Monday
September 22, 2014

Posts by Graham


Total # Posts: 404

physics
A 2.41 kg ball is attached to a ceiling by a 1.86 m long string. The height of the room is 3.38 m. The acceleration of gravity is 9.81 m/s 2 . What is the gravitational potential energy associated with the ball relative to a) the ceiling? Answer in units of J b) the floor c)a ...
December 6, 2013

Calculus
Find the number b such that the line y = b divides the region bounded by the curves y = 4x2 and y = 1 into two regions with equal area. (Round your answer to two decimal places.)
November 18, 2013

math
Let the folders cost f. Let the rulers cost r. Sarah paid: 8f + 3r Lea paid: 8r + 3f Sarah paid 1.25 more than Lea. 8f + 3r = 1.25 + 8r + 3f 5f = 1.25 + 5r f = 0.25 + r The rulers cost: r = 0.45 .: f = 0.70 Each folder costs 70 cents. Check. 8*(0.70) + 3*(0.45) = 6.95 1.25 + 8...
November 1, 2013

Physics
A satellite moves in a circular orbit around the Earth at a speed of 5.3 km/s. Determine the satellite’s altitude above the surface of the Earth. Assume the Earth is a homogeneous sphere of radius 6370 km and mass 5.98 × 1024 kg. The value of the universal ...
October 29, 2013

algebra
Redistribute for like terms. = (8+8)m3+(-3+3)m2+(1-4)m+(-5-2) = ...
October 10, 2013

Calculus
f(x) is continuous over the domain. [-3,3] f(x) is differential. f'(x) = 3x2 -9 f(x) has two equal value points on the independent axis. f(-3) = f(3) = 0 Therefore Rolle's Theorem Applies .: Exists c such that f'(c)=0 Solve for c: 0 = 3c2 - 9 ...
October 10, 2013

Physics
The centre of gravity is the point around which the weighted distribution of mass of the body sums to zero. Its relative placement within the body is independent of the orientation of the whole body; though of course it is affected by redistribution of parts of the body. ...
October 9, 2013

Math-Algebra
Again, use Pythagorus. d2 = 152 + 152 d = 15√2
October 9, 2013

Math-Algebra
Use Pythagorus. 122 = 22 + h2
October 9, 2013

Chemistry
Use: E = hc/λ Where: Planck Constant: h = 6.62606957(29)×10−34J∙s Speed of Light: c = 2.99792458×10+9m∙s-1 Wavelength: λ = 0.130m
October 8, 2013

math
a) S'(t) = dS(t)/dt S'(t) = ((d5t/dt)(t2+1) - 5t d(t2+1)/dt)/(t2+1)2 S'(t) = (5(t2+1) - 10t2)/(t2+1)2 S'(t) = (5-5t2)/(t4+2t2+1)
October 6, 2013

Physics
m1 × 3.10m/s2 = m2 × 2.00m/s2 m2 = 1.55 × m1
October 6, 2013

chemistry
Use V = m / (w c) Where: V : volume m : mass w : molecular mass c : concentration
October 6, 2013

Calculus
Don't forget the constants of integration. ------------- A = ∫ √(a2-x2) dx Let x = a sin(θ) dx = a cos(θ) dθ A = ∫ a2cos(θ)√(1-sin2(θ)) dθ A = ∫ a2cos2(θ) dθ A = (a2/2) ∫ (cos(2θ)+1) dθ A...
October 3, 2013

Calculus
(B) You have two simultaneous equations in two variables. The original equation, and the derivative for specified values of dy/dx. When dy/dx=1/2 : 1/2 = y/(2y-x) Rearrange: 2y - x = 2y Hence: x = 0 Substitute back into y2 = 2 + xy: Therefore: y = ±√2 Answer: (0...
October 2, 2013

Chemistry
Compare to the tossing two coins. P(Head ∩ Head) = P(Head) × P(Head) = 1/4 P(Head ∩ Tail) = 2 × P(Head) × P(Tail) = 1/2 P(Tail ∩ Tail) = P(Tail) × P(Tail) = 1/4 (Note that there are two ways to toss a head and a tail.) The formation of...
October 1, 2013

MATH
Which of what following? ... And what do you think is the right one?
October 1, 2013

