Posts by MathMate
Total # Posts: 12,086
Let s=specific gravity of mercury=13.6 K=point at lower end of water column h=height of mercury above K in the other column then equate pressure at K on both arms: 13.6*1.00 = h*13.6 solving, h=1.00 cm This means that the mercury level was at 1.00/2=0.50 above K before adding ...
physics (to Cameron/Tyler)
Among the 9 physics questions you have posted within the last 24 hours, you have not shown any effort on your part. Is it because you have absolutely no idea about the subject, or is it because you'd like someone else to do the work for you? If it is the former, I suggest ...
Assuming no loss in the impact(s), then, let M=mass of Juggles and equate gravitational potential energy (g=acceleration due to gravity) 75kg*g*2.5=M*3.7*g Solve for M.
PLEASE HELP BEEN STUCK ALL DAY CALCULUS
If we apply linear approximation using calculus, then: V=πr^2h dV/dr=2πrh ΔV≈2πrhΔr =2π(4)(12)(+0.2-(-0.2)) =2π(4)(12)(0.4) =38.4π
Newton is kg-m/s² Since both sides of the equal sign must have the same units, we conclude: a * m = kg-m/s² and B *kg/m = kg-m/s² Find the units of a and B by solving the two given equations.
Ignoring dissipative losses (air resistance, friction, etc.), difference of kinetic energy equals work done, => (1/2)m(28.3^2-23.3^2)=226000 j Solve for m.
There is at least one great circle that passes through any two non-coincident points lying on a sphere. If the two points are diametrically located, there is an infinite number of great circles that pass through the two points. The proof is relatively simple. The two points ...
Assuming the earth is a perfect sphere, and with a radius of 6400 km, there are exactly two parallels with a radius of 2500 km, located at approximately cos-1(2500/6400) =67° N or S.
See response to related/similar problem. http://www.jiskha.com/display.cgi?id=1454498132
The reflex angle of a given angle is the larger between the angle itself, and the angle formed by 360 minus the angle. For example, the reflex angle of 150° is 360-150=210°. Since angle pqr=1 1/2 right angles = 135°. Calculate the reflex angle of 135° by ...
We started with k tags. after students, we have k-k/2=k/2 left. after parents, we have k/2-100 left after teachers, we have (k/2-100)(1-3/5) left You can simplify the last expression to present the final answer.
Use Z=(X-μ)/σ where Z=z-score X=variable value μ=mean σ=standard deviation Assuming normal distribution, the left-tail normal distribution table gives the probability of the z-score (or less). Example, part (a): If N=300 and random sampling, we can assume ...
Draw a Venn diagram with three overlapping circles A, B and C. Hint: start with the area A∩B∩C (in the middle) and work outwards. When completed, it will be a snap to answer the given questions.
(a) N = 11 choose 2 (=11C2) (c) 11 choose 2 less 7 choose 2, i.e. N minus number of ways of choosing two men.
If there are 14 people, there are 14C2 ways to choose the 2 alternatives. If there are 15 people, there are 15C14 ways to choose the 14 people. So the number of ways of choosing 12 jurors and 2 alternatives is 15C14*14C2
We know that time=distance / speed In this case, time = total distance / total speed =1029 miles / (45+53) mph = ? hours
Use the ratio of atomic mass to the molecular mass. For example, to find the number of grams of Na in 20 g of NaOH atomic mass of Na = 23 molecular mass of NaOH=23+16+1=40 mass of Na in 20 g of NaOH =20g*(23/40)=11.5g
Yes, because (-6.8)² =(-1)²(6.8)² =(1)(46.24) =46.24 Be aware of usage of parentheses, for example: (-2)² =(-1²)(2²) =(1)(4) =4 BUT -2² =-(2²) =-(4) =-4
The standard equation for depreciation is FV=PV(1-i)n where FV=future value PV=present value i=depreciation rate per annum, in decimals n=number of years Example: Find the value of a car after 10 years if it was purchased for 50000 and depreciated at 20% per year. PV=50000 i=0...
Geology and soils
Void ratio, e, is the volume of voids, Vv, divided by the soil volume Vs. Total mass, M=37.82-16.15=21.67 Mass of solids, Ms=34.68-16.15=18.53 Gs=S.G. of soil particles = 2.7 => Vol of soil, Vs=Ms/Gs=18.53/2.7=6.863 mL air-void content, ac=0 => all voids are filled with ...
