# Posts by MathMate

Total # Posts: 11,748

Trig laws
Given Area of triangle ABC=7.52 m² ∠B=40° c=6 m Need to find a. We can use the trigonometric formula for area, namely Area=(1/2)ac(sin(B)) which can be solved to give a=(2*Area)/(c*sin(B)) =(2*7.52)/(6*sin(40°))

Probability
The sample space consists of 24=16 outcomes. A. more tails than heads: 1. exactly three tails: TTTH TTHT THTT HTTT 2. exactly four tails: TTTT So calculate the probability. You can try in a similar way to solve the second part.

Probability
Use the relation: P(A∪B)=P(A)+P(B)+P(A∩B) and solve P(A) Note: ∩ = & c a p ;

Probability
Choosing r unordered sets from n is given by nCr = n!/((n-r)!r!)

Compute
Missing information. You'll need three pieces of information to find the fourth in the following relation: P(A∪B)=P(A)+P(B)-P(A∩B)

Probability
7P5, where nPr=ordered set of r items chosen from n. =n!/(n-r)!

Trig laws help
Use cosine law: a²=b²+c²-2bc(cos(A))

Probability
If P(B)=p, then P(B')=1-p

Physics
Friction or not, the work done is W = F.D (scalar product) If force is applied in the same direction as the displacement, then work done is simply the product of the magnitude of the force and the distance travelled, namely W= 21N*3.3m = 69.3 J

physics
Not really. For an object which accelerates from rest, the variation of speed with time is given by: final velocity=initial velocity + acceleration * time = 0 + 10 m/s² * 2 s =20 m/s (note how the units cancel to give m/s)

Physics
Total distance = 120 km For an average of 60km/h, total time available = 120/60=2 hours Distance left = 120-30=90 km Time left = 2-1 = 1 hour What is the speed need for the remaining distance?

Algebra/Steve
Mary Ann, Hope your surgery goes well and have a speedy recovery.

math
largest 9 digit number without repeating: - must have 9 digits 999999999 - must use different digits - zero excluded (to have the largest number) - must be in reverse order starting from 9 987654321 - must be even, so invert last two digits Say 987654321 987 654 312 So what is...

physics
The fundamental frequency of a wave along a taut string is f=√(T/m)/(2L) T=tension in N m=mass of string in kg/m Since the fundamental mode of vibration consists of only half a wave, the wave velocity is f*2L, or λ=√(T/m). Here N=139 N, m=0.0036 kg/m v=&...

math
fraction of tank filled by A per minute = 1/3 fraction of tank filled by B per minute = 1/6 Fraction of tank filled in first two minutes = 1/3+1/6 = 1/2 Can you take it from here?

Physics :)
You're welcome! :)

Physics
Yes, but only in the first part. m was inadvertently omitted in the second part, my apologies. k=2mgh/x²

Physics
Initial velocity=√(2gh) h=height reached. Spring constant=k compression = x = 0.125m Potential energy=(1/2)mv²=mgh =(1/2)kx² solve for k in (1/2)kx² = mgh k=2gh/x²

physics
Assuming no air resistance, and PE at bottom of tower to be zero, then At the maximum height, mgh=(224mg+m(80²)/2 h=224+80²/(2g) [assume g=32.2 '/s² =224'+99.38' =323.38' At bottom of tower, mv²/2 = m(80²)/2+mg(224) solve for v to get v...

venn diagram
If 10 failed in both, that means 130-10=120 passed at least one subject. Since 85 passed math, 60 passed science, there are 145 passes from 120 students. We conclude that 145-120=25 passed both. Hence (b) 120-25=95 passed (or failed) exactly one subject. For (a), 60 passed ...

Maths
Q1. HCF and LCM could be found using 1. factoring 2. Euclidean algorithm Q2. Let H(p,q) denote the HCF of positive integers p,q, and L(p,q) denote the LCM of p,q, then H(p,q)*L(p,q)=pq

Physics
26 m/s is about 10% from stalling for a Cessna 150. With a tailwind, the airspeed does not change, but it will be added to the ground speed ("actual velocity"). With a headwind, the airspeed does not change either, but it will be subtracted from the ground speed. ...

physics
Explained with the help of diagrams here: http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/64.42.html

Math - correction
*1,499,999

Math
149,999 is the greatest integer that may be rounded to the nearest million.

