Posts by MathMate

Total # Posts: 12,102

Student needs to learn the position value of decimal numbers, and that a carry should not shift the digits to the right.

use final velocity = initial velocity + acceleration * time Note: deceleration is a negative acceleration.

math - typo?
Do you mean: "You need 210 snowballs to make the perfect snow fort you make 15 snowballs in an hour but 10 melt every 15 minutes how long will it take you to make the perfect amount?" Checking your question before you post helps you get your answer fast.

If AB is the longest side, then O cannot divide AC and BD in the ratio 1:2 since mAB>mDC. We will use A(BOC) to represent the area of triangle BOC, and so on. Draw a diagram of the trapezoid ABCD with AB//DC and AB>DC. The diagonals AC and BD meet at O. If the division ...

In the case of a hydraulic lift, the pressure is (almost) identical, so that Force/area is a constant, where area is the area of the respective piston.

The keyword here is energy reserves. All except one provide energy, but under different conditions. Discover about all four at the link:

Ethyl alcohol has a formula of C2H5OH. C8H18 is octane. In any case, you would work out the number of moles of alcohol in 16.5 mL. (note: 16.5 mL*0.789=13.02g) Each mole of alcohol gives out 2 moles of CO2. (Write out the combustion equation). So by proportion, you will get ...

MAth 10 (probability
Make a table for the two spins X| 1 2 3 4 --------- 1| 2 3 4 5 2| 3 4 5 6 3| 4 5 6 7 4| 5 6 7 8 Out of the 16 possible outcomes, count how many satisfy the given condition, and divide this number by the number of possible outcomes.

We'll first find the limit, and I'll let you continue with the derivative. Let Y=Lim x->∞ (2^x+5^x)^(1/x) =Lim x->∞ ((5*2/5)^x+5^x)^(1/x) =Lim x->∞ ((5^x)(2/5)^x+5^x)^(1/x) [law of exponents] =Lim x->∞ ((5^x)((2/5)^x+1)^(1/x) [...

Correction: the answer is more appropriately given as 1.54 J/(g-°C) as all the original information is given to 3 significant figures.

Use ΣmcΔT=0. For metal, mcΔT=100*c*(29-90)=6100c For water, mcΔT=250*4.184*(29-20)=9414 Applying ΣΔT=0 => 100*c*(29-90)=250*4.184*(29-20) Solving for c gives 1.543 J-g-1-°C-1 as you had it.

It depends on the given information. If base radius (r) and height (h) are given, then angle of cone is given as 2tan-1r/h.

the parabola y=x² has it's vertex at (0,0). Tangent to parabola has slope dy/dx=2x, at point (±x, x²). For tangents to pass through (0,-25), we have the slope joining (0,-25) and (x,x²) equal to 2x. Slope=(y2-y1)/(x2-x1) => (x^2-(-25))/(x-0)=dy/dx=2x ...

There is not enough context to give an answer without making assumptions. However, if we assume this is an itinerary for Élaine, the second date (8 days later) could be assumed to be the return (to San Diego) from Marseille, which is reasonable for a tourist. Assuming ...

It would appear as homework dumping if you don't show your work. Also, if you make an effort to solve the first one, there is a chance you can apply what you learned to solve the other ones, or at least get a good kick-start. I suggest you review class material, attempt ...

The best way to include a picture is to upload the picture to an image server and post the link. It is not always possible, but give it a try and teachers are likely to help you get it done if there are difficulties.

At the beginning, there are 22*760=16720 food days. After 2 days, there are 20*760=15200 food days left. If this should last only 19 days, it will feed 15200/19=80 persons. You can therefore figure out how many more people came (in addition to the original 76).

Since we are given the hypotenuse and one leg, we can find the other leg using Pythagoras theorem. The area is then the product of the two legs divided by two. Height (of the other leg) =√(3.7²-1.2²)=3.5 Base (given)=1.2 m So you have all information to find ...

in a class of ,26 offer mathmatic and 28 offer physics if 8 student do not offer any of the two subject This means that there are 60-8=52 students take at least one subject. Since total number of subjects taken is 26 and 28=54, we know that 54-52=2 students take both. I'll...

