July 28, 2014

Posts by MathMate

Total # Posts: 10,590

math :)
You're welcome!

Assuming you mean A= -3(a + b - (1/3)c) when parentheses are used correctly. Divide both sides by -3, and swap sides a+b-(1/3)c = -A/3 -(1/3)c = -A/3-a-b Divide both sides by -(1/3) c = A+3a+3b

You're welcome!

Airplane speed = <270,0> (components in the x,y directions) Wind speed 75 km/hr eastwards =<75,0> Resultant speed = <270,0>+<75,0> = <345,0> = 345 km/hr eastwards. Wind speed blowing 75 km/h west Resultant =<270,0>+<-75,0> =<195,0&g...

If the acorn fell from rest, equate energies mgh=(1/2)mv² h=v²/2g =100/(2*9.8) =5.1 m Time =v/g =10/9.8 =1.02 s

Assuming it is a 20 m bridge. Initial vertical velocity = 0 time to reach base = t then t=√(-2Δy/g) =√(2*20/9.8) =2.02 s Horizontal distance =2.02*35 m/s =70.7 m approximately

Distance between wave crests, λ = wave length = 2 metres Time complete one wave = period = 60 s / 20 waves = 3 s Frequency f is number of waves per second = (1/3) Hz Speed = f * λ = (1/3)Hz * 2m =2/3 m/s

Next easiest is by comparison. Solve the quadratic by factoring -3x+5 = x² +2x -45 x²+5x-50=0 (x+10)(x-5)=0 x=5 or x=-10 Substitute x to find corresponding values of y.

Find the vertex of the parabola by completing the square: h(t)=-16t²+20t+6 =-16(t²-2(5/8)t+25/64)+6+25/4 which means that the vertex is at t=5/8 and it will hit the ground at h(t)=0, or t=3/2 s (rejecting negative root). Maximum is at the vertex, or h(5/8)=49/4 ft.

Which one is correct?
Eden is right. Multiplying two numbers with the same base is the same as adding the exponents.

Algebra/can you help me
log710 =log(10)/log(7) =1.183294662454939 approximately (use your calculator) I'll leave the other problem for you to practise.

Some characters are not properly displayed on my computer, I assume it to be: A particle moves along the x-axis from an initial position xi to a final position xf. Of the following values of xi and xf, which results in a negative displacement? (a) xi = 6 m, xf = 4 m (b) xi = -...

The starting number (initial value, or y-intercept) is not subject to the power, so the rule for the function is y=2(3)^x year 0: 2(3)^0 = 2 year 1: 2(3)^1 = 6 year 2: 2(3)^2 = 18 ... year 6: 2(3)^6 = 1458

{L,M} is the Ω (sample space) for one single draw. When there are two draws one after another with replacement, the sample space will contain LL LM ML MM

Ignoring air resistance, equate potential and kinetic energies: mgh = (1/2)mv² Cancel m, v=√(2gh) =√(2*9.8*15) = 17.1 m/s

Please look up a diagram of the parts and then give a try at the answer.

The area can be found by using cross multiplication of elements in a rectangular matrix formed by the coordinates of the 4 (or any number) points. Let P be a 5x2 matrix, where the columns represnt the x and y coordinates. Rows 1 to 4 represent the (x,y) ordered pairs of the 4 ...

Gravity acts on bodies of mass m with a force of mg equal to its weight. g is the acceleration due to gravity. The given weight is 10N, so gravity is already included, and the net force acting on the table is 10N.

rounding to the nearest meter
51 is the nearest metre, and 51.4 is the nearest tenth of a metre.

Future value, F = 5*125000=625000 Interest, i = 6% annually = 0.06 compounding frequency, f = 2 Time, t = 2.5 years Let P = present value then use the compound interest formula F=P(1+i/f)ft Solve for P P=F/(1+i/f)ft =625000/(1+0.06/2)2*2.5 =539130.49 =

Please do not use more than one name for your posts.

Isn't 1500 already the present value? Could you double check to see if there is a typo?

Distance = speed * time = (1.25*speed)*((1/1.25)*time) = 25 min./1.25 = 20 minutes

helppppp math helppp!
Future value, F Interest, i = 0.045 compounding frequency, f = 12 Time, t = 3.5 years Let P = present value, = 250000 then use the compound interest formula F=P(1+i/f)ft

Horizontal component of the normal force.

Use Ek=(1/2)mv² Equate Ek=mgh h=height

Good, so Frictional force = ma = 1kg (-2.5)m/s² = -2.5 N Normal reaction =mg =1kg * 9.8 m/s² =9.8 N Coefficient of kinetic friction = Frictional force / Normal reaction = -2.5 / 9.8 = 0.255 (omit sign).

trigonometry, check my answer please?
It doesn't sound right when you have a 15 ft. ladder leaning against a wall with the foot of the ladder 36.9 ft away. So you need to recheck your work when it does not look right. The length of the ladder is the hypotenuse of the right triangle. The base of the ladder is a...

