Saturday
July 4, 2015

# Posts by MathMate

Total # Posts: 11,301

Calc
dy/dt=-0.15y dy/y = -0.15t ln(y)=-(0.15/2)t²+C f(t)=y=Ce-0.075t^sup2; At t=0, y=3 ml. f(0)=C=3 so, let t=time for second dose, f(t)=3e-0.075t^sup2; solve for f(t)=1 ml. -0.075t²=ln(1/3) t=sqrt(-ln(1/3)/-0.075) =3.8273 (approx.) Time for third dose (after second dose...
May 11, 2014

chemistry
Convert 811 cg to kilograms 811.0 cg = 811.0/100 g = 8.110/1000 kg =0.008110 kg Then use formula to calculate concentration in ppm. Keep the answer to 4 significant figures.
May 11, 2014

chemistry, first year university
Assuming the temperature was at STP (0°C). Consider a 1-L volume. Total pressure = 421959.129Pa = 421.96 kPa = 4.1654 atm at 0°C Partial pressure of each product = 2.08272 atm This implies PN2=PH2 =2.08272 atm Kp=PN2²PH2² = 2.0827^4 = 18.8158475075608 = 1.882...
May 11, 2014

chemistry
oops! The example reaction should read: HCl + H2O -> H3O+ + Cl-
May 11, 2014

chemistry
Ionization of an acid in water is typically the formation of hydronium ions, H3O+ and the associated spectator ion. Example: HCl + H2O -> HH3O+ + Cl- (A) Hydrobromic acid: HBr It is very similar to ionization of hydrochloric acid above. For the rest, the reactions are ...
May 11, 2014

Hints: Trachea is a part between the throat and the lungs. The alveoli perform the major function of the respiratory system, namely exchanges intake of fresh air (O2) with waste carbon dioxide (CO2). They are also the ultimate destination of intake of fresh air.
May 10, 2014

Physics
Note: the degree symbol is written as & d e g ; (suppress all spaces) Difference in elevation, Δh = 270m × sin(6.5°) total mass (cyclist + bicycle), m = 95 kg total weight = mg Work done (on cyclist & bicycle) =mgΔh Component of force along slope, F = mg ...
May 10, 2014

Physic
Assume diver is 8.2 m below surface (and not 8.2mm), and at the surface, P=101.3 kPa. Pressure below surface =ρgh =1000 kg/m² * 9.8 * 8.2 + 101.3 = 80.36+101.3 kPa = 181.66 kPa Assuming temperature below water and at the surface are identical, use Boyles law: P1V1=...
May 10, 2014

calculus
Unless I am mistaken, the paraboloid looks like a mountain, tapering off to zero along a circle of radius 3. The cylinder has a radius of 2 and its axis is along the z-axis. So the volume of the paraboloid outside the cylinder is like you drilled a vertical hole of radius 2 ...
May 10, 2014

calculus
First find out where z(x,y) intersects the x-y plane, which turns out to be a circle given by x²+y²=9 So you would need evaluate the volume of the paraboloid above the x-y plane between the circles x²+y²=2² (cylinder, radius = 2) and x²+y²=3&...
May 10, 2014

#1 is not correct. Breaking down large molecules into smaller ones helps the body absorb nutrients from different kinds of food. #2 The circulatory system has the main function of collecting carbon dioxide excreted by cells in different parts of the body and exchange for ...
May 10, 2014

Science
1. incorrect Food gets digested in the stomach, and nutrients absorbed in the small intestine, and finally excess water extracted in the large intestine. 2. Not sure about the "two servings", and the left and right. 3. incorrect. It is used for grinding hard food, ...
May 10, 2014

Science-3 question
#1 incorrect. Question asks which function is not one of the circulatory system. #2. incorrect. Blood has the dual function of supplying oxygen to different parts of the body and also to exchange excreted carbon dioxide with oxygen of fresh air. #3. correct.
May 10, 2014

Engineering skill
Are you able to understand the problem without the accompanied plan/sketch? If you can, kindly describe what you understand in words, or post a link to the plan. Thank you.
May 10, 2014

physics
Since the question asks for time in the air and distance from the building, we will use vi (initial velocity) as a parameter, and solve accordingly. Assume: '=feet fps=feet per second g=32.2 m/s² vi=initial velocity in fps Horizontal component of velocity, vih =vi cos...
May 10, 2014

physics
What are being asked depends on the initial velocity. Do you know the velocity, or you are expected to come up with an algebraic expression in terms of the initial velocity? Is the ball thrown at 60° above the horizontal?
May 10, 2014