Physics
It will gather speed because of acceleration due to gravity. The acceleration is g=9.8 m/s²

Physics-half way fin.
I get 62.5 using g=9.8

mathematics
The same as X or Z.

Physics
Kinetic energy is proportional to mass and also varies with the square of the velocity. So the new kinetic energy =(5*105 joules)*(114/50)²

ap physics
Magnitude:use Pythagoras theorem (note 90° between the teammate and the green). Angle (from point of view of teammate) = atan(120/60)+75° West of south since the golfer is at 75° west of south from the point of view of the teammate.

Physics
Assuming both sides of the canyon are at the same elevation, then use the range equation: range = vi²sin(2θ)/g 6.5=vi²sin(2*9.45°)/9.8 vi=sqrt(6.5*9.8/sin(18.9°) =14.0 m/s

Physics-check plz
All correct!

physics
vi=-30m/s a=-g=-9.8 m/s² vf=vi+at =-49.6 m/s Height =average velocity*time =(-30-49.6)/2 * 2 sec =-79.6 m The negative sign means that the rock is lower than the initial position.

physics
Ignore air resistance => no energy loss PE at 40.0 m = mgh = 40*9.8m J =392 J PE=KE=(1/2)mv² vi=sqrt(2gh)=sqrt(2*9.8*40) = 28 m/s Time = 2 * time it takes to reach highest point = 2*(28/9.8) = 5.71 s

physics
vf=vi+aΔt =0-9.8*3 =-29.4 m/s Distance =average velocity*time =-14.7*3 =-44.1 m

Survey of Mathamtics
Calculate the effective interest, i.e. actual performance over a year: Local bank = (1+0.065/12)^12 =1.066971852002543 Credit union = (1+0.0675/2)^2 = 1.0686390625 So the credit union pays a little more.

engineering economics analysis
You cannot, directly. You can always try to put a link, or copy and paste.

college physics
The signal has to make a return trip, so the total distance is 2*1.5=3m Number of round trips per second = 344/3 = 114.7

math
Starting from 102, the minimum number of chicken sandwiches has to be divisible by 8 and 3, i.e. 24, that leaves 78 tunas, etc. So possible combinations may be Chicken/Tuna 24 / 78 48 / 54 72 / 30 96 / 6

physics
1. Use substitution x=u-&pi/2; dx=du ∫csc(u-π/2)cot(u-π/2)du =∫csc(x)cot(x)dx =∫cos(x)dx/sin²(x) =∫d(sin(x))sin²(x) =-1/sin(x)+C

question incomplete

Physics
To find the velocity in the last two seconds, we need to first find the time it takes to arrive at the end of the street of 250 length, and assuming uniform acceleration. The distance travelled is given by Δx = vi(t)+(1/2)at² where vi=initial velocity (m/s) a=...

I assume you forgot the parentheses in the numerator, Lim (sin(x)-(x^3/6))/x^5 as x->0 It would be easy to change sin(x) to a polynomial, the limits of which are easy to find. If you expand sin(x) by Taylor's series, you'd get sin(x)=x-x³/6+x^5/120... So the ...

Math
Each coin can land heads or tails with equal probability of 1/2. Dropping a coin four times has 2^4=16 possible outcomes. (a) three heads By enumeration: There are four possible outcomes, so the probability is 4/16. THHH,HTHH,HHTH,HHHT. The number of combinations for 3H can be...

Math
Calculate the product of the net gain (i.e. gain minus the bet of \$3) and the probability of each outcome. Add all the products to get the expectation of the game. Note that the probabilities of all the outcomes must add up to exactly 1.0

ALGERBRA
Number of possible combinations of 5 (distinct) numbers out of 30 = 30C5 Probability of winning if n different tickets are bought = n/(30C5) where 30C5 =30!/((30-5)!5!)

math
There three ways of choosing 1 girl out of three (3C1) and (5C2) ways of choosing 2 boys out of 5. Total number of ways = (3C1)(5C2) = (3)(10) = 30

Math
Assuming all three coins are fair, you could use a probability tree or a table to list all possible outcomes (Ω) and calculate the probabilities accordingly. H=head T=tail All 8 possible outcomes HHH HHT HTH HTT HHH THT TTH TTT You can use the table to answer the above ...