Pre-Calculas 11
I cannot see the diagram, so I am going to assume the new fencing is formed into an 'E' shape, with the opening pressed up against the existing fence line. That is: one long side (l), two short sides and the divider (3w). The fence length is: 800 = 3w + l So the area ...
October 1, 2013

la sallle
Three consecutive even integers are: 2n, 2n+2, 2n+4, where n is an integer. The rule is thus: 2(2n+4)/2n = (3/5)(2n+2) - 3 Rearranging gives: 0 = 6 n2 - 19n - 20 Find the integer root(s) of this quadratic. Solve for integer n. Use n to find the three consecutive even numbers.
September 30, 2013

maths
y = 7x + 21 a = 7*8 + 21
September 30, 2013

maths
Hint: The first sequence is: 1/(1+1), 2/(2+1), 3/(3+1), 4/(4+1)
September 30, 2013

Dice Probability
No. The probability of the first die rolling a 2 is 1/6. The probability of the second die rolling a 3 is 1/6. The combined probability is 1/36.
September 30, 2013

Card Probability
There are 52 cards in the deck; 13 in each of the four suits, and two of the suits are red. The four face cards in each suit are: jack, queen, king, and ace. P(face card) = 4/13 P(red) = 1/4 The events are independent. The probability of an intersection of independent events ...
September 30, 2013

Probability With Cards
The events are independent. Use: P(Ki ∩ ♥) = P(Ki)×P(♥)
September 30, 2013

maths
Hint: the sequence is: 21,22,23,24,25,...
September 30, 2013

MATH
Let N = a.bcd c = d+3 -> 3 ≤ c ≤ 9 b = c-2 -> 1 ≤ b ≤ 7 a = b+c a = 2c-2 -> 4 ≤ a ≤ 8 c = (a+2)/2 -> 3 ≤ c ≤ 5 .: c = 3, N= 4.130... c = 4, N= 6.241... c = 5, N= 8.352... Though of course the rules only fix the first ...
September 30, 2013

chem-redox
Opps. Cut and paste error. 2 Ca + Cr2O72- + 14 H+ = 2 Ca2+ + 2 Cr3+ + 7 H2O
September 29, 2013

chem-redox
In acidic aqueous solution you use water to balance oxygen and hydrogen cations to balance hydrogen. Ca = Ca{2+} + 2 ē Cr2O7{2-} + 14 H{+} + 6 ē = 2 Cr{3+} + 7 H2O ===================================================== 3 Ca + Cr2O7{2-} + 14 H{+} = 3 Ca{2+} + 2 Cr{3...
September 29, 2013

physics
Hint: What affect does horizontal velocity have on vertical fall? Use: vector displacement equation. x(t) î + y(t) ĵ = [x(0) + u(0)t] î + [y(0) + v(0)t - ½ gt^2] ĵ xt î + yt ĵ = (x0 + u0 t) î + (y0 + v0 t - ½ g t2) ĵ
September 29, 2013

Math
Check the bracket placement. ±√(10/3) = ±√(10)/√(3) = ±√(30)/3 = ±(⅓)√(30)
September 29, 2013

Chemistry
An ionic exchange reaction only occurs when dissolved ions are removed from solution as (1) a precipitate (solid), (2) a gas, or (3) form a molecule that remains in the liquid phase. Sodium- and Potassium- -Biphosphates (and -Phosphates) are soluble. Sodium- and Potassium- -...
September 29, 2013

Math
When y = 0 then x = 1. As y rises towards positive infinity, x rises towards positive infinity. As y falls towards negative infinity, x falls towards 0. There is no real value of y corresponding to any negative value of x. -∞ ≤ y ≤ +∞ 0 ≤ x ≤...
September 29, 2013

Computer Science
The main should declare and load the list structure (or object), and also a variable to hold the result. The list structure cannot be fixed length; it needs to grow arbitrarily long. You'll also need a way to input numbers into the list. Given your modular design, this ...
September 28, 2013

Calculus & Vectors
Use z = x + yi Plot on the Cartesian (x,y)-plane a) Plot (x, y) = (2, 0) b) Plot √(x^2 + y^2) = 2 c) Plot (x, y) = (5, 4) d) Plot (x, y) = (√2, -√2)
September 28, 2013

math
Yes. Exactly. (x^2 -7x -8) / (x+1) = x + (-8x -8)/(x+1) = x -8
September 28, 2013

math
Do you mean: 4 (x^2 + x) / (x-3x) = -2 (x+1) = -2x -2
September 28, 2013

math
Please be clearer. What does the bracketed 4 mean? Is everything to the right of the division sign on the denominator, or just the first x?
September 28, 2013

Math
Consider the quadratic: 9z^2 - 148z + 64 Its roots are: (148 ±√(21904-2304))/18 = (148±140)/18 .: either 4/9 or 16 Thus we can factorise the quartic: 9x^4 - 148x^2 + 64 = (9x^2 - 4)(x^2 - 16) Next, factorise each of these two quadratic terms in turn.
September 28, 2013

physics
Rearrange the equation: A = F_x / t^2 Then simply substitute the numbers: .: A = (781.25/1.45^2) N/s^2 Answer in three significant figures.
September 28, 2013

