# Posts by MathMate

Total # Posts: 11,748

**physics**

Kinetic energy, KE = (1/2)mv² resistive force = constant Retaining half the velocity means (1/2)^2=1/4 of the kinetic energy. Since 50% of the KE penetrates 25 cm, so 25% of the (remaining) KE penetrates 12.5 cm.

**physics**

p(t)=3t²-2t+1 W Δp =p(4)-p(2) =41-9 =32 W

**physics**

Power =mgh/Δt / efficiency =100kg*10m/s²*10m/5s / 60% = 2000/0.6 = 3333 W = 3.33 KW Thank you for posting the answers, but there are too many decimal points that I cannot make anything out of them. In addition, (C) and (D) seem identical to me.

**Physics**

585 zag/zoyear =585 *(1/0.18) zig/ (0.4 years) =(585/0.18) zig / (0.4*365*24 hours) = 0.928 zig/hour

**Engineering**

Try http://faculty.uoh.edu.sa/m.touahmia/CE353-CH3.pdf

**math**

The distance between two points with coordinates P1(x1,y1) and P2(x2,y2) is given by the distance formula: D(1,2)=sqrt((x2-x1)²+(y2-y1)²)

**Math**

36 students B:G = 3:1 = 27 : 9 Add x girls, 27/(9+x)=9/5 Solve for x by cross multiplication.

**algebra 2**

|x|-2≤-3 |x|≤-3+2 |x|≤-1 => x≤-1 or -x≤-1 => x≤-1 or x≥1 => on the number line: <------ -1.......0...... 1 ------>

**Chemistry**

The question is not complete. I assume you are asked to find the quantity of CO2 produced by heating 25g of CaCO3. Molecular mass of CaCO3=40+12+48=100 From the equation, 1 mole of CaCO3 produces 1 mole of CO2. Since 25g is 0.25 mole of CaCO3, we conclude that 0.25 mole of CO2...

**Chemistry**

The question is not complete. I assume you are asked to find the quantity of CO2 produced by heating 25g of CaCO3. Molecular mass of CaCO3=40+12+48=100 From the equation, 1 mole of CaCO3 produces 1 mole of CO2. Since 25g is 0.25 mole of CaCO3, we conclude that 0.25 mole of CO2...

**algebra**

* outcome 3 is "hit neither"

**algebra**

Calculate expected gain, E(X), of the venture. If E(X) is positive, it would probably be advantageous to sink a well. Expected value is the following sum: E(x)=Σ G(X)*P(X) where X is a possible outcome, G(X) is the net gain of the outcome, and P(X) is the probability of ...

**computer science**

Looks good to me!

**algebra**

To find the x-intercept, set y=0 and solve for x.

**maths**

You're welcome!

**maths**

Area of each triangular face = (1/2)base*height Surface area of tetrahedron = 4*area of each face.

**Math**

3768 grains mean 3768*1 second=3768 seconds. Convert to hours, minutes and seconds: 3768 seconds / 60 s/min. =62 minutes 48 seconds = 1 hour 2 minutes 48 seconds. The other rewards may be worked out in a similar way.

**math**

4C3(1/2)^3(1/2)^1 =4(1/16) =1/4

**math**

2=2^1 3=3^1 4=2^2 5=5^1 6=2*3 7=7^1 The least common multiple must have factors that satisfy all of the above: 2^2*3*5*7=420

**math**

Mid-point of (3,8) and (9,16) =((3+9)/2, (8+16)/2) =(6,12) Mid-point of (8,11) and (x,13) =((8+x)/2, (11+13)/2) =((8+x)/2, 12) To have the same mid-point, the x- and y-coordinates of the mid points must match. so (8+x)/2 = 6 Solve for x.

**statistic**

Total number of balls = 5+6+6=17 P(RR)=Probability of two reds =(5/17)*(4/16) P(WW)=(6/17)*(5/16) P(BB)=(6/17)*(5/16) Probability of two same coloured balls =P(RR)+P(WW)+P(BB)

**math**

You have assumed compound interest compounded monthly. Assuming these assumptions are correct, then we have total amount F, R=monthly installment deposited at the end of the month, i=monthly interest, n=48, I=1+i, F=R(I^(n-1)+I^(n-2)+...+I^(0)) =R(I^n-1)/(I-1) =500((301/300)^...