The first three questions may be solved using the relation: molarity (mols) = number of moles / volume (L) where number of moles = mass (g) / molar mass (g). Example: 10.0 g of NaCl is dissolved to make 0.523 L of solution. Find molarity of the NaCl solution. number of moles...
Regular price = 4 shirts at sale price 2*regular price = how many shirts at sale price ?
First write the neutralization equation: NaOH+HNO3 -> NaNO3+H2O so C1V1=C2V2 2.0M*0.25L=XM*1.050L Solve for X and compare with 0.48. Pay careful attention to significant figures.
Convert initial velocities to m/s 60 km/h=60*1000/3600 m/s=16.67 m/s 180 km/h = 50 m/s Use kinematic equation: v^2-u^2=2aS where u=initial velocity v=final velocity a=acceleration (deceleration is negative) S=distance travelled before stopping
The minimum of a parabola is the y-value of the vertex. See previous response.
By completing the square, y=x^2-4x-32 =(x-2)²-4-32 =(x-2)²-36 The line x-2=0 passes through the vertex, hence the vertex is (2,y(2))=(2, -36) The line of symmetry of a parabola that opens up or down is the vertical line through the vertex.
When the leading coefficient is positive, a parabola opens up. Leading coefficient is the coefficient of the term with the highest degree.
Answer is good up to (0.4k+0.6w) L. Since we do not know the values of k nor w, their coefficients cannot be added together. The correct answer would be (0.4k+0.6w) L.
Example to help you: 30% of 4L of orange juice is added to 70% of 5L of grapefruit juice, find the total volume. Volume of orange juice = 30% of 4L =0.30*4 =1.2L Volume of grapefruit juice=70% of 5L =0.7*5 =3.5L Total volume = 1.2L+3.5L=4.7L
(a) Law of conservation of momentum: m1v1+m2v2=(m1+m2)v since m2=0.1m1 m1v1+0.1m1v2=(1.1m1)v solve for v v=(m1)(v1+0.1v2)/(1.1m1) =(v1+0.1v2)/1.1 (b) Assuming no loss in total energy, and assuming v1>v2, then the shark itself (without food) has lost energy, since its ...
In geometry, drawing a sketch from given information is half-way to the solution. Note bearing is measured clockwise from North. If you draw the sketch in Cartesian coordinates, using P at the origin, you will have P(0,0) Bearing 150°? ?=90-150=-60° in Cartesian ...
You're welcome! :)
By the law of segments, mCB+mBD=mCD so 4w-4 + 2w-8 = 24 Solve for w.
Yes, your approach is correct, except watch for the following. (1) In principle, part (A) should be done using calculus. If you have not done calculus before, what you did is appropriate, EXCEPT that the interval for p between 4 and 2 is way too large because q(p) varies ...
Solubility is the amount of solid that dissolves in 100g of water at the given temperature. 10.1 g dissolves in 50 g H2O at 25°C X g dissolves in 100 g H2O at 25°C Solve for X.
Cu(II) oxide is CuO so 3CuO+2NH3 → 3Cu+N2+3H2O From 2NH3 and 3CuO, we conclude that 2 moles of NH3 reacts with 3 moles of CuO to form 1 mol of N2. Find the molar masses of NH3 and CuO and determine which is the limiting reagent. Use stoichiometric ratios to ...
Kinematics equation with zero initial velocity: h=(1/2)gt^2 => time, t = √(2h/g) seconds h=49', g=32.2 ft/s² speed = distance/time = (80-3)/t ft/s =44.14 fps
horizontal lines have zero slope, so rate of change (=slope)=0. Any straight-line function has the form y=mx+b where m is the slope, and b is a constant. Compare this with the equation of function 2 to determine the slope. Since rate of change of function 1 is zero, so ...
smallest number with 3 different digits: 100000...000002 assuming leading zeroes do not count. Add enough zeroes in the middle to satisfy the minimum number of digits. Example: 1,002 in the thousands 1,000,002 in the millions, etc.
It depends on how many tests you have had, and what you will get for the final.
Distribute and simplify: (1/3)x(15x-12y)-(1/2)(6x-4y) =x(5x-4y\)-(3x-2y) =5x²-4xy -3x +2y
A rhombus has four equal sides. One way is to prove that the two triangles on each side of a diagonal are congruent. Since the altitudes of these isosceles triangles are congruent and are the altitudes of the rhombus, the altitudes of a rhombus are congruent.
