Graham

Hi, I have been asked to simplify the square root of 28 by writing it as a product of an integer and a surd. By practising other calculations I have come up with the answer of 2/7 (sorry couldn't do a square root symbol so have used / instead). I think I...

15 years ago

dara spent 25% of his money in one shop , he spent 33 1/3 of the remainder and had £6.80 left , how much had he at first

14 years ago

Predict the products and then write the complete balanced chemical equation with states of matter: 1. Sulfuric Acid and sodium hydroxide 2. Aluminum and copper (II) sulfate 3. Silver nitrate and iron (III) chloride 4. Magnesium heated 5. Aluminum oxide

14 years ago

Can you tell me how you arrive at the answer to this question: if you multiply meby2, I become a number greater than 20and less than 40. If you multiply me by 6 I end in 8. If you multiply me by4,I end in 2.

14 years ago

I have a question concerning this problem:I just want to make sure my formulas are correct before I do problem It is a hyperbola equation (y-4)^2/49 - (x-6)^2/72 = 1 1.It is a vertical hyperbola, correct? 2. the a^2 is 49, correct? 3. the b^2 is 72, corre...

13 years ago

Write the polynomial in simplest form with roots 4, 5i and -5i(multiply it out so no parentheses remain (x-4)(x+5i)(x-5i)(NOT SURE ABOUT THIS ONE) (x-4)(x^2-25i^22) (x-4)(x^2+25) x^3+25x-4x^2-100 x^3-4x^2+25x-100 Is this correct

13 years ago

I had a 1.094g of mystery Alum. "AB(SO4)c. dH2O" (I assume that that the Alum is KAl(SO4)2-12H2O but we don't know A B c or d, we do know that mass percent of water is 51.9) After processing the alum (Ba(NO3)2 and HNO3 through a gooch crucible) we end up...

12 years ago

I'd like to do a titration test, I've got a sulphuric acid solution @ 1M (2N) but I need one @ 0.12N. How many ml of the 1M (2N) solution do I need to add to distilled water to make up 100ml please?

12 years ago

the length of a rectangle L metres and the width of the rectangle is W metres. Each measurement is correct to the nearest cm. Find, in terms of L and W the difference between the lower bound and the upper bound of the area of the rectangle.

10 years ago

If the absolute temperature ooh 6 inches cubed of a gas decreases by a factor of 2, what will be the new volume? How do set up this problem and solve it?

10 years ago

How many Sq metres is there in a area of 200cm x195cm x10cm deep?

9 years ago

Find how many digits the base seven number 7^(7^7) has when written in base seven.

6 years ago

KE= 0.0046 x 41 x 41 x 0.5 = 3.8663 Joules

13 years ago

ABS resins = acrylonitryl, butadiene and styrene

13 years ago

I forgot one question-in a hyperbola, the "a^2" is always under the first variable, whether it be "x" or "y", correct

13 years ago

So if I change the formula to = (-1), then I have to change the a^2 to be under the "x" is that correct? Thank you for your help

13 years ago

okay-thank you I got it now

13 years ago

Anonymous, Ken also has some ducks. If Mark has x pigs, he has 3x ducks. That's 4x heads and 10x feet. Ken has x pigs too. If Ken also has y ducks, then that's x+y heads and 4x+2y feet. Together they have (1) Heads: 5 x + y = 17 (2) Feet: 14 x + 2y = 42 S...

12 years ago

Your calculation is correct; just multiply it out to 0.32m^3. Gauge pressure is pressure in excess of atmospheric pressure. 1 atmosphere is 101.325kPa. So guage pressure is: (550.280-101.325)kPa.

12 years ago

1. Divide like terms. (2 x^4 y)/(6 x y^2) = (x^2)/(3 y) 2. Multiply, not add. (8 x^2)(-3 x^y) = -24 x^(2+y)

12 years ago

A sequence of coin tosses has a Binomial Probability Distribution Function. Event probability: π=0.5 Sample Size: N = 60 Mean: Nπ = 30 Variance: σ^2 = Nπ(1-π) = 15 Std. Deviation: σ = 3.873... So a result of 34 heads lies just outside of one standard devi...