Algebra 2
an=8n Substitute n=1,2,... a1=8*1=8 a2=8*2=16 ... guess you can take it from here.
May 10, 2014

physical
Write "brake", and "braking" when stopping a car. m=2500 kg vi=25 m/s vf=0 t=20 s vf=vi+aΔt 0=25+a(20) solve to get a=-25/20=-5/4=-1.25 m/s² Use Newton's second law to get force force, f = ma =2500 (-1.25) N =-3125 N Ignore the negative sign ...
May 10, 2014

Math (Calculus)
The challenging part of this problem is to find the limits of integration, which is the intersection of the two curves. As a hint, they meet at x=1.9 and 4.5 (approximately. You can use Newton's method or other iterative methods to improve the solutions. After that, the ...
May 9, 2014

Algebra
Ratio of 80% and 30% acids is 62-30:80-62 =32:18 =16:9 To make 50 L of 62% Volume of 80% acid = 50*(16/25)=32 L Volume of 30% acid = 50*(9/25)=18 L
May 9, 2014

Calculus
For #1, y′= x(1+ y) write y'/(1+y) = x put p=y+1 p'/p = x ln(p) = x²/2 + C p=ex²/2+C y=ex²/2+C-1 =Cex²/2-1 or =Cex²/2
May 9, 2014

Oh, sorry, I had the two terms divided and not multiplied.
May 9, 2014

I do not have the same value as yours. Can you post the derivative?
May 9, 2014

physics
Newton's second law: F=ma if F and m are both identical, the a would be the same, where a=deceleration in m/s². Using the kinematic equations for the first car, vf²=vi²+2aΔx vf=final velocity=0 vi=initial velocity Δx=stopping distance and solve ...
May 9, 2014

ALGEBRA
Not sure what your choice is, and also if the actual question should read: Y(x)=sqrt(x+4)-3 or Y(x)=sqrt(x+4-3) [as you had it] Can you check if there is a typo?
May 9, 2014

ALGEBRA
I suppose you mean Y(x)=sqrt(x+4)-3 in which case you can evaluate the function for the various given values and see which one, if any, gives Y(x)=0.
May 9, 2014

Chemistry
[H3O+]=10-4.67 = [BrO-] [HBrO]=0.200-10-4.67 Ka=[H3O+][BrO-]/[HBrO]=2.286×10^(-9)
May 9, 2014

Physics
Assuming the "semicircular shape" is like the loop of a roller-coaster, and we want the body to complete the circle. At the top of the loop, of diameter d (radius d/2), the velocity must be such that the centripetal force exerted by the rails ≥0, or mv²/(d/2...
May 9, 2014

Physics
Assuming the first sentence to mean: "A 10kg box is initially at rest on top of a hill 10m above the ground level." I.e. the box is resting at the top of the hill, which is 10 m. above ground level below. Using ground level as zero potential energy, then At top of ...
May 9, 2014

Physics
Does the missing figure show the mass of the ball? There is centripetal force of magnitude mv²/r (horizontal) and the weight (vertical) of mg to form the resultant tension of the string of 7.7N. r is the horizontal radius, so must be adjusted for the angle the string ...
May 9, 2014

Economics & Statistics
20 represents the slope. Slope is defined as the increase in y-value divided by the increase in x-value, that is: slope = Δy / Δx
May 8, 2014

math probability
1/11 is correct. We can do it in two different ways, easy and difficult. Easy way: Pick 2 of the 5-marbles and any of the remainder. 2/12*1/11=2/132=1/66. The two 5-marbles can be arranged in 4P2 = 4!/(2!2!)= 6 ways, so probability = 6* (1/66) = 1/11 The difficult way: We ...
May 8, 2014

Physics
Correction to equation (a) W=kx^2 ÷2 (watch units) (b) use same equation, with W=50 ft-lbs = 600 ft-in. solve for x.
May 8, 2014

Physics
(a) W=kx^2 (watch units) (b) use same equation, with W=50 ft-lbs = 600 ft-in. solve for x.
May 8, 2014

Chemistry - Science (Dr. Bob222)
Some of the heat generated would have been diverted to convert 2H2O(l) to 2H2O(g), so heat generated would be reduced by 2*40.7=81.4 kJ/mol. Can you take it from here?
May 8, 2014

Trig
Use: cot(θ)=cos(θ)/sin(θ) sin²(θ)+cos²(θ)=1
May 7, 2014

chemistry
C1V1=C2V2 (a) 1.0 mol/L * 0.2L = C2 * 1.0 L Solve for C2 (b) C2 (from a) * 25 cm³ = (1.6 mol/L)*V2 Solve for V2.
May 7, 2014