See answer to your previous question: http://www.jiskha.com/display.cgi?id=1483510596
Answer is in the products of the reaction. The reactants are already known. H2S (g) +Zn(NO3)2 (aq) &rarrow; ZnS (s) + 2HNO3 (aq)
Each free cube has a surface area of 6(10²)=600 cm² exposed. Each cube with one face connected has 5(10²)=500 cm² exposed. Each cube with two faces connected has 4(10²)=400 cm² exposed. If n cubes are joined together, there are 2 (end) cubes with ...
Sorry, I don't understand what your "working" is trying to do, but in any case, 8+5≠13/2≠11.5 and so on, so some corrections on your part need to be done. Given that a:b = 8:5 and b:c= 3:4 What we need to do is to multiply each ratio appropriately so that ...
complement of angle X=90-X supplement of angle X=180-X => complement (C) =supplement (S) -90 C+S=126 C+(C+90)=126 2C=126-90 Solve for C and hence X.
Given R=6400 km arc=Rθ The first leg is equi-latitude at 40N with a meridian difference of θx=(38-22)=16° Distance travelled =Rθx cos(40) =6400*(16*π/180)cos(40) =1369.09 km The second leg is along a meridian with a latitude difference of θy(40-...
height : shadow = 25 :15 = 40 : X? Cross multiply to get X=40*15/25=24 m
See related questions, for example: http://www.jiskha.com/display.cgi?id=1350232603
Chemistry HELP! CONFUSED!
First write the equation of the reaction: reactants: NaHCO3+CH3COOH products: CH3COONa+CO2+H2O From the molar masses of NaHCO3 = 23+1+12+3*16 = 84 CO2 = 12+2*16 = 44 We find the stoichiometric ratio of the two compounds to be 84:44 (approximately) Hence by proportions/ratios, ...
Assuming probabilities work evenly for 30 times, then you would have won the $5 prize 30*0.15=4.5 times, with a total value of 4.5*5=$22.5 while paying $30 to play. So your expected winning (for one play) is 22.5/30-$1=0.75-1=-$0.25 i.e. you expect to lose 25 cents each time ...
If you substitute any of the four answer choices into the equation: (y-2)^3=(y+2)^3 you will find that none of them is a good answer. So I suspect there is a typo for the question. The equation as shown above can be solved by assuming y=a+bi Expand both sides to give 12b^2-...
Area of the (orange) right triangle =(3*4)/2 =6 units Area of the rectangular board =20*15 =300 units Assume that 1. a dart always falls within the rectangular board 2. the probability of hitting anywhere in the rectangle is equal then the probability of the dart striking the ...
In chemistry, since there are more than 26 elements, some elements are represented by two letters of the alphabet. The first (or the only) letter of an element is ALWAYS written in capital letters to avoid confusion, since formulas of compounds are written without delimiters. ...
Work from inside the parentheses, (g(f(3x))' for x=1 =(g(f(3(1)))' =(g(f(3))' =(g(2))' [from table] =g'(2) =5 [from table]
Assume "store one year" means 365 box-days and not "a year or part thereof". k=320000 boxes/year = 320000/365 boxes/day = 876.7 boxes/day If supplies are produced every n days, then it must produce nk boxes at each production, and storage requirements are P...
What does [ABCD] represent? If it is the area of the kite, then we know that the area of a kite is the product of the diagonals ÷ 2. Note: You are fully expected to draw a duly labelled sketch in order to follow the following explanations. So AC*BD/2=60 AC*BD=60*2=120 ...
For a (complete) sphere, volume=(4/3)πr³ The volume of material is the volume of whole sphere (radius r2) minus the volume of empty spherical space (radius r1). The thickness t is the difference between r1 and r2, i.e. r1+t=r2. Vm=(4/3)π(r2³-r1³) The ...
Area of a rectangle = Length * width (or breadth) = L*W Take out your calculator to calculate the product. For someone who has done factoring, 11.5*12.5 =(12-.5)(12+.5) =12²-0.5² =144-0.25 =143.75 without using a calculator.
We know that diagonals of parallelograms bisect each other. Using this fact, we would draw two intersection lines with an included angle of 60° (and 120°). From the intersection, measure out four vertices 5/2=2.5 cm on each side of one line, and 7/2=3.5 cm on each side...
suggested approach: create a class for each Employee, with class properties as integer code string name double salary char category double bonus double totalSalary with class methods called double calculateBonus() void printEmployee() Use switch-case to calculate bonus. Add ...