Work on the left-hand side first: csc60 cot30 tan60 =(1/sin60)(tan60)(tan60) =(1/sin60)(tan²60) =(1/sin60)(sec²60-1) =(2/√3)(2²-1) =2√3 Work on the right-hand side: 2sec²45cos30 =2(2/√2)² (√3)/2 =8/2 (√3)/2 =2√3 Thus...

Geometry :)
You're welcome!

Assuming my interpretation of the word "back" is correct, I said: "... because we usually consider the positive x-axis as going forward" so it would be A.

A sphere has infinite planes of symmetry, a cube does not. All the given choices (A) to (C) are solids. A polygon is a plane figure. We cannot make a solid out of plane figures. We can make faces of polyhedrons out of plane figures, but that's not what the question is aski...

If you notice that all the coordinates of the image are half the corresponding values in the pre-image, this means that the transformation is a contraction about the origin, with a factor of 0.5.

Algebra 1
Slope of segment, a = (y2-y1)/(x2-x1) = (8-4)/(6-2)=1 Mid-point =( (x1+x2)/2, (y1+y2)/2 ) =( (2+6)/2, (4+8)/2 ) = M(4,6) Slope of line perpendicular to segment,a1 = -1/a = -1/(1) =-1 Equation of perpendicular line: (y-y1)=a1(x-x1) y-6 = -1(x-4) or y=-x + 10 Check that it goes ...

For every 100 people, there were 40 men 30 women 30 children. Use proportion to figure out the number for 2400 people.

Sum and difference: (sum+difference)/2 = larger number (sum-difference)/2 = smaller number

1 foot = 0.3048 m (exactly) so 1 m² = (1/0.3048)² ft². Area of rectangle = 48 m × 24 m = 1152 m² = 1152/0.3048² ft² = 12400.0 ft² (approximately)

The picture is not complete. Are the two blocks identical (in mass) ? Does block B hang free? If it is, B will descend as A moves up. Draw the free body diagram of each block. Let the tension in string be T. mass of each block = m acceleration due to gravity = g angle of incli...

biology Please Help
I am not a biology expert, but here are some mathematical aspects of the problem. If both parents are heterozygous (contains one PKU allele, or Pp), the outcomes are: PP has PKU (probability 1/4) Pp carrier pP carrier pp non-carrier (probability 1/4) Probability of being a car...

Round trip distance is double the earth-moon distance. Speed of light is 3*10^8 m/s. Distance = Speed * time, so Time = Distance /Speed Plug in numbers and calculate time accordingly.

If you mean to find the value of cos(2θ) given cos(θ)=7/13, then use the double angle formula: cos(2θ)=cos²(θ)-sin²(θ) where: sin²(θ) =(1-cos²(θ)) =120/169

90+6(80)+10(70)+3(60)+2(50)+3(40)=1670 I'll leave the rest to you.

math 1 question!!!!!!
Put the first number (x) of the ordered pair into the equation and check if y evaluates to the second number (y). For example, for B(8, -98), x=8, y=-98. Check: y=–12x – 3 = -12(8)-3=-96-3=-99, so no, B is not the answer. Try all the other options until you get the r...

None of them, unless you mean A.(x,y)--->(x+3,y-2)

Start with a free-body diagram (FBD). It solves most statics problems automatically when you isolate the system into individual pieces. Start with the 500g block, mass m1. Normal force=m1g coefficient of friction, μk=0.25 Frictional force = μkm1g Let tension in string, T...

Centripetal force, same as normal force on the "wall" = mrω² Static friction =μs*N =μsmrω² For the people to be "glued" on the wall, static friction must exceed the weight of the riders due to gravity. Therefore, μsmrω&s...

intro to computers
It could be: She does not have admin privileges.

Solution and colloids
I would put H2O and CH3OH are miscible since they are both polar, and hexane and CCl4 as well since they are both non-polar.

Thank you Dr. Bob.

molarity is the number of moles per unit volume (L). 6.25 m means 6.25 moles per L of solution, or per 1221.9 g of solution. Calculate the mass density accordingly.

Mass of 1 L of solution = 1.55 g/mL * 1000 mL/L = 1550 g/L Percentage of H2SO4 by mass = 65% Mass of H2SO4 in 1 L = 1550 g/L * 0.650 = 1007.5 g = 1.01×10³ g approximately.

Sum and difference Man:(15+5)/2=10 Water: (15-5)/2=5

physics - circular motion
Speed=v (in given units) magnitude of velocity of each particle = v direction: opposite Velocity of particle 1: <v cosθ,v sinθ> velocity of particle 2: <-v cosθ -v sinθ> Distance between particles: √(((vcosθ-(-vcosθ))²...