**Basic Algebra**

Also, note that factors must exceed 8, from the context of the question.

**Basic Algebra**

See http://www.jiskha.com/display.cgi?id=1408443950

**Science**

You're welcome! :)

**Science**

The independent variable is the amount of money offered, which in this case takes on only two values, $0 and $5. Evidently other experiments could be carried out to have varied incentives, assuming the teacher keeps the job long enough to do further experiments.

**Applied Programming**

Technically you do not need to ask for a 2D or 3D calculation because there is no overlap of the shape names. You will need a string of if-else-elseif-endif statements, or more conveniently a switch statement. Use the "default:" option in case the user feeds a wrong ...

**chemistry calculations**

It is given that the reaction at the given temperature is in equilibrium. Next check if the reaction is homogeneous: all gases, so homogeneous. Now denote the stoichiometric coefficients by a,b and c for the reactants and products respectively (all equal to 1 in this case). ...

**Basic Algebra**

This is more a riddle than math. In my opinion, it is hinged on the word "equally", which could mean equally to the dollar, or to the cent. Taking the first case: everyone has an equal number of dollars. Factoring 5130, we have as prime factors: 2,3³,5,19, which...

**maths**

If we assume that the ordered pairs (x,y) follow a linear rule y=ax+b, we will be able to solve for the rule using two of the ordered pairs, and use the third to check if the rule is appropriate. Thus, for the first ordered pair: y=ax+b => 14=180a+b .... (1) For the second ...

**MAth**

The question as it is has a large number of solutions. In general, optimization problems have an objective function, such as minimum cost, minimum surface area, etc. and subject to constraints, such as maximum number of fruits per box, or maximum sizes, etc. An example ...

**Precal**

Hint: look up triangle inequality. Basically, it says that the sum of the lengths of any two sides of a triangle is greater than or equal to the length of the third side.

**calculus**

The diagonals are obtained by the sum and difference of the two vectors: a+b=<-2,5>+<3,2>=<1,7> a-b=<-2,5>-<3,2>=<-5,3>

**Geometry**

A plot of the three lines L1, L2 and L3 may be viewed here: https://imagizer.imageshack.us/v2/500x300q90/674/pUzIJX.png

**Geometry**

This problem is very interesting, and as Steve pointed out, there are 4 circles each of which is tangent to all three lines. This prompted me to look for a general solution for all four circles. If we first examine the condition of tangency of a circle C: (x-a)²+(y-b)&...

**math**

You're welcome! :)

**math**

When the perimeter of the triangle is doubled, it is 24. The perimeter before it is doubled is therefore half of 24=12. An equilateral triangle is a triangle with three equal sides. Perimeter = 12 Number of sides of an equilateral triangle = 3 Can you find the length of each ...

**loyla**

There is a black and a white ball left in the bag after pulling out the first. Can you find the probability of pulling out a black ball from a bag containing one black and one white ball?

**physics**

Use ratios, 15 g : 0.1 L 75 g : x L solve for x by cross multiplication.

**physics**

Let maximum velocity be x then x/α+x/β=t Solving, x=t/(1/α+1/β) =αβt/(α+β)

**riddle?**

Is this a question or a riddle?

**Math: Equivalence Classes**

To explain in more detail, we would investigate the relation: (a-2d)=(c-2b) Transposing terms, we get the same relation as (a+2b)=(c+2d) Hence all elements (a,b) in the equivalence class would have the same sum a+2b. For example, if the sum is 10, we can have 4 elements: (2,4...

**Math: Equivalence Classes**

If you haven't read the following link, you can read it before reading on: http://www.jiskha.com/display.cgi?id=1407879480 The idea of solving parts (a) and (b) of the linked question is to establish a methodical way to solve (c) and (d). The typical approach to solving ...