The most important part of answers of this type of physics problems is the assumptions made to arrive at the answer. With a given answer, these assumptions are usually given, but not in the present case. The given answer corresponds to the following assumptions: 1. D>>H ...
1. Calculate moles of CoCO3 =6.0/(58.933+12.0+3*16.0) =6.0/118.9 =0.0504 mol 2. Calculate moles of HCl =40/1000*2.0 mol =0.080 Using stoiciometric ratios CoCO3 used = 0.08*1/2=0.04 mols => CoCO3 is in excess (<0.0504). The remaining answer can be obtained by finding the ...
Principal and interest after 8 months =8000(1+0.0276/12*10)=8184 Let a=initial repayment amount (n=1), then the repayment amount at month n a(n)=a*r^(n-1) where r=2 Total repayment amount Sum=a(1)+a(2)+...+a(10) =a(r^10-1)/(r-1) =1023a Equate total amount owing with amount ...
Do you mean volume=54 dm³ ? Use 1 dm³=1000 cm³ volume=length*width*height and solve for height.
Analyse the name piece by piece. Pentene = a 5-carbon hydrocarbon with a single double bond. Pent-2-ene has a double bond in the second carbon atom. (Z) at the beginning means that the two CH3 groups are on the same side of the double bond (Zusammen) means "together"...
The rebound height is a geometric sequence, i.e. H(n)=H0*r^n where n=number of bounces. For H0=16', r=0.25 H(1)=16*(0.25)^1=4' H(2)=16*(0.25)²=1' ...
Yes, I did it differently, and this time I can eliminate all other variables. I get 0.06 m/s only if the final speed has been reduced by 0.59 of the original speed. If the final speed is 0.59 of the original speed, then μ=0.1396. Let: t=theta=16.1° g=acceleration due to...
Fun Physics (to Rose)
It's an interesting problem. Do you happen to be given the initial velocity as 0.7 m/s ? I have an impression that μ is dependent on the initial velocity.
Propagation value of variable is a very useful iterative method for solving system of equations, especially if certain variables have constraints. The given example is especially favourable example for the method because the coefficients are diagonal dominant. We rewrite the ...
discrete mathematics (to yopo)
Thank you! I appreciate your comments. Feedbacks are appreciated, good or bad!
Number of arrangements of n persons in n positions is n!. Example, 3 people, 3 places, there are 3!=6 possible arrangements. a) If Syahirah mush be in the third position, there are 5 people left for 5 places. Use the formula above. b)If Dinesh must be second, and Felina third...
How many are in the family?
algebra (to Rehan)
Please check your own posts and "related questions" before reposting. This is the sixth post of the same question in the last 50 hours, answered by 5 different tutors.
This question has been answered 4 times in the last 50 hours. The links are the first four under "Related Questions" below. It is always to your advantage to go through the "Related Questions" before you even press the "Post Answer" button. Also, ...
a shorter way. 1/sin(x)+1/cos(x)=2√2 multiply by sin(x) on both sides, 1+tan(x)=2√2 sin(x) square both sides (1+tan(x))²=8sin²(x)=8tan²(x)/sec²(x) using 1+tan²(x)=sec²(x), (1+tan²(x))(1+tan(x))=8tan²(x) set t=tan(x), and ...
maths (to Steve)
Nice thought! Thank you!
Perhaps there is an easier way to solve this problem, but this is all I have for now. Where there is no confusion, sinX=sin(x), cosX=cos(x) We'll work on the left side first cscX+secX =1/sinX+1/cosX =(cosX+sinX)/(sinX*cosX) =2(cosX+sinX)/sin(2x) [use sin(2x)=2sin(x)cos(x...
Clock runs 10 minutes fast every 24 (real) hours. So clock shows 24*60+10=1450 minutes after 1440 minutes. 3PM-10PM=2+15 hours = 17 hours = 1020 minutes. Actual time passed from 10PM = 10pm + 1020*(144/145) =10 pm + 1012 28/29 minutes =14:52:57.93
If you know the ascii code, 48-57 0-9 65-90 A-Z 97-122 a-z Most of the remainder (0-127) are special characters, except space (32) and perhaps other white space characters. It will consist of one while loop to check each of the above. For the extended ascii table, see http://...