12 years ago

h(t) = 125 - 5t^2 Take the derivative to find the velocity: v(t) = dh(t)/dt = -10 t Now: Find the time when height is 0. Find the velocity at that time.

12 years ago

(f+g)(x) = f(x) + g(x) (fg)(x) = f(x) g(x) (f/g)(x) = f(x) / g(x) so: a) (f+g)(x) = x+3 etc.

12 years ago

The instantaneous rate of change at x = 2 is zero. Means: A peak trough or inflection. The curve levels off there; the tangent is paralel to the x-axis. The instantaneous rate of change at x = 3 is negative. Means: There's a downward slop at x=3 The avera...

12 years ago

bullet mass: M = 3.00g initial velocity: V0 = 640m/s initial temperature: T0 = 313.15K final velocity: V1 = 0m/s melting point of Lead: T2 = 600.61K specific heat of lead: C = 0.128J/g/K latent heat of melting: L = 22.4J/g (a)Find the available kinetic en...

12 years ago

For a 95% confidence interval, 95% of the sample lie within (μ - 1.96
σ/√n) and (μ + 1.96 σ/√n). Thus the width of the interval is: 3.92 σ/√n  So we need to find: n = (3.92 σ/ 6%)² To do this we need to know (or estimate) the standard deviation (σ).

12 years ago

Hint: It's the complement of the probability that none of them is among that group. Let En be the indexed event that the nth person selected is not one of the three oldest. 1 - P(E1) P(E2|E1) P(E3|E1 and E2) = 1 - (9/12) (8/11) (7/10) = 0.61818....

12 years ago

Alternatively: It's the complement of the probability that none of them is among that group. Let E[n] be the indexed event that the [n]th person selected is not one of the three oldest. 1 - P(E1) P(E2|E1) P(E3|E1 and E2) = 1 - (9/12) (8/11) (7/10) = 0.618...

12 years ago

The probabilities of colors of each pill are independent. Let m[n] = C, be the event that the [n]th pill is a color (C). eg: P(m1=Blue) = 0.12 (1) P(m1=Blue and m2=Blue) = P(m1=Blue) P(m2=Blue) (2) P(m1<>Red and m2<>Red) = (1-P(m1=Red))(1-P(m2=Red)) (3) P...

12 years ago

In the beginning: Minette had T, Mark had K, and Michelle had L. After step 1: Minette had (T-K-L), Mark had 2K and Michelle had 2L. After step 2: Minette had (2T-2K-2L), Mark had 4K and Michelle had (3L-T-K). Solve 3 simultaneous equations of 3 variables...

12 years ago

The amount at period n is the amount at period n-1 plus interest earned on that plus the periodic payment. x[n] = x[n-1](1 + I) + P x[n] = x[n-2](1+I)^2 +((1+I)^2 -1)P/I x[n] = x[n-3](1+I)^3 +((1+I)^3 -1)P/I ...and so on... x[n] = x[0](1+I)^n + ((1+I)^n -...

12 years ago

KE = 1/2 m v^2 Kinetic energy is proportional to the square of the speed.

12 years ago

M = 100kg F = 1800N S = 4.0m W = F S W = (1800N)(4.0m) = 7200Nm W = 7.2 kJ A = F / M V = V0 + A T S = S0 + V0 T + ½ A T^2 Assume initial velocity and displacement are 0. S = ½ F T^2 / m T = √(2 M S / F) V = F √(2 M S / F) / M V = √(2 F S / M) V = √(2 1800...

12 years ago

a=-1, b=5

12 years ago

The sum of the angles: 180 = 3x + y If it's an Isosceles triangle then two angles are the same: Either: y=x, or y=2x Pick one then substitute and solve.