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Sum of exterior angles of any polygon is 360°. So if we add up all five exterior angles of the pentagon, we have 2(3x)+2(2x+22)+x+41=360° Solve for x.

Start with Googling "history of aids" and read up the first 5 or 10 articles. Otherwise, try and

Most of the time the floating is due to deterioration/decay of the body tissues and gases (CH4, H2S, and CO2) are produced, hence reducing the overall density of the body. Read more about it, for example:

A dart board has sectors numebered from 1 to 20. We require combinations, so order does not count. Here's how we could proceed: 1. to avoid repetitions, we assume the smallest number is thrown first, then the next smallest, and the largest numeber. 2. There are no limit to...

Counting and Probability
Let k=number of 4's to add then E(x)=Σx*P(x) =(8*2+(2+k)*4)/(8+2+k) If E(x)≥3.5 then (8*2+(2+k)*4)/(8+2+k)≥3.5 solve by cross multiplication 16+8+4k≥35+3.5k 0.5k≥11 k≥22

partial fraction
step 1: decompose denominator into factors (x³_x²-x-1) =x²(x+1)-1(x+1) =(x²-1)(x+1) =(x+1)²(x-1) Now decompose expression into partial fractions: (Ax+B)/(x+1)² + C/(x-1) = (2x²+7x-1)/(x+1)²(x-1) .....(1) Now match coefficients of powers ...

What's left is is 100-80=20% So the original amount A can be found by proportions: P100/20%=X/100% solve for X: P100*100%/20%=P500

french(le passe compose)
To help you better, I suggest you propose your translation and we will be glad to help you make necessary corrections. For example, (for a male speaker) "I went to school yesterday" would be Je suis allé à l'école hier. Recall that in French...

Hint: read up about Newton's first law, for example, at the following link:

Inelastic collision means the two objects do not rebound and move at a common velocity. Yes, choice a is correct.

* related to sign of...

monotonicity of ln(x) is equal to sign of (ln(x))'=1/x, and domain of ln(x) is D=(0,+∞) Since 1/x is strictly positive for x∈D, so ln(x) is strictly monotonically increasing.

physics...perhaps horizontal plane
I assume that the block of mass m=80 kg slides horizontally, and that the force F=400N pushes downwards at an angle of θ=37° below the horizontal. Initial horizontal velocity is u=20 m/s, and we look for velocity v at time t=6 seconds. Further assumption: friction &...

Math - typo?
The question as is would provide 3 equations for two unknowns. It would be a good idea to check the question before/after posting.

Fraction of work accomplished W at the end of day t will be denoted W(t). W(0)=0 W(10)=5/6 W(12)=5/6-2/3=1/6 W(22)=1/6+5/6=1 work completed.

Hint: adjacent angles of parallelgrams are supplementary, i.e. they add up to 180°. For the given problem, if one angle is x, then the adjacent angle is 2x. Since they are supplementary, we have x+2x=180°. Solve for x and hence the angles of the parallelogram.

Let time t=0 when mass is 3500 and speed is 1220 m/s. then F(t)=500 kN m(t)=3500-80t a(t)=(500*1000/m(t))=acceleration => (i) v(10)=v(0)+∫(500000/(3500-80t))dt for t=0 to 10. =1220-500000[ln(3500-80t)]/80 =1220+1621.945 =2841.945 m/s (ii) using initial mass v(10)=v(0)+(...

In four years, the total of the ages will be 46+4+4=54 years. The ratio in four years will be 7:2 So age of daughter in four years = 54*(2/(7+2))=12 age of mother in four years = 54*(7/(7+2))=42 Continue to find their present ages.

chem question?answer_to=1210023143
(115 psi)/(14.7 psi/atm) = 7.82 atm assuming the air in the tire has room temperature.

Assuming the 10N force is along the positive x-axis. Then the three forces in (magnitude, angle °) are P(10,0), Q(30,120), R(50,240) or in component form: P<10,0> Q<30cos(120),30sin(120)>=<-15, 25.9808> R<50cos(240),50cos(240)>=<-25, -43.301> ...