**math**

Area of a square = (length of each side)² If each side is measured in inches, the area is in square inches, or in².

**statistics**

Start with a table: R=rain (20%), ~R=no rain (80%) W=windy (30%), ~W=not windy (70%) If rain and wind are independent, the combined occurrence is the product of the respective probabilities. Example: (a)P(R∧W)=.2*.3=0.06 (b)P(~R∧~W=0.8*0.7=0.56 (c)... Will leave (c) ...

**statistics**

Total number of males =25+10+8=43 Total number of clients = 100 Selection is random. => Probability, P(M) = 43/100 = 0.43 You can proceed with the remaining questions in the same manner.

**Math**

As Reiny pointed out, the rings and chirps will occur at the same time every 6 seconds, or at 6, 12, 18, 24, 30, 36,.... seconds. So which of the 4 choices will be a moment where the two sounds will occur together?

**math**

Draw a diagram on paper according to the given information, and the answer will be on paper.

**math**

You don't have to solve each one, and you don't even need a calculator if you understand the following rules for integer calculations: Multiply: only odd*odd will give odd power: only odd to any power will give odd Add/subtract: only odd±even will give odd. Note...

**phy**

The few problems you have posted at the same time indicates that you are in the process of learning how to draw a free-body diagram (fbd). Follow your instructor's directions to draw a fbd and identify the triangle to be solved. You should end up with a right triangle in ...

**Chemistry**

Ammonia is NH3. The mass composition is the ratio of atomic masses (AM) within the molecule, i.e. mass composition of nitrogen =AM(N)/(AM(N)+3AM(H)) =14.0067/(14.0067+3*1.0079) =0.822 approximately.

**ias question**

If the question were "how do we write 13 aug 2014 in 5 letters without using numbers." then see http://www.jiskha.com/display.cgi?id=1400681438

**math**

The factor theorem helps us to say that the possible integral roots are in the form of (x±k), where k is a possible factor of the constant term (12) divided by a possible factor of the leading coefficient (1). Thus for the given problem, the possible integral zeroes are &pm...

**Math**

Hints: It can be shown by calculus that the maximum area of a polygon enclosed by a fixed length of perimeter is a regular polygon, i.e. a polygon with all sides and interior angles equal. It follows from the above that the maximum area enclosed by a fixed perimeter is a ...

**Physics**

1 HP = 745.6999 W 4 HP = 2982.7996 W 4t = 4000 kg Use mgh=PΔt h=PΔt/mg =2982.7996*10/(4000*10) =0.75m approximately

**maths**

Correct! Well done! :)

**maths**

use proportions/ratios: 1 7/8 : 2 1/2 ≡ x : 4 Simplify ratios: 15/8 : 5/2 ≡ x : 4 15 : 20 ≡ x : 4 3 : 4 ≡ x : 4 Solve for x.

**math**

Use ratio/proportions: 5.58 : 318.76 ≡ x% : 100 Product of means = product of extremes 318.76*x% = 5.58*100 x% = 5.58*100/318.76 = 1.75% approx.

**fractions/math / Help!**

With what Reiny showed, there should be sufficient information to work out 425 by yourself as an exercise. I will give you another example, 525: 525÷5=105 105÷5=21 21÷3=7 since 7 is a prime we cannot go further. so 525=5*5*3*7=3*5²*7 You're ...

**collge sydney**

Hints: Kinetic energy of a rotating object is given by: KE = Iω² I is moment of inertia in kg-m² and ω is angular velocity in rad/s. 1 RPM= 2πradians/60 s = π/30 rad/s.

**Algebra**

Correct! Well done! :)

**math**

one-to-one (injection): every element in the codomain is mapped by at most one element of the domain. onto (surjection): every element in the codomain is mapped by at least one element of the domain. We can see that f(x) is both one-to-one but not onto, since f(1)=4, f(2)=7, ...

**Algebra**

(E)--- 8x-14 ----(G)--- 4x+1 ----(F) Since EF=59, => 8x-14+4x+1 = 59 Solve for x.