12 years ago

100 less than _twice_ the preceeding number. (200)*2 -100 = 300 (300)*2 -100 = 500 (500)*2 -100 = ... et cetera

12 years ago

1.87m + 27.0m tan(18.0°)

12 years ago

The numbers: x and x/5 The reciprocals: 1/x and 5/x The sum of the reciprocals: 6/x

12 years ago

There are eight digits that can be in the first place, ten in each of the remaining two. Repetitions are allowed. The universal theory of counting says: multiply 8, 10, and 10 together to get the answer.

12 years ago

F = m a When acceleration is equal: F2 = m2 F1/m1

12 years ago

Let there be 'c' chicken nuggets and 'f' fish nuggets There are 48 more chicken nuggets than fish nuggets on the plate. c = f + 48 ...(1) After some children ate 12 chicken nuggets and 12 fish nuggets there were 3 times as many chicken nuggets as fish nug...

12 years ago

To be balanced the angular acceleration must be equal (but opposite). α = mg/r So: m_b/r_b = m_f/r_f .: r_b = (60)(0.65)/(70) ≈ 0.56m

12 years ago

probability = 13/(13+225) = 13/238 = 0.0546...

12 years ago

A fair game would be when the price of all the tickets sold is equal to the total prize money. That is $10600. So the price of one ticket would need to be just one-thousandth of that.

12 years ago

(Eh? Gas activity measured as molar concentration instead of partial pressure? Odd, but...) Kc = {NH3]^2 / [H2]^3 [N2] = (2.0M)^2 / (0.50M)^3 (0.50M) = 64 M^(-2)

12 years ago

Ca(IO3)2 (s) <=> Ca{2+} (aq) + 2 IO3{-} (aq) LeChatelier's principle (general form): Any change in status-quo prompts an opposing reaction in the responding system. So increasing the starting concentration of calcium cation will oppose its production. Tha...

12 years ago

Kc = [NH3]^2 / [N2] [H2]^3 so [N2] = [NH3]^2 / [H2]^3 Kc

12 years ago

Kc = [H2O] [CO] / [H2] [CO2]

12 years ago

Kc = [NO2]^2 / [N2O4] so [N2O4] = [NO2]^2 / Kc

12 years ago

Kc = {NH3]^2 / [H2]^3 [N2] [N2] = (8.0×10^−2M)^2 / (0.20M)^3 (1.7×10^2)

12 years ago

The titration is: 2 Na2S2O3 + I2 = Na2S4O6 + 2 NaI moles NaOCl in 20mL aloquat = moles I2 = (1/2)moles Na2S2O3 = 0.345 L * 0.0409 M / 2 moles NaOCl in original (25mL) sample = 0.0345 * 0.0409 * (500/20) mol / 2 mass NaOCl in original (25mL) sample = 74.44...

12 years ago

Just multiply the matrices a = (1)(-5)+(-2)(7) b = (1)(6)+(-2)(-8) c = (3)(-5)+(3)(7) d = (3)(6)+(3)(-8)

12 years ago

I need 0.12N not M, I'm not sure of the scale change between M and N?

12 years ago

I'm not a chemistry student and it was 40 years ago that I did any equations but... A little more research has reveled that Sulphuric Acid has 2 protons (H+) in a molecule of the acid. So in this case the scales of Normality and Molarity 1M=2N or N=M/2 I...

12 years ago

Oh I see what you're saying, but my old chemistry teacher would have killed me if I'd added water to acid. He would have told me to put at least 75% of the expected DI water content into the flask first then the measured amount of acid, then top up to 100...

12 years ago

Thanks for all your help, it's much appreciated and my titration of nicotine solution for my ejuice worked a treat :)

12 years ago

Second Problem: Momentum is still conserved on each leap (of course) but note that when the boy jumps off at 3m/s _relative_ to the boat, the boat is no longer at rest. M1 = 75 kg mass of man M2 = 25 kg mass of boy M3 = 300 kg mass of boat V1 = 3 m/s laun...

12 years ago

This is impossible to answer without knowing the incline of the slope, For an incline angle of θ, the force exerted by the rope on the child is: 77N sin(θ).

12 years ago

1. Determine the mass of nitrogen that washes into the river each year, in milligrams. ( Multiply the mass of fertilizer by both percentages. ) 2. Determine the volume of river that flows through the farm each year, in litres. ( Convert cubic feet to litr...

