have lost 4/9 of his previous sale value.
January 15, 2017

Pre Calc
This is a typical 3-circle Venn diagram. When you fill in the areas, the question should be easy. Start with the central 3-circle intersection. That is 4. ...
January 15, 2017

Math
10x+12=32
January 15, 2017

math
that's "lead" not led. The area of a disc of diameter d is pi/4 d^2. So, the area of the lead cross-section is pi/4 (2.4^2 - 2.2^2) = 0.723 cm^2 So, the mass of the lead is volume * density, or 0.723cm^2 * 350cm * 4g/cm^3 = 1012.2g
January 15, 2017