Physics
Calculat the distance d (metres) it hits the ground when there is no wall. Use reflection to calculate the bounce off the wall. Then case 1: if d>10 m. Ball hits ground at (d-10) before the wall. case 2: if d<10 m. Ball hits ground at d m. from the girl.
May 7, 2014

Java
This is different from public, or private. Sometimes it is call package or default access. Read up at: http://docs.oracle.com/javase/tutorial/java/javaOO/accesscontrol.html
May 7, 2014

physics
use mv²/r = mg solve for v.
May 6, 2014

Data Structure
Assume the boat and the boys are on the same side of the river at the start and finish. To get one villager across, the two boys must row over, leave a boy on the other side, row back alone, let a villager row over, then then boy on the other side will bring the boat back, ...
May 6, 2014

Procedure should be correct, did not check the calculations.
May 5, 2014

math
If the assumption is that the population growth is constant at 4.5%, then Let x=population in 2000, 8791894=x*1.04510 Solve for x.
May 5, 2014

Math
transpose terms to the form y=ax+b, then a is the slope and b is the y-intercept. 6x=y+1 becomes y=6x-1, compare with y=ax+b and find what a (slope) and b (y-intercept) are.
May 5, 2014

algebra
Translating in English, you have defined a universal set of integers from one to ten. Then you defined sets (presumably belong to the universal set) which combine ("unioned") to form a new set. The first, {x|x is multiple of 2} means the set of even numbers between 1...
May 5, 2014

chemistry
Use: C1V1=C2V2 Measure all concentrations in mol/dm^3, and volumes in dm^3 2.0*V = 0.5*2.5 V=1.25/2=0.625 dm^3 or, approximately, 0.63 dm^3 rounded to 2 significant figures.
May 5, 2014

Programming
Do you need help with the flow-chart, algorithm, the coding or debugging? It would be best for you to tell us what you have learned, and what you have done so far.
May 5, 2014

math mrs. sue HELP!!!
Say you have a data set {4,6,8,9,10} 1. Find the mean = (4+6+8+9+10)/5=7.4 2. Sum the deviations from the mean (absolute values, no negatives) |(4-7.4)|+|(6-7.4)|+|(8-7.4)|+|(9-7.4)|+|(10-7.4)| = 9.6 3. Divide the sum by the number of data (n=5) to get 9.6/5=1.92 4. 1.92 is ...
May 4, 2014

Math
Use comparison method: 6-x=y=x-2 means 6-x=x-2 Solve for x and substitute into the original equations to solve for y.
May 4, 2014

math
Your work is correct, but probably made some mistake with the calculator. Volume = πr²h*1.06 = π(51)^2(120)×1.06; =330847.2π =1039387.133 mm³ approximately.
May 4, 2014

engineering
For the experiments to verify water-cement ratio, go with Bob Pursley's idea. Water is necessary for the concrete to set, but too much water will weaken the concrete. Too little will make it unworkable, and will end up having voids. Plastisizers are usually added to ...
May 4, 2014

Science
Weight = total air resistance, so by Newton's first law, the skydiver free-falls at uniform (terminal) velocity.
May 4, 2014

Algebra 2
Games are random processes. All we can say is that if he wins, he gets one point, and if he loses, he loses one point. We also know (or believe) that the probability of winning or losing is each 50%. The actual outcomes depends naturally on chance. But in the long run, the ...
May 4, 2014

Algebra 2
oops The probability on the second line should read 0.5 (not negative).
May 4, 2014

Algebra 2
Find probability of numbers matching (2/4) and not matching (2/4). Construct table for A: Outcome value,x P(outcome) x.P(x) Win..... +1 ...... 0.5 ....... 0.5 Lose.....-1 ...... -0.5 .......-0.5 Sum(x.P(x))=0, so game is fair.
May 4, 2014

Chemistry
Let K=[HI]²/([H2][I2]) The given reaction is in equilibrium at 430°C, if K=Kc=54.3 Substitute given concentrations to get K=[HI]²/([H2][I2]) =0.5²/(1*1) =0.25 < 54.3 Therefore the reaction is not in equilibrium and will proceed in the forward direction ...
May 4, 2014

Algebra
Divide each term of the numerator by 2m^3: -6m^9/(2m^3) = -3m^6 -6m^8/(2m^3) = -3m^5 -16m^6/(2m^3) = -8m^3 Choose your answer accordingly.
May 4, 2014

Precalculus
Yes, the square bracket means the value is included in the interval, and ( or ) means excluded. There are other notations where ( or ) is replaced by a square bracket pointing outwards, for example, [0,2π) is the same as [0,2π[ To solve the above problem: cos^2x=2+2sinx ...
May 4, 2014