12 years ago

Speed of ball is distance traveled divided by (time of hearing minus time the sound travels). 16.5/(2.51-16.5/340) m/s = 6.70 m/s

12 years ago

Let event s represent a Shaft defect and event b represent a Brushing defect. The given probabilities are: P(s ∩ ¬b) = 0.08 P(b ∩ ¬s) = 0.06 P(b ∩ s) = 0.02 Note: these are mutually exclusive What you wish to find are: a: Brushing defect. P(b) = P(b ∩ ¬s)...

12 years ago

1: 1400.0 * 10^6 * 0.100 * 0.150 = 2.10E7 mg 2: 0.410 * 28.32 * 3.154E7 = 3.66E8 L 3: 0.574 mg/L

12 years ago

Amount of Iron in sample: n[Fe] = 3 m[Fe3O4]/w[Fe3O4] Amount of Iron in assay: n[Fe] = 2 m[Fe2O3]/w[Fe2O3] The amount of iron is conserved, so: m[Fe3O4] = (2/3) m[Fe2O3] w[Fe3O4] / w[Fe2O3] Substitute: m[Fe2O3] = 26g w[Fe2O3] = 159.6887 ± 0.0002 g/mol w[F...

12 years ago

Not sure how to be clearer. From the formula, the mole amount of iron in the magnetite sample is three times the mole amount of iron(II,III) oxide. This amount is the mass of magnetite divided by its molar weight. n[Fe] = 3 m[Fe3O4]/w[Fe3O4] The amount of...

12 years ago

Known: Mass of sample: s = 28.4858 g Mass of residue: r = 17.3014 g Unknown: Mass of Impurities: x Mass of MgCO3: m0 = s - x Mass of MgO: m1 = r - x Therefore: m1 = m0 + r - s Lookup: Molecular mass of MgCO3: w0 = 84.31413 ± 0.00005 g/mol Molecular mass o...

12 years ago

Given: m{sample} = 40.93g m{Fe2O3} = 30.7g w{Fe2O3} = 159.6887 ± 0.0002 g/mol w{Fe3O4} = 231.5333 ± 0.0003 g/mol And the stoichiometry: 3 m{Fe3O4}/w{Fe3O4} = 2 m{Fe2O3}/w{Fe2O3} The percentage of magnetite in the sample is: m{Fe3O4} / m{sample} = (2/3) m{...

12 years ago

Given: m{sample} = 40.3g m{Fe2O3} = 10.5g w{Fe2O3} = 159.6887 ± 0.0002 g/mol w{Fe} = 55.8452 ± 0.0001 g/mol And the stoichiometry: m{Fe}/w{Fe} = 3 m{Fe2O3}/w{Fe2O3} The percentage of iron in the sample is: m{Fe}/m{sample} = ...

12 years ago

Typo correction: m{Fe}/w{Fe} = 2 m{Fe2O3}/w{Fe2O3}

12 years ago

Yield = practical/theoretical Given: Practical mass: Pm{ClF3} = 4.6g Reactant mass: m{F2} = 5.3g The equation: 3 F2 + Cl2 = 2 ClF3 Lookup the Molecular Weights: w{F2} = 37.99680650 ± 0.00000002 g/mol w{ClF3} = 92.4484 ± 0.0001 g/mol So theoretically, the...

12 years ago

Two bugs found. There are two "while" bit only one "endwhile", and also one "if" but two "endif". Thus it appears that the second "endif" should be an "endwhile". Also, you have "while category = QUIT" when it seems you wish to loop _until_ that condition...

12 years ago

Yes. It is possible. Just cut off the wings will give three pieces. 5 ----< cut 123 ----< cut 4

12 years ago

180 rounds per minute = 3.00 Hz Angular momentum of each mass is: L = (m r^2)ω Mass and Angular momentum are conserved, so: r0^2 ω0 = r1^2 ω1 or r1 = r0 √(ω0/ω1) r1 = 0.800 √(3.00/4.00) r1 ≈ 6.93m

12 years ago

(454g/16oz)(oz/$523)($/100¢) = _____ g/¢

12 years ago

Given: v = 22.0m/s a = -4.00m/s² Use the equations: (1) 0 = v + a t (2) s = v t + a t²/2 Solve (1) for t. Substitute to solve (2) for s.