Start salary=700 Top of scale = 1500 Number of increments to reach top = (1500-700)/40=800/40=20 Assume increment is annual, so it takes 20 years to reach the top of the scale.
If it is open at both ends, then the lengths are the same. Volume of steel is obtained by subtracting the inner area from the outer area and multiplied by the length. V=(π/4)(24²-20²)(55) cm³ = 2420π
annual interest = 4*22.05=88.20 $1960 earns 88.20 interest in one year, so annual interest, i=88.05/1960=0.045, or 4.5% per annum
total loan=$20092 Down=$2000 Amount to finance, A=20092-2000=$18092 term = 5 years compounded monthly monthly interest, i= $0.069/12=0.00575 R=1+i=1.00575 number of periods, n = 5*12=60 Monthly payment, P=AR^n*(R-1)/(R^n-1) = 18092*(1.00575^60)*(0.00575)/(1.00575^60-1) =357.39...
For the diluted acid, C1,V1=diluted acid C2,V2=sodium hydroxide NaOH+HCl=NaCl+H2O Use CiV1=C2V2 C1*25.0 mL=0.5M * 15.00 mL C1=0.5M*15.00/25.0= 0.3 M Concentration of original hydrochloric acid = 0.3 M * (250.0/25.0) = 3 M (note only one significant figure is retained as a ...
The translation rule is T(Δx,Δ)(x,y)->(x+Δx, y+Δy) .......... (1) Now we need to find Δx and Δy. We know that 7+Δx=2 -3+Δy=5 Solve for Δx and Δy and substitute in the transformation rule (1)
use sec²A=1+tan²A and let t=tan(A) sec(A)-tan(A)=10 √(1+t^2)-t=10 √(1+t^2)=(t+10)² 1=20t+100 t=-99/20 A=atan(-99/20)=-78.5788 (approx.) sec(A)=1/√(1+t^2)=101/20 cos(A)=1/sec(A)=20/101 sin(A)=-sqrt(1-(20/101)^2)=99/101 (note: A is in Q4, so sin(...
Probability & Statistics
Calculate Z as follows: z=(x-μ)/σ =(11000-8000)/1000 =3 From probability tables, find P(Z>z). P(Z>3)=1-P(Z<3)=1-0.99865=0.00135
Use the point of division formula. Let the divided segment be PABCQ Then r1=PA/PQ=1/4 r2=PB/PQ=2/4 r3=PC/PQ=3/4 Applying the point of division formula to points A, B and C: A(a+r1(c-a), b+r2(d-b)) B(a+r2(c-a), b+r2(d-b)) C(a+r3(c-a), b+r3(d-b)) For more explanations and ...
"Will paid 1/3 of the dinner bill." means Micah and Sue paid (1-1/3)=2/3 of the bill. If Micah and Sue paid in the ratio 2:5, that means Sue paid 5/(2+5)=5/7 of their portion. $6÷5/7=$8.40 which is 2/3 of the cost of dinner. Proceeding the same way, 8.40&...
algebra (To adiba)
The question is not clear when out of context. Are you working with arithmetic or geometric progression? "rate of growth" could be an amount (arithmetic) or a ratio (geometric). Your answer is (almost) correct for linear growth (arithmetic). You only have to put the ...
We have AD perpendicular to BC. So triangle ABD is right-angled at D. AB=7, BD=3, therefore by Pythagoras theorem, AD=√(AB²-BD²) =√(7²-3²) =√40 Construct triangle ABD with the given dimensions. Extend BD to C such that BC=13. Join A and C ...
Transformations (to Keith)
Keith, please refrain from using different screen names. Also, please mention that you are reposting the question, and reposting within a short time could mean duplicate efforts by tutors, and hence slow the answering process. Your previous question has also been answered here...
Compound interest (info please)
Sorry, more details required. The following details seem to be subject to interpretation. Please give your comments. 1. the advance payment in December is a prepayment for the next two months. Does that practice continue for the rest of the loan repayment? 2. Is the 13th month...
Compound interest (info please)
Is the interest rate given? When was the 13th month advance payment paid, Dec.15 or January 15?
Transformations - Maths
The general transformation equation is: g(x)=a*f(b(x-h))+k where h=horizontal translation (right if h>0) b=horizontal scaling (stretch if 1/b>1) a=vertical scaling (stretch if a>1) k= vertical translation (up if k>0) applied in the above order, i.e. according to ...
similar to the APGAR test for newborns. Give it a try and post what you get.