Assuming parentheses around the denominator have been omitted, the expression is x²+x+4/[(1-x)(x²+1)] partial fractions for the third term is required, namely 4/[(1-x)(x²+1)] =-4/[(x-1)(x²+1)] =A/(x-1)+(Bx+C)/(x²+1) By adding the right-hand side, we ...

Constraints: A. x≥0 B. y≥0 C. y-x≤100 D. x+2y≤1400 (please check this constraint) Draw the graph of the constraint equation to have a visual understanding. Solve for all possible corners of the feasible polygon. Note that all inequalities are inclusive, i.e. all ...

We know that 5*7=35, so the three digit number probably starts with a 3, and the two digit number starts with a 7. We also know that we should put small digit after 7, and large digits after 3, so the numbers are 384/71 Check: 5 < 384/71=5.408 < 6 There may be other ...

Good catch Reiny! I read too fast! To "Help", please go along with Reiny's answer.

Yes, that would be correct, because 10+20+30+40=100 so the the probability that she selected French hens would be 10/100.

There are 10 French hens. Try to enumerate the number of each kind of pet and then add up the numbers to get the total number of pets. 40 is the number of American chickens.

Let success be choosing a French hen out of all possible choices (Ω) and we need to assume the probability of choosing any pet is equal. Probability of success (choosing a French hen) =Number of French hens ÷ Total number of possible choices (&Omega). Here you see...

Assuming uniform deceleration and constant friction (independent of speed). Equate energies: (1/2)mu²=μmgX X=distance u=30 m/s g=9.81 m/s² Solve for X=61.1621 m Acceleration v²-u²=2aX solve for a=(0²-30²)/(2*61.1621) =-7.3575 m/s²

The requirements for an experiment's to be considered binomial are: 1. probability of success remains constant throughout the experiment 2. all trials are independent and random 3. the number of trial is constant and known. This problem satisfies the requirements for the ...

Distinguish between relative maximum and absolute maximum. Statement (a) is true for absolute maximum since x0 is where f(x) has the highest value over the domain of f. Relative maximum at x0 only guarantees that f(x0)>f(x0-) and f(x0)>f(x0+), i.e. a local maximum.

Work to transformed water to steam = 4*10^8 J Work to overcome safety valve=2*10^8 J. Both work are added to the internal energy.

To Paige -- French
Also a version with the accents.

Here a version with the accents filled in. Good luck! Vous avez besoin de: -1 c. à s. de l’huile -200 g du riz -2 oeufs -3 tranches de fromage -300 g de haricots noirs -2 tomates -1 oignon -1 c. à s. des épices mexicains -2 gousses d’ail -(...

M1. The direction of the initial velocity of 3.5 m/s is not mentioned. Use S=ut+(1/2)at^2 to solve for time t. S=-100m (distance) a=acceleration due to gravity = -9.81 m/s^2 u=initial velocity u=0 if 3.5 m is horizontal u=-3.5 if he dove into the ocean at that velocity.

Counting and Probability
These are very interesting problems. If you show some efforts in solving them, there would be likely to be more chances of response.


Algebra 2

Hint: the ratio is 2:3, so from A to B, it is 2/(2+3)=2/5. The coordinates of M are: M(xa+(xb-xa)*2/5, ya+(yb-ya)*2/5)

Algebra 2
x-intercept is obtained by solving for x after setting y=0. For example: f(x)=x^2+2x+1 set y=f(x)=0, then x^2+2x+1=0 (x+1)²=0 x=-1 (x-intercept) y-intercept is obtained by solving for y after setting x= 0. For example : f(x)=x^2+2x+1 Set x=0, then f(x)=y=0^2+2(0)+1=1 y=1 ...

Numerical Analysis MATLAB

Math - ratios
Let N=number of papers graded in 1.5 hours (90 minutes). Use ratio (assuming the grading rate is constant) 5 papers: 45 minutes = N papers : 90 minutes. Cross multiply: N=(5/45)*90=10 papers.

There are two ways to solve this problem. A. The intuitive (and fast) approximation is by prorating the ratio, assuming that the ratio is constant. Let N=total population, then N/30=20/4 => N=150 B. The more accurate (and elaborate) way is to use the hypergeometric ...