12 years ago

v(t) = v(0) + ½ a t Given: g = -9.8m/s t = 7.99s Half way up the ball will reach 0 velocity. 0 = v + ¼ g t Alternatively, all the way back, the ball will have a velocity equal but opposite to its initial. -v = v + ½ g t Use either equation to solve for v.

12 years ago

Given: s(0) = 0 v(0) = 0 s(t) = -4.94m g = -9.8m/s² Use the equation to solve for t. s(t) = s(0) + v(0) t + ½ g t²

12 years ago

Correction: use v(t) = v(0) + a t v(½ t) = 0, so: 0 = v + ½ g t v(t) = -v, so: -v = v + g t

12 years ago

Technology advancements have changed the answer. It depends on what lighting system they use. The old Incandescent Lamp 'light bulb' emits most of its energy consumption as heat, and would reduce the load on the heater. However, a modern Compact Fluoresce...

12 years ago

My apology for the typo. I must have miskeyed during calculation, but I should have realised that seven meter was a bit of an arm stretch. So yes, r1 ≈ 0.693m Because angular momentum and mass are conserved, the angular velocity is inversely proportional...

12 years ago

Rearrange into incomplete quadratics: (x² + 2x) + (y² - 2y) = 1 Complete the squares: (x² + 2x + 1) + (y² - 2y + 1) = 1 + 1 + 1 Express in the required form: (x + 1)² + (y - 1)² = (√3)² Thus: h = -1, k = 1, r = √3

12 years ago

A stationary point occurs when the derivative of the curve is 0. Find the derivative, y'. Solve for x when y'=0. Evaluate y at these values of x.

12 years ago

1/8 is a constant. What is the derivative of a constant?

12 years ago

The perimeter of a rectangle is: P = 2(l+w) You're given: l = w + 10cm w = x Substitute and simplify.

12 years ago

(1) Find out if it has a Stationary Point. Take the derivative of y. Solve for x when the derivative is 0. (2) If it does, determine their status as maxima, minima, or inflection(s). Inspect the values of the curve slightly before and after the point(s).

12 years ago

The equation of a line passing through point (a,b) at gradient m is: (y - b) = m (x - a) You're given (a,b)=(3,4). What is the gradient of the perpendicular?

12 years ago

(a) Take the derivative and solve for x when y' is 0. Evaluate y at that value. (b) Solve the equation for x when y is 0. --- Alternatively, note that a ballistic curve of that form (quadratic) is symmetric around the maxima/minima and use the solution of...

12 years ago

An arc length l of radius r and angle θ (in radian measure) is: l = rθ Convert the angle from degrees to radians. Multiply the radius by that measure.

12 years ago

Use the ideal gas law: P = n R T / V Given: n = 0.804mol T = (16.0+273.15)K V = 29.2L Looking up: R = 62.36367(11) L .mmHg. Kˉ¹. molˉ¹

12 years ago

If 2x²+4x+1 = 0 Then: x = (-2±√2)/2 let α = (-2+√2)/2 let β = (-2-√2)/2 log_2(α) + log_2(β) = log_2(αβ) = log_2((-2+√2)(-2-√2)/4) = log_2(1/2) = -1

12 years ago

Assuming each child has only one mother. Let m be the number of mothers who lost both children. Let n be the number who lost only one child. 36 mothers had lost one or both of their children: (1)... m + n = 36 62 children had lost their mothers: (2)... 2m...

12 years ago

Let the trapezoid ABCD be of height h. Given: AB = 22 CD = 12 DAB = 65° ABC = 40° Construct a diagram and consider the trigonometry: (1) AB = CD + h cot(DAB) + h cot(ABC) (2) BC = h sec(ABC) (3) DA = h sec(DAB) Substitute the values into (1) to solve for...