Science
You simply need to express 2.16 micrometres in 5.0 seconds as some kilometres per hour, retaining the appropriate number of significant figures during conversion. 1 μm = 1×10^–6 m 1 km = 1×10^+3 m 1 hr = 3600 s 2.15μm / 5.0s = _._ ×10^__ km/hr
September 27, 2013

Physics
Use the classical mechanic equations of force, displacement, and velocity under constant acceleration from rest. (1)... F = m a (2)... s = a t^2 /2 (3)... v = a t From (1), doubling the force will double the acceleration (for the same mass). From (2), doubling the acceleration...
September 27, 2013

Significant figures
The count of significant figures for the product is the least count of significant figures of the terms. To determine how many significant figures to use, count the significant figures of each of the terms and use the least one.
September 27, 2013

chemistry
(CH3)2NH + H2O = (CH3)2NH2{+} + OH{-} Kb = [(CH3)2NH2{+}] [OH{-}]/[(CH3)2NH] At 11.98 the contribution of OH{-} concentration from dissociated water is negligible. [OH{-}] = 10^(11.98-14.00) [(CH3)2NH2{+}] = [OH{-}] [(CH3)2NH] = 0.164M - [OH{-}] Kb = [OH{-}]^2 / (0.164M - [OH...
September 27, 2013

AP CHEM
This question is incomplete. It contains insufficient information to answer.
September 26, 2013

Combinatorics
C(4,1) C(5, 1) C(6, 1) = (4!/1!3!) (5!/1!4!) (6!/1!5!) = ...
September 26, 2013

Math
x ≤ -1
September 25, 2013

Math
6 ≤ 4 + (-2x) 2 ≤ -2x x ≤ 1
September 25, 2013

chemistry
You have 5.6 mL of NH3. There are 22.4 L per mole of gas at STP. So 5.6e-3 / 22.4 mole of NH3. Balance the equation to determine the corresponding number of H2.
September 25, 2013

calculus
ln(2) = 0.69314718... (A) P(6)/P(0) = 2 .: k_g = ln(2) /6mth (B) P(3mt) = 4000 e^{3 k_g} (C) k_d = -ln(2) /10day
September 25, 2013

physics
Given: v1 = 34.5 [cos(50°) W + sin(50°) N] km/hr v2 = 16.1 [0 W + 1 N] km/hr Let: s = 3 v1 + 0.5 v2 Find: |s| s = (3*34.5*cos(50°)) W + (3*35.6sin(50°)+0.5*16.1) N |s| = √((3*34.5*cos(50°))^2 + (3*35.6sin(50°)+0.5*16.1)^2)
September 24, 2013

calculous
cannot see figure.
September 24, 2013

physics
The same current flows through the same cross-sectional area, but with only half the diameter, P has only ____ the area. Thus it passes ___ the current. [If you halve the diameter what happens to the area?]
September 24, 2013

Chemistry
You also need the molar mass of water. Let x represent the amount of sodium sulfate in the sample. Solve these simultaneous equations: 142.05 x + 18.015 nx = 8.5 18.015 nx = 4.776
September 24, 2013

vector physics
Using the standard orthogonal unit vectors î and ĵ. Momentum of the system: 0.045*9.0 î - 0.145*7 ĵ kg∙m/s Magnitude: √((0.045*9.0)^2 + (0.145*7)^2) kg∙m/s Direction: angle measured off x-axis -arctan((0.145*7)/(0.045*9.0))
September 23, 2013

Physics
If a 100%-efficient engine transfers 100% of the fuel's energy to work then, 0% of the fuel's energy would be wasted as heat, vibration, or otherwise. If it extracts 100% of the available energy from the fuel then anything left will have 0% available energy; that will ...
September 22, 2013

math
Let the number of Zerg be z, and Borges be b. Heads: 45 = z + 4b Feet: 55 = 3z + 2b Solve the simultaneous equations. Hint: multiply the first by 2 and subtract the second, then simplify. Hint 2: multiply the second by 3 and subtract the first, then simplify.
September 22, 2013

math
Let the number of Zerg be z, and Borges be b. Heads: 45 = z + 4b Feet: 55 = 3z + 2b Solve the simultaneous equations. Hint: multiply the first by 3 and subtract the second, then simplify. Hint 2: multiply the second by 3 and subtract the first, then simplify.
September 22, 2013

physics
Solve for t to find the breaking time. 0 = 19m/s - t_b 4.6m/s^2 Substitute to find the breaking distance. d = t_b 19m/s - t_b^2 2.3m/s^2 Find the time to travel to that point. t_d = (48.2m - d) / 19m/s.
September 22, 2013