Geometry
π is equivalent to 180° So 7π/4=7*180/4=315°
May 4, 2014

Trignometry
Since it is a rational number, the numerator and denominator can be replaced by integers. Using (b), you can create any integer, and using (a), you can divide the two numbers, which means you can create any rational number. Hope that helps.
May 4, 2014

Trignometry
Assuming (c) is the equivalent of the original question: "given any positive rational number q, show that pressing some finite sequence of buttons will yield q" then we need a transformation from q -> q using the given functions. We look for mapping R to R, or ...
May 4, 2014

Math
The important term to consider is 60(1/3)^t, which has a domain of R (all real) and a range of (0,+∞). Therefore dom T(t) = R ran T(t) = (10,∞)
May 4, 2014

Math
The model is an exponential function such that e^rt=(1/2) where t=14 hours. e^(14r)=1/2 14r=ln(1/2) r=ln(1/2) / 14 =-.04951 (approx). In 22 hours, factor=e^(-0.04951*22) =0.336475 approx.
December 14, 2013

math
Step 1: Define variables: c=number of cars t=number of trucks "a dealer has 30 cars and trucks" translates to c+t=30 which means t=30-c .....(1) "If 2 more cars are delivered, the dealer will have 3 times as many cars as trucks." translates to c+2=3t .....(...
December 14, 2013

Math - Trig
Assume the observations were made from the same building. Let the distance of the building from the tree is D in m. Then D(tan22+tan50)=150 D=(150)/(tan22+tan50)
December 14, 2013

CHIMIE - English translation of question.
90 mL of 1.5N BaSO4 is mixed with 75 mL of 0.6M Na2SO4. 1. Calculate the ionic force of the resulting salt solution. 2. Deduce the value of the activity coefficient of Na+. Thank you. Rahil: SVP vérifiez si les valeurs sont bien 1,5N et 0,6M (surtout le mélange ...
December 14, 2013

SAT Math
An example problem could be: between 1 and 1000, how many numbers are neither divisible by 2 nor by 3. So from 1 to 1000, 500 numbers are divisible by 2 (even numbers), and from 1 to 999, there are 333 numbers divisible by 3. However, between 1 and 996 (next number is 1002)...
December 7, 2013

physics
It depends on the speed of the plane if the frame of reference is terrestrial, namely if the object is considered stationary on firm ground. If the frame of reference is the airplane itself, which cruises at a constant speed in rectilinear motion relative to the terrestrial ...
November 29, 2013

MATHS
If you are working on number theory, look up Chinese remainder theorem. If you have a puzzle or problem to solve, you can do it as follows: If we took one apple from the box, then the number of apples must be divisible by 2, 3, 4, 5, and 6. Therefore the number of apples would...
November 27, 2013

german
I do not speak German, but the little I know tells me that the "other" verb is placed at the end of the sentence, such as: Ich muss dort Deutsch sprechen. There I must speak German. One of our math teachers speaks fluently German. Hope he can give you a more detailed...
November 27, 2013

math
Bill amount * (1-0.03) to give the discounted amount, then add 6% tax Bill amount * (1-0.03) * (1+0.06) For \$26.14, the final amount comes to \$26.88, after rounding.
November 27, 2013

trig.
The tree top is 100*tan(52) feet higher than the person's eyes. To get the height h, above ground, h=100tan(52)+5 feet = 133 feet, approximately
November 27, 2013

Physic: Projectile Motion
let α be the angle of the projectile with the horizontal as it leaves the muzzle. Here α=0 degree. Let vi=initial muzzle velocity, then horizontal velocity, vh=vi*cos(α). Time taken to reach the target t=Horizontal distance/vh where horizontal distance = 100m...
November 26, 2013

Math
To find the x-intercept, let y=0 and solve for x in 3x=12, or x=4. So the ordered pair would be (4,0). Follow similar rules for the y-intercept.
November 18, 2013

math urgent
Use your calculator to find 26×56. Since they are both raised to the 6th power, if you are interested in mental calculations, you can apply the law of exponents and multiply the two bases before raising to the given power.
November 17, 2013

algebra
There are two equations with one unknown, and the two possible solutions are inconsistent.
November 17, 2013

math check
69 is correct!
November 17, 2013

chemistry
M*V=2.01*711/1000
November 17, 2013

Calculus - Optimization
Good catch, Steve. Thank you.
November 16, 2013

Calculus - Optimization
Let the size of the square (cross-section) be s. Then we need to maximize V=s²(24-2s) with respect to s. First find the derivative and equate to zero: dV/ds = 48s-6s²=0 means s=0 or s=8 s=0 corresponds to a minimum volume and s=8 corresponds to a maximum volume. So ...
November 16, 2013