12 years ago

Are you looking for the roots of the quadratic? Use: a=-¾ b=-4 c=-1 in: x = ( -b ± √(b²-4ac) )/2a x = (-8±2√13)/3

12 years ago

Or do you want to express the function in terms of x? x = (-8±2√(13-3y))/3

12 years ago

Geometric Progression: x(n) = a r^n First term x(0) = a Second term x(1) = ar etc. So a = ar^2 +12 ar^3 = ar +4 Rearranging gives, a(1-r^2) = 12 a(1-r^2)r = -4 Thus solve for r by dividing, Substitute into the original to solve for a,

12 years ago

Area of Triangle = (1/2) x base x height A = (1/2)(y/2)(2y/5+4) rearrange A = (1/10)y^2 + y That is, assuming that 1/2y means (1/2)y rather than 1/(2y).

12 years ago

checkBoth() has a glaring logic error. detailLoop() need to consider what happens if you come to the end of one file before its room?Name is greater than that of the other. Avoiding an infinite loop would be a good idea.

12 years ago

a) Correct. b) What. How did you even? It is 122±2g

12 years ago

volume = height * length * width density = mass / volume

12 years ago

Initial mass of H2SO4 = final mass of H2SO4 in solution Initial mass is (87.0%) of target solution (X). Final mass is (35.5%) of the initial solution (200g). X = 200g * 35.5/87.0

12 years ago

To find the group size, divide the group's saving by the individual reduction.

12 years ago

The ratio of Mg to F is constant. f2 / m2 = f1 / m1 To find the second mass of fluorine (f2), rearrange and substitute appropriate values.

12 years ago

Given: C1 = 2.5x10^-4 M C2 = 7.4x10^-5 M V2 = 10.0 mL Use conservation of (mole) amount: C1 V1 = C2 V2 Rearrange to find the initial volume (V1).

12 years ago

Just subtract a negative number.

12 years ago

Positive integers less than 1000 consist of {1 ... 999}. This may also be written {001 ... 999}. So you need to count, {003, 007, 013, ... 987, 993, 997}. Which is the same result as counting {00, 01, ... 98, 99} twice over. (Once for ??3, once for ??7)....

12 years ago

If the speed is increasing, the acceleration cannot be zero. If the particle also remains moving along the x-axis, the velocity and acceleration must have the same direction.

12 years ago

Yes, but why is this so? What is it about the Southern Hemisphere that makes its climate different from the Northern?

12 years ago

y(x) = b sin^2(πx/a) The mean of the curve over the range b to a is: y_ave = 1/(a-b) ∫(x=b to a) y(x) dx sin^2(πx/a) = 1 - cos(2πx/a) ∫y(x) dx = (b/2) ∫ (1 - cos(2πx/a)) dx = (b/2) (x - a sin(2πx/a)/(2π)) + constant = bx/2 - ab sin(2πx/a)/(4π) + constant...

12 years ago

And, that is just about as far as it goes. You can play around with the sine identities, but it doesn't simplify much further.

12 years ago

The tilda means "not". ~(p ᴗ q) : not (p or q) ~(pᴗq)=(~p)ᴖ(~q) In English: Neither condition is true. It is neither one nor the other. It is not one and it is also not the other.

12 years ago

Use: (y-y1)=(x-x1)(y2-y1)/(x2-x1) Substitute (x1,y1)=(50,30) and (x2,y2)=(150,80). When you get the right answer, the mistake is obvious. And simple.

12 years ago

Use Hooke's Law: |F| = k |d| Use Coulomb's Law: |F| = ke |q1 q2| / r^2 Equate forces and rearrange. k = ke |q1 q2|/(|d| r^2) Where: q1 = 0.840×10^(-6) C q2 = -0.546×10^(-6) C d = 3.18×10^(-2) m r = 4.95×10^(-2) m ke = 8.9875517873681764×10^9 N·m^2/C^2 (Co...

12 years ago

Good work. For completion, do the final division. m = -0.97

12 years ago