This (or a similar one) question has been answered before. If you have a follow-up to the answer, please respond to the previous question, or make reference to it. If it is a similar question, then please show your efforts by first studying the previous answer, and attempting ...

finite math
This question has been answered before. Do you check your previous posts?

finite math
B=bachelor's degree H=high income P(H)=0.105 P(H|B) =P(H∩B)/P(B) =0.215 => P(H∩B)=P(H|B)*P(B) =0.215*0.105 >0 So H and B are not independent.

finite math
Is it (a) P(F/E), (b) P(F\E), or (c) P(F|E)? If it is (c), conditional probability, then P(F|E)=0.1/0.4=0.25 (a similar question was answered before)

finite math
How many are "succesful picks", and how many in total?

finite math
Please refer to your previous batch of questions. An almost identical question was answered completely and explained.

Physics
equate PE=spring potential energy (1/2)kx²

finite math
Judging from other questions, I am sure you are capable of answering this question.

probability - question incomplete
There are three statements and no question.

finite math
Do you mean P(F|E), the conditional probability that F happens given that E has happened? P(F|E)=P(E∩F)/P(E)=0.1/0.5=0.2

finite math
If at least one has not written, then there are only 5 to consider. p=0.29 q=(1-0.29)=0.71 P(at least one out of 5) =1-P(none out of 5) =1-q^5 =1-0.18 =0.82

finite math
is part (a) a given condition or you're expected to calculate the said event?

finite math
Assume random selections and outcomes. P(1 snake)=0.94461=p P(2 snakes)=p² P(3 snakes)=p³ ...

probability
#of orange balls=2 #of red balls = 5 Total number of balls = 25 P(orange ∪ Red) =P(orange)+P(red)-P(orange∩red) =2/25+5/25-0 =7/25

probability
P(E∪F)=P(E)+P(F)-P(E∩F) If E and F are mutually exclusive (ME), then P(E∩F)=0, and consequently P(E∪F)=P(E)+P(F)=0.41+0.47=0.88

finite math
Do you use "outcome" to mean elementary events? The elementary events of F are 3,6,7.

math
Set up: M=J+2000 J=B-400. L=S+1500 S=443 S=B-60 From the chain of equations, it would be possible to substitute backwards from the known values. Given: S=443 and S=B-60, so B=S+60=? L=S+1500=? J=B-400=? M=J+2000=?

physics
Angles of incidence and refraction are angles measured from the normal. If n represents the refractive index between air and the medium, the equation that governs the relationship between them is n=sin(θi)/sin(θr) which gives the value of θr as θr=sin-1...

statistics
μ=42 σ=1.5 so Z(38)=(38-μ)/σ Look up a normal distribution table for the probability of exceedingZ(38), which is the same as the probability of not exceeding -Z(38). Post your answer for checking if you wish.

Stats
Have you started looking at the question? What are your thoughts?

Physics
The force required to produce the acceleration is given by Newton's second law F=ma. If m is mass in kg, a is acceleration in m/s² then force F is in newtons. To this force must be addded the frictional force 740 N to overcome friction. Note: the force unit newton is ...

Math: Trig
arcsec(-2) is the same angle as arccos(-1/2) The angle 2pi/3 is correct, so is 4pi/3. Depending on the domain required, you may have to put in both values (for 0-2pi). If that is not the problem, then you have to read carefully the instructions how to answer the question, how ...

Geometry
If you just want the area, use Hero's formula: Let p = (a+b+c)/2 = half-perimeter Area = √(p(p-a)(p-b)(p-c)) If it's really the altitude you need, then find each angle using the cosine law: cos(A)=(b²+c²-a²)/(2bc) where a,b,c are lengths of sides ...