Physics
Given: speed of v = 30[m/s] radius of r = 25[m] Use: Centipetal-acceleration of: a_c = v^2/r
September 22, 2013

Chemistry- that is correct.
Yes. 34m/s = 34m/s * 1000mm/m * 60s/hr = 2040000mm/hr ≈ 2.0×10^6mm/hr
September 22, 2013

Physical Chemistry
∫ β δT = ∫ 1/V δV Since β independant of T, ∫ β δT = βT + constant. βT = ∫ 1/V δV Use ∫ 1/x dx = ln(x) + constant βT = ln(V) + constant .: V = k e^(βT)
September 22, 2013

Science
Let u be the horizontal speed and v the vertical. u(0)=8.0m/s, v(0)=0m/s Let x be the horizontal height and y the vertical. x(0)=0m, y(0)=20m y(t) = y(0) + v(0) t -(9.81/2) t^2 Find t when y(t) = 0m So: 0m = 20m - 4.905(m/s^2) t^2
September 22, 2013

Algebra
If n is the least of the three consecutive odd numbers, the others are: n+2, n+4. So: 5(n) +35 = 2(n+2+n+4) Solve for n, then find 3n+6
September 22, 2013

Math
A(x+5)+2(−Bx+2) = (A-2B)x+(5A+4) So: (A-2B) = 17 (5A+4) = 219 Solve the second for A, substitute into the first and solve for B, then find A-B.
September 22, 2013

Math
b + 2c = 859¢ b + 2d = 951¢ b + c + d = ((b + 2c) + (b + 2d))/2
September 22, 2013

Science/ Chemistry
P: 30.973762(2) O: 15.999(4) Ratio of O to P is: ((0.967-0.422)/0.422)*(30.973762/15.999) = 2.50 The empirical formula is correctly derived from the given masses. The empirical equation also balances.
September 22, 2013

Chemistry
Three times as many.
September 22, 2013

Discrete Mathematics
Consider that for any integer (n), (2n+1) is an odd number. By expansion and collecting terms, (2n+1)^2 = ______. Since _______ is an integer it follows that (2n+1)^2 is odd. Therefore the square of any odd number is also an odd number.
September 22, 2013

Discrete Mathematics
An argument is valid if and only if its conclusion is entailed from its premises, A valid argument is not necessarily sound. That is, the premises do not need to be true. Hence you only need to examine the form of the argument, not the soundness of the premise. The form is as ...
September 22, 2013

Chemistry
Exchange the acidic proton.
September 22, 2013

Math
find: a) carlo's speed in the last part of the journey. Carlos travels 16km at 20kph for: 20/16 hours. Thus Carlos travels the remaining (35-16) km for (2-20/16)hours at: (35-16)/(2-20/16)kph. b) the time when Arnold reaches town A. Arnold travels 35km at 25kph for: (35/25...
September 22, 2013

Math
distance = speed multiplied by time. Measure all distance in kilometres and all time in hours. The car travels: c(t) = 40 t The bus travels: b(t) = 56 (t - 0.5) Solve for t when c(t)=b(t)
September 22, 2013

Math
Parallel lines have the same gradient. The gradient of the first line is: 4/7 The gradient of the second line is: -9/m Thus: 4/7 = -9/m Solve for: m = ...
September 22, 2013

Math
2. Profit of n items made and sold is: P(n) = (45.00-30.00)n - 1200.00 a. Find n when P(n)=0 b. Find: -P(400) (Loss is negative profit) c. Find: P(1000)
September 22, 2013

Math
1. The area of a parallel trapezoid is half of the product of the height and the sum of the lengths of the parallel sides. The height is difference between the projections of A and B on the y-axis. (Ie: 5-2) The length of each side is the difference between the x-axis ...
September 22, 2013

Math
Let the scores be x, y, z. Solve the three simultaneous equations: x + y + z = 225 x + y = z + 61 x = y + 6 Start by substitution: x=y+6 2 y + z = 219 2 y = z + 55 et cetera...
September 22, 2013

Chemistry
Use Nt/N0 = e^{-kt} 1[yr] = a = 31557600[s] (1/2) = e^(-kh) Where: Half life: h= 4.5e9 * a = 1.420092E+17[s] k = -ln(0.5)/1.420092E+17 .: k = 4.8810019E-18[/s] Okay, so far. To continue... Assume there is n atoms of U238 in the sample. t=1 second latter there is n-29. (via 29 ...
September 22, 2013

algebra
The sum is this: X = (1/5 + 1/4 + 1/3 + 1/6)*X + 12 X = (57/60)*X + 12 Simplify and solve for X
September 22, 2013