**MATH help please**

(a) An equivalence relation must satisfy the following three requirements: 1. reflexivity (a,b)R(c,d) is reflexive if (a,b)R(a,b)is defined. Since a-2d=c-2b ≡ a+2b=c+2d so (a,b)R(a,b) is defined since a+2b=a+2b Therefore R is reflexive. 2. symmetry R is symmetric if (a,b...

**math**

In general, days of the week advance one day per year (on the same day/month). For leap years, days from first of January to the 28th of February will jump TWO days if it is a leap year. For example, January 1st 1900 was a Monday. January 1st 1901 was a Tuesday (note that 1900...

**math**

Break up 6^8 => 2^8*3^8 10^6 => 2^6 * 5^6 Multiply together the odd factor of each number to get the largest odd factor of the product.

**math**

Original square area = n*n u² New dimensions: (n+m), (n-m) New area = (n+m)(n-m)=n²-m² u² Change in area = difference of above areas.

**math**

Song 1: 1,2,3,4 song 2: 5,6,7,8 song 3: 9,10,11,12 ... song 9: 33,34,35,36 ... song ?: 73,74,75,76

**phy**

Given a=<-1,-4,2> b=<3,2,-2> c=<2,-3,1> bxc= i j k 3 2-2 2-3 1 =<-4,-7,-13> so a.(bxc) =<-1,-4,2>.<-4,-7,-13> =4+28-26 =6

**Chemistry**

Start with writing a balanced equation: 4Fe3O4+O2 => 6Fe2O3 Then use stoichiometric coefficients and molar masses to solve the remainder of the problem.

**phy111**

We assume that the wind is blowing east at x km/h, represented by the vector <x,0> The truck is moving along the vector <p,q>, where sqrt(p²+q²)=70 km/h, or <sqrt(70²-q²), q> We also know that the resultant of the two velocities equals <...

**phy111**

In what direction is the truck moving, due south, south-west? Answers will vary depending on the direction.

**phy111**

Displacement=0 velocity=displacement/time =0

**Maths**

The solution of this problem is based on finding numerical values of parameters a and b in the PDF f(x). Recall that the given PDF is zero over the domain R except that f(x) is non-zero over (0,1). Therefore all integration should be performed from -∞ to +∞ but for...

**Math**

1. Total area = 30*20 ft² Let x=width of walkway, final area = (30-2x)(20-2x)=400 Solve for x. 2. Lawn area = 60*80 m² Final lawn width = x Pool area = (60-2x)(80 2x)=(1/6)(60*80) Solve for x.

**math**

Solve by elimination: Eliminate y by adding equation (3) to equation 1: 4x+z=12 Similarly, add 2*(3) to equation (2): 5x+5z=30 You can continue the elimination process to find x and z. Back-substitute to find y.

**math**

Use the binomial distribution, p=P(chemistry)=0.4 n=12 (sample size) r=number taking chemistry P(n,r)=nCr*0.4^r*(1-0.4)^(n-r) where nCr=n!/((n-r)!r!) is binomial coefficient. For probability of getting AT MOST 4 taking chemistry, add up all possible cases, i.e. 0,1,2,3,4, or P...

**college physics**

360 degrees in 27.3 days. Angular speed = angle/time 360 degrees / 27.3 days = ? degrees/day? If necessary, use conversion 1 day = 86400 seconds to find degrees/s.

**college physics**

Assuming the mass of 5kg is suspended freely, i.e. under influence of gravity, then the force (tension) on the wire is equal to 5g, where g=acceleration due to gravity, 9.8 m/s².

**Geometry**

The longest side is the hypotenuse, 6a+1 So use Pythagoras: (a+1)^2+(6a)^2=(6a+1)^2 and solve for a, reject all values of a≤0.