Let x=cost of pizza. then 3x/8+4=5x/8+1.5 solve for x.

math-legs and heads, again
See response at

math-legs and heads
You can choose to do the sum mentally as follows: If all the animals were ducks, there would be 2*22=44 legs. Since there are (60-44)=16 more legs, there must be (16/2)=8 dogs, the rest (22-6)=14 ducks. If you prefer to solve the sum mathematically, you would set up an ...

Since the area is bounded by two parallel lines y=5 and y=-3, the area is a trapezoid, with a height of (5-(-3))=8. We need to find the intersection of the line y=2x-5 with each of the parallel lines. Setting 5=2x-5 => x=5 Setting -3=2x-5 => x=1 So the upper width is (8-...

(2+x)(-sinx) is an expression, and cannot be solved. To solve an equation, the expression must be equated to a value, such as x²+2x+1=0

This is an elastic impact problem. Impact problems have one available equation, namely conservation of momentum. m1u1+m2u2=m1v1+m2v2. u, v represent initial and final velocities respectively, and m1, m2 are masses of bodies involved. Note that velocities have signs, e.g. ...

To Physics nerd
When expression exponents, please precede the exponent by the ^ sign. For example, 10² should be written as 10^2. 102 means one hundred and two, (write 10^2) 103 means one hundred and three, (write 10^3) Confusions will arise if the numbers are not expressed correctly.

Hint: un repas

Discrete Mathematics. Need Help
For R to be an equivalence relation, it must satisfy all the following conditions: 1) Reflexivity, i.e. (a,b)R(a,b) ∀(a,b). 2) Symmetry, i.e. (a,b)R(c,d) => (c,d)R(a,b) 3) Transistivity, i.e. (a,b)R(c,d) and (c,d)R(e,f) => (a,b)R(e,f). Use the definition of R to ...

Cht Ningi
T(9)=29.............9th term T(22)=55............22nd term If the AP is T(n)=T(n-1)+d, then d=(T(22)-T(9))/(22-9)=26/13=2 T(1)=T(9)-(9-1)d = 13 and therefore T(n)=11+2n T(1)=13 T(60)=11+120=131 To find the sum of the 1st to the 60th term, we use Little Gauss's method: T(1...

This we need to make two assumptions: 1. The car is on a perfectly horizontal plane/road 2. The car is in neutral AND friction is negligible. Use Newton's second law: F=ma F=400N m=(200 + 50n ) kg n=number of bags. a=1 m/s^2 (acceleration is measured in m/s^2) Set up ...

Ap physics
Use continuity equation, namely the volume of sand coming out per second equals the diameter * speed of sand. Volume = 75 L/min = 1.25 L/s Total area of jets (d=diam in dm) =2π(d²)/4 Speed of sand = 45 m/s = 450 dm/s Equate volumes of sand 450*2π(d²)/4=1.25 d=...

Let the number be x. then x+1/x=29/10 Solve for x. The answers are rational fractions.

First we have to decide how many slices we cut the pizza! It could be 8, but inspiring from the mushroom of 4/16 slices, I assume it is a large pizza cut into 16 slices. Then we add up the fractions to get toppings to cover 3/4+5/8+4/16=26/16 of the pizza. Evidently, if we ...

Mechanical engineering
With a point load in the middle, draw the bending moment diagram, which is a triangle with zero at both ends, and linearly increasing to the middle at R1*L/2. In fact, the standard formula for the maximum bending moment for a centrally placed point load is PL/4. Review your ...

Physics 101
Increase in length = Length (m) * ΔT (° C) * coefficient of expansion (°-1)

0 HP if there is no friction, pulling at a steady speed on a level road does not do work. If there is kinetic friction μk, then F=force = μk * mg v=velocity = 10 m/s Power = F.v j/s = F.v watts

In the long run, it would be equivalent to 120 plays with 120*0.60=72 as revenue and the following payouts: 97 green at 0.95 22 yellow at 0.40 1 red at 11.00 Subtract payouts from revenue and divide by 120 plays to get gain on individual play.


This is a free fall situation. The horizontal velocity has no effect on the time to reach ground. Vertical distance, X=0+(1/2)at^2 =0+(1/2)(-9.81)*3^2 =44 m approximately.