Geometry
* = 2√(3)b

Geometry
Hint: Call the lengths of medians 3b, 3b and 3a. The length of the base = 2√((2b)²-a²) The length of one of the congruent sides = 2√((2b)²-b²) = 2&radc;(3)b

physics
F=ma => a=F/m F=-(13.4+14.7) N m=71 kg evaluate acceleration (should be negative)

Math
Since it is open ended, only "lateral area" is significant. AL = p*h p=perimeter of base h=height of prism

physics
Use the same equation as before: F=(m-ρv)g N where v=volume of the iron object, and v=m/8000 m³ Be sure to convert all values into SI units.

Algebra II
Is πn a sequence or is it a function? At the beginning of the question define what πn is to represent?

Algebra II
To me, Πn=product of integers from 1 to n, which is equivalent to n!. It evidently is not because the expression would way exceed 1. So please explain what Πn is supposed to represent.

physics
Archimedes principle states that the buoyant force equals the weight of fluid displaced. Fresh water has a density of ρ=1000 kg/m³ Sea water from deep in the ocean has a mass density of ρ=1050 kg/m³. Average sea water has a mass density of ρ=1030 kg/m&...

math
* Y'∪Z'= YΔZ= {30,40,70,80,90,100}

math
When you deal with complements, the first question to ask is do we know the universal set E? Here we assume E=Z (integers) X'∩Y = Y\X = {10,20,40,60,90,100} Y'&cup'Z'= YΔZ= {30,40,70,80,90,100} (X\Z)'={10,20,30}' depending what E equals (Y\Z...

algebra
hint: x=1/3

algebra
At 8%, she gets RM1200. At 7%, she gets RM1050. Let x be the fraction he invested at 8%, the 1-x is what he invested at 7%. we have x*1200+(1-x)1050=1100 Solve for x.

Math
Would you like to calculate lateral surface areas or volumes of solids? Please post an example of what you'd like to calculate.

math
If you know the rule between exterior angle θ and the number of sides, n: θ=360/n then 360/(n-1)-360/(n+2)=6 Solve for n, then calculate θ for each polygon. (answer is between 10 and 15, reject negative root)

physics
The equation for range is R(θ)=v²sin(2θ)/g Examine the values of sin(2θ) to arrive at the correct ratio .

Chemistry
One mole of HCl is required to prepare 1 L of 1N solution. Calculate number of moles (n) required to prepare 200/1000 L of 0.5N solution. Find molecular mass M of HCl in g mass of pure HCl required = nM g Volume of given acid required = nM ÷ (1.18*0.37) g÷(g/mL)

physics
What is the question? Need to find the period, T? use T=2π√(L/g) for small oscillations.

Physics
The minimum initial velocity will create at least the kinetic energy (1/2)mv² to equal the potential energy gained, mgh, where h is the height difference between the horizontal rod and the cg of the person from the ground. Make assumptions to the value of this difference...

Physics
Magnitude: F=ma Direction: see figure.

physics - insufficient information
Sorry, wish we could help, but without the figure or a text version of it, we do not know what the given data are.

physics
This is a problem of levers which can be solved by taking moments. Three forces are involved, L the left hand, R the right hand, and W the weight of the pole equal to 50N. It is not clear but will be assumed that the cg of the pole is 2.00m to the left of the left hand, as ...

Physics :)
You're welcome!

Physics
Time (hours) = Distance (km) ÷ Speed (km/h) Divide by 24 to convert into days.

Physics
T (period) = time/rev = 20 sec/ 30 rev = 2/3 sec/rev ω(angular speed) =30 rev/20 seconds =30/20 rev / sec =30/20*2π radians / s Velocity =rω =0.008m*ω m/s

math check
5P5=5!/(5-5)!=?

Physics
Upstream=300 metres/(2-1)=300 s Downstream=300/(2+1)=100 s

Math
If you follow the rules of PEDMAS, what you wrote means: a + (b/10) = a - (0.1b^2/a) -b Please confirm if you really mean if(a+b)/10 = (a-0.1b²)/(a-b) Also, post what your answer is, and explain.

PHYSICS
For a projectile with initial velocity=vi projection angle = θ with horizontal The time of flight =2visin(θ) If time is doubled with θ unchanged, vi is doubled. From range = vi²sin(2θ)/g you can figure out the increase of the range when time (and ...

PHYSICS
There is no rule. It depends on the path. Average velocity = (final position-initial position)/Δt Average velocity = ∫c dx /Δt (line integral)

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