Principal, P = \$10000 interest per period of 6 months, i = 0.06 number of periods, n = 5 yrs/0.5 yr = 10 Value at maturity =P(1+i)^n He will have money to pay for the Jeep, and perhaps the sales taxes as well.
November 10, 2013

Math
7×6=42 7×7=49 so there are 6 and (48-42)=6/7 apples, or 6 6/7 apples.
October 15, 2013

Homework Help Calculus
Problem of units conversion. 0.4071504079 m³ =0.4071504079×10^6 cm³ =407150 cm³ approximately.
October 15, 2013

Algebra 2
The first equation has a y-intercept of -17. The x-intercept is -17/7=-(2+3/7) =-2.4286 approx. The second equation has a y-intercept of -2.4, and x-intercept of -2.4/(-0.3)=8. If you produce the two lines to intersection, the estimated solution would be (-2, -3)
October 15, 2013

Practice Exam Calculus
you can use the same approach as for the paint on sphere. A=4πr² dA/dr=8πr ΔA=8πr Δr =8π(20)(1/5) =32π
October 15, 2013

Math
If you mean (4/8)y - 21 = 3 then y=48 as you got. If the question were (4/8)y-21=0 then y=42
September 23, 2013

Chemistry
MC12H22O11=342 MCO2=44 C12H22O11+xO2=12CO2+... Ratio of mass of C12H22O11 to CO2 =342:12*44 =342:484 Mass of C12H22O11 that produces 3.6g CO2 =3.6*(342/484) =2.544g Mass ratio NaCl:C12H22O11 =(5.5-2.544):2.544 =2.956:2.544 Calculate mass percentage and reduce to 3 significant ...
September 23, 2013

geometry
The question defined what complementary angles are, but did not say that a and b are complementary. The question has a solution if a and b are complementary, and will be assumed as follows. if a and b are complementary, then a+b=90 angle a is 21 degrees more than twice angle b...
September 21, 2013

Surveying
Are you measuring the vertical angle (from the horizon) where 90 degrees is vertically up, or the zenith angle (from zenith, vertically up) where 91 degrees is just below the horizon? A vertical angle of 91 degrees requires a special eye-piece/prism, and is past the vertical...
September 21, 2013

math
There are 9 choices for each of the first three digits, and 25 choices for the last two digits. Use the multiplication rule to get: 93252
September 20, 2013

statistics
Use a probability tree: Next person male: 42% wash his hands: 43% female: 58% wash her hands 66% P(wash)=42%*43% + 58%*66% =0.5634
September 20, 2013

chemistry
When heated: 1. acetic acid phase change 2. sodium bicarbonate decomposition into sodium carbonate, carbon dioxide and water. 3. arsenic trioxide phase change
September 7, 2013

Chemistry
First establish the combustion equation and have it balanced: C8H18 + O2 -> 8CO2 + 9H2O. Balances for C, but not for O. Since there are 16+9=25O on the right, we need to double the number to make the number of molecules on the left a whole number. So it becomes: 2C8H18 + ...
September 7, 2013

physics
Hydrostatic pressure p varies linearly with height h, i.e. p=ρgh For a height of H and width of W, total force, F = W∫ρgh dh =ρgH²W/2 Ensure that all values are in SI units.
September 7, 2013

math
Trade discounts are successive discounts. The net price factor is equivalent to the net price of a \$1 list price. Thus \$1*(1-0.25)(1-0.15)(1-0.10) =0.57375 Use this factor to calculate the net price of \$800 list.
September 6, 2013

geometry
I was thinking of something along the same lines, but couldn't find a good way to put it in action. Thank you for sharing the bright idea.
September 1, 2013

physics
Make a free body diagram of the staging. Sum forces acting on the staging, and the total should be zero. Upward (reaction) forces=660+410=1070 N Downward forces = 620 N + W Sum to zero 620+W=660+410 W=660+410-620 =450 N.
September 1, 2013

maths
Set up a system of equations: Let W=width L=length then Perimeter = 54 = 2(L+W) ...(1) L=2W-3 ...(2) Solve W by substituting (2) in (1), and hence solve for L.
September 1, 2013

math
Trade discounts are calculated successively. Thus for a list price of \$1000, net price = \$1000(1-0.3)(1-0.35)(1-0.2) = \$364 Thus the trade discount amount (for a list price of 1000) is 1000-364=\$636. For the list price of \$29000, follow the same procedure.
August 24, 2013

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