Algebra
Ah, I see now. Then it looks all good. The numbers are sorted in increasing order, and a surd is an irrational number.
September 21, 2013

Algebra
Provide your answer and we'll check it.
September 21, 2013

Chemistry
[H|D]2O + Cl2 = [H|D]Cl [H|D]Cl + AgNO3 = AgCl + [H|D]NO3 Molar mass H2O: W1 = 18.01532 g/mol Molar mass D2O: W2 = 20.02763 g/mol Molar mass AgCl: W3 = 143.3214 g/mol Sample mass: Ms = 1g Precipitate: Mp = 0.3800g Assay Volume: Vs = 1.00L Aliquot Volume: Va = 25.00mL Let n1 ...
September 21, 2013

algebra
There is insufficient information. You need to know the angle of the vertix that joins the two given sides. Height: 14*sin(angle) Area: 22*14*sin(angle)
September 21, 2013

algebra
(fg)(x) is the function that is the multiple of the two functions f and g. (fg)(x) = f(x) * g(x) (fg)(x) = (-6x-1) * (4x^2) ...So then just multiply the terms.
September 21, 2013

algebra
One way to indicate a subscript in plain text is to use the underscore in the same way the hat indicates a superscript. Like so: {a_n : a_n = 2^n -1} = {0, 1, 3, 7, 15, ...} That is: a_0 = 0 a_1 = 1 a_2 = 3 a_3 = 7 a_4 = 15 ... Using the array notation of most programming ...
September 21, 2013

Math
Given: point and line. Point: (P, Q) Line: Ax + By = C Since a line perpendicular to the given line will have a gradient of (B/A), and since the equation of a line with that gradient passing through the given point is: (y-Q)=(B/A)(x-P) Just rearrange to required format: y = (B...
September 21, 2013

Math
100 cm = 1 m
September 19, 2013

Math
1 g = 1/1000 kg
September 19, 2013

Math help Ms. Sue please
The answer to 1 and 4 is to rearrange to collect like terms. I suspect _Question_ 4 is wrong. 3x - 2/9 was probably meant to be : (3x-2)/9
September 19, 2013

Math 75%
Answer 1. is correct Answer 2. is correct Answer 3. is correct Answer 4. is _wrong_
September 19, 2013

Math
Find the cubic root of 1800.
September 19, 2013

Math
One advantage of the metric system is that its units of measure scale by multiples of 10. You just have to memorise the prefices. In this case "milli-" means 0.001 times. That is, there are 1000 milligrams to the gram. 1000 mg = 1 g 2000 mg = ___ g
September 19, 2013

math
Just multiply. Distance equals the product of time and speed. d = t * v
September 19, 2013

physics
Determine the initial speed. Use the classical mechanics equations. Speed: 0 = u -g t → rearrange to substitute for t into: Displacement: h = ut - (1/2) gt^2 → find u in terms of h and g. Determine the maximum range. Use a 45° trajectory. d = u^2/g → ...
September 19, 2013

science
______ is composed of ____. A _____ is a unit of matter composed of one or more _____. An _____ is a _______ composed of same kind of _____. A _______ is a ________ composed of two or kinds of ______. A ______ is an arrangement of ______ composed of _____ in a repeating latice.
September 19, 2013

chemistry
Find the Ksp of KI at 30C. Ksp = [K{+}]*[I{-}] That will determine the mole concentration of dissolved KI. Multiply by volume (in L) and molecular mass to determine the mass. Subtract that from the mass of supersaturated KI to determine the mass of precipitate.
September 19, 2013

chemistry
Balance the equation C3H8 + _n_ O2 = 3 CO2 + 4 H2O mass(O2) = n * mass(C3H8) * molarmass(O2) / molarmass(C3H8)
September 19, 2013

Calculus (math)
Begin with: sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
September 19, 2013

chemistry
Divide that mass by the molecular mass of CaCl2 then multiply by twice that of a Chlorine atom.
September 19, 2013

physics
Power is rate of work. Work is force times displacement. Force is weight of each brick under gravity. Measure weight in [kgf] (kilogram-force: the weight of 1[kg] in normal gravity). The conversion rate to metric horsepower is: 1[hp] = 75 [kgf·m/s] Use: P = Ws/t Where...
September 19, 2013

arithmetic
28000*(1.05)^33
September 19, 2013

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