The "jerk" depends on the difference between static friction (the stickiness) and kinetic friction. The former is always greater than (perhaps or equal to) the kinetic friction. You need to estimate the mass m of the drawer, the force F required to overcome the ...

Resolve the initial velocities into the horizontal component, vx =v0 cos(θ) and the vertical component, vy= v0 sin(θ) where θ=-20 degrees (below horiz.) The horizontal component is subjected to only air resistance which in general is neglected, so travels at ...

basic chemistry(projectile)
Use sum of potential and kinetic energies = constant when air resistance is neglibible. Potential energy = mgh at a height h from datum kinetic energy = (1/2)mv^2 when moving at a speed of v.

Physics - Inverted pendulum
* d²y/dt²

Physics - Inverted pendulum
Interesting problem. The vertical motion exerts an acceleration of d²y/dy² on the mass. Intuition tells me the mass will move on each side on successive vertical strokes, hence frequency = ω/2. Next time ask him to drill his calculus and give the bambin a mug ...

In the absence of air resistance we can split the movement of the bullet into the vertical and horizontal components. The former is a free-fall. Using the kinematics equation below, we can solve for the time it takes to free-fall through 2.4 cm: S=(v0)t+(1/2)at^2 with v0=...

We have a right triangle ABC, CA lies on the equator, where C is the destination (where plane intercepts the equator). B is the initial position of the plane, and is immediately south of A. So AB=150 km, ∠ABC=30°. We need length of BC. Using definition of cosine, AB/BC...

The faster automobile is basically playing a catch-up game, with a distance (gap) of 146 m. at a catch-up speed of 72.5-55.5=17 km/h. Converting this speed to m/s: 17 km/h = 17*1000 m/3600 s = 4.72 m/s How long will it take to catch up a distance of 146m at a speed of 4.72 m/s...

ignoring air resistance, we can apply the kinematics equation v1^2-v0^2=2aS S=distance travelled = 3 m v0=initial velocity (to be found) v1=final velocity =0 m/s at highest point a=acceleration due to gravity = -9.81 m/s^2 Solve for v0 and show that it is approximately 7.7 m/s...

1. draw a free-body diagram. 2. Let T be the tension in each of the wires, which makes an angle of 27° with the vertical. 3. Sum forces on the sign in the y-direction (vertical) to get 2Tcos(27°)=23kg * 9.81 Solve for T.

I am not sure if I understand what you're supposed t find. But here's what I have found. I have mod(23*17,26)=1 (and not 9), so 23 cannot be the multiplier. I found it by trial and error, that mod(25*17,26)=9, (encrypting) mod(25*9,26)=17, (decrypting). So 25 is the ...

P(A and B) represents the probability that both events A and B occurring. Physically, it means that a person has both private and government insurance, which is unlikely. The probability of having any insurance is the sum of the two probabilities, i.e. P(A or B) = P(A) + P(B...

If we assume uniform acceleration, we can use: ΔX=(v0)t+(1/2)at^2 v0=initial velocity = 0 m/s t=time=8.6 s ΔX=displacement=0.1994 m Solve for a (in m/s^2)

It is decelerating over the three seconds, with v0=initial velocity=+58 m/s acceleration due to gravity, a = -9.81 m/s^2 time, t=3 s Use kinematics equation: Displacement=(v0)t+(1/2)at^2 Substitute above values to get displacement.

Use v1^2-v0^2 = 2aS v1=final velocity v0=initial velocity a=acceleration S=distance Use an appropriate frame of reference such as positive = upwards.

Use v1^2-v0^2 = 2aS v1=final velocity v0=initial velocity a=acceleration S=distance Use an appropriate frame of reference such as positive = upwards.

Z table
Draw a sketch of what you want, similar to this: THen look up the standard normal distribution table (left tail) the number of standard deviations that correspond to 92%. (it should be between 1.4 and 1.5). Since each standard deviation corresponds to...

This is an expression derived from Bernoulli's equation, so use all the values and substitute in the given equation, making sure that the dimensions are compatible. Check dimensions (C is dimensionless) F=(1/2)CAρv^2 =m^2*kg/m^3*(m/s)^2 =m-kg/s^2 = same unit as Newton...

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