**statistics**

Number of children = 3 Possible number of boys = {0,1,2,3} X=number of boys - number of girls ={-3,-1,1,3} P(X)= probability of event X. b g X P(X) 0 3 -3 1/8 1 2 -1 3/8 2 1 1 3/8 3 0 3 1/8

**science (physics)**

Initial velocity v0= <1,2> a(t)=<0,g> v=∫a dt = <0,gt>+C => v(t)=<1, gt+2> x(t)=∫v dt = <t,(1/2)gt²+2t>+C Assume x(t)=<0,0> at t=0, then C=0 x(t)=<t, 2t+(1/2)gt²)

**PHYSICS**

radius of earth = 6378.1 km Assuming g is not affected by other heavenly bodies, then Newton's law of gravitation applies: g=GMm/r^2=k/r^2 (k=a constant) => g'r'^2=gr^2 r'^2=r^2(g/g') r'=r sqrt(g/g') =6378.1 sqrt(9.80/0.980) = 2.02*10^4 km approx.

**operating system**

In simple terms, a deadlock is a situation where two or more (minimum 2) processes are stubbornly holding on to a resource while waiting for another, creating a situation where certain resources are never available, and hence no work gets done for either of the processes. ...

**physics**

1 kW = 1 kJ/s Work done = 22 kW * 60 s = 22*60 kJ = 1320 kJ If the efficiency changes to 75% from 100%, the work done is reduced in the same ratio.

**math**

Assuming you are referring to the normal distribution, and depending on the context, it could be sample value, observed value, sample limit, etc.

**phy113**

Degrees fahrenheit = deg.C*(9/5)+32

**Geometry**

First find area of base: hypotenuse = 13 one leg = 12 other leg = √(13²-12²)=5 Area of base = 5*12/2=30 unit² Volume of prism =(area of base)*height/3 =?

**maths needed fastly**

I'll solve one, and will let you try the others as exercise. x=(4/5)(x+10) multiply by (5/4) on both sides: 5x/4 = x+10 subtract x from each side 5x/4-x =10 x/4=10 x=40 Check: (4/5)(x+10)=(4/5)(40+10)=40=x ok.

**mathe**

Let the cone radius = R cone height = H Let cylinder height = h then cylinder radius, r = R(1-h/H) Volume of cylinder, V =πr²h =πR²(1-h/H)²h For maximum volume, dV/dh=0 π(1-h/H)^2R^2-(2πh(1-h/H)R^2)/H=0 which simplifies to: (H^2-4hH+3h^2)=0 which ...

**physics**

Initial speed = 98 km/h = 98/3.6 m/s Work done = KE(final)-KE(initial) = (1/2)1370(0²-(98/3.6)²) = -508 kJ (approx.)

**physics**

Work done = F.D = 1.57*0 = 0 J.

**statisticss**

Calculate Z=(x-μ)/σ and look up the normal distribution table for the probabilities.

**physics**

First 30km with a speed of 30km/h means it took 1 hour. For an average of 40km/h over 60 km, total time = 60/40 = 1.5 hours. Time left for 30 km = 1.5-1 = 0.5 h. Can you calculate the speed needed for the second half of the journey?

**Physics**

Both correct!

**Physics**

Just answered your question a moment ago. Please check your previous post.

**Physics**

Correct for both.

**Physics**

Let initial velocity = vi final velocity = vf (negative if opposite in direction) Change in momentum, ΔM = m(vf)-m(vi)=m(vf-vi) a) Case A: vf=0, ΔM=-m(vi) Case B: vf=-vi, ΔM=-2m(vi) The absolute value of the change is greater in case B. b) Force = ΔM/&...

**math**

x=blue, y=green x/(25+x+y)=1/4 Cross multiply and simplify 4x=25+x+y => 3x-y=25 y/(25+x+y)=1/3 Cross multiply and simplify 3y=25+x+y => -x+2y=25 Solving: 5x=75 => x=15 y=3*15-25=20 z+15/(60+z)=4/13 Cross multiply 13(z+15)=4(60+z) 9z=45 z=5 5 blue beads must be added.

**math**

If the roots of a quadratic equation are equal, that means the discriminant equals zero, or b²-4ac=0 (for ax²+bx+c=0) So expand the expression and see if you can factorize the result to suit the conditions.