At height 4h/5, KE=h/5 PE=4h/5 Ratio of KE:PE=?

Algebra 1-- Explain How to Solve
I suspect #1 is missing parentheses. If it is a big fraction made up of two small fractions, it would read: 1.((x^2 + 8x)/(x - 2)) / ((3x + 14)/(x - 2)) Remember that parentheses are always there around the numerator and denominator. These questions are solved using factors. F...

Unless I misunderstood the numbers, the value 45 cm does not match the sequence 80,60,40,20. Please check or clarify.

Tension, T=2640 N Length of wire, L = 2.6 m frequency, f = 330 Hz length density, μ = to be found Using equation: f = (1/(2L))√(T/μ) Solve for μ (kg/m) Multiply be the length of wire, L to get the mass of the wire.

Find n using PV=nRT and multiply by molecular mass. R=8.3144621 J K−1 mol−1 or 0.08205746 L atm K−1 mol−1 depending on the units of pressure used Watch number of significant figures used in calculations (at least 4) and the...

mass, m = 2.5 kg spring constant, k = 320 N/m compression of spring, Δx = 0.075 m Coefficient of kinetic friction, μk = 0.25 acceleration due to gravity, g = 9.8 m/s² Let initial velocity of block, u =u m/s final velocity of block, v = 0 m/s Work done by block, W...

(a) KE=(1/2)mv² (b) At maximum height, KE in y-direction = 0, i.e. loss in KE =(1/2)m(v sin(θ))² (c) Maximum height, h equate mgh to loss in KE, or mgh = (1/2)m(v sin(θ))² Solve for h.

Volume of a sphere =4πr³/3 Volume of hemisphere is half of the above.

math problem
If triangle ABC is right-triangle right angled at B or C, then by the definition of sin(A), it is the opposite side length divided by the hypotenuse.

See previous post

Solve using momentum. Initial momentum=0, since both astronaut and satellite are stationary with respect to shuttle. Assuming velocity away from shuttle is positive, and m1=mass of astronaut, m2=mass of satellite, then m1v1+m2v2=0 97v1+1100*0.13 Solve for v1 to get v1 = -1100*...

Solve using momentum m1u1+m2u2=m1v1+m2v2 u=initial speed v=final speed m1,m2 masses Using the ground as reference, m1=69.5 kg m2=0.470 kg u1=u2=2.15 m/s v2=16 m/s m1u1+m2u2=m1v1+m2v2 Solve for v1 to get v1=2.056 m/s approx. B) v2=16+2.15=18.15 Solve similarly to get 2.042 m/s ...

algebra/Can you see if I am right
If you mean conditional probability, meaning P(Face|King), or probability of a face card given it is a king, then start with the definition of conditional probability: P(A|B)=P(A∩B)/P(B) P(Face|King) =P(Face∩King)/P(king) =(4/52)/(4/52) = 1 A king is a face card, that ...

physics-force and pressure
Pressure (pascals) = Force (N) / Area (m²) 700 cm² = 700/10000 m²

A: plot 1 has a smaller range (spread) Interpretations regarding C and D. Plot 2 has a higher grade in all quartiles than plot 1, so class of plot 2 has better scores in general.

Probability of not repeating, P(no repeat) =10*26*25*24*9*8*7 / (10^4 * 26^4) Probability repeated =1-P(no repeat)

You're welcome! :)

R∩P means find the set of members which are in both R and P. You can type the symbol ∩ as follows: & c a p ; but omit all spaces. The other symbol can by typed similarly as: & c u p ; For example, 1 is in both R and P. Can you find the other one?

The hypotenuse of a right triangle, using Pythagoras theorem, is Length of cable =√(200²+85²) feet The angle would be arc tangent(85/200)

intermed Algebra
R=timing, t=years after 1925, for example in 1950 t=25, and so on. The problem you need to solve is R=48.8 s and need to solve for t. 48.8=-0.037t+50.1 Solution : t=35.1 This means by 1925+35.1=1961 (round up), world records will be 48.8 seconds or less.

θ is not defined. It is assumed to be the angle with the horizontal. By finding resultant of two cables at θ with horizontal. W=2Tsin(θ) Solve for T=tension in one of the cables.

Using Newton's second law: F=ma and since F=constant, we have m0a0=m2a2 Knowing that m2/m0=(1-0.11)=0.89 you can solve for a2. Note: it does not seem realistic that an aircraft accelerates horizontally for two hours and continue accelerating!

Multiply the matrices on the left-hand side and equate cell by cell with the right to get: the equations 6x=-24 y/2-4x=19 Solve for x and y. The two bottom cells turn out to be -6=-6 and 5=5.

college physics
Centripetal acceleration =v²/r or it varies with the square of the velocity. When acceleration is doubled, the velocity is increased by a factor of √2. This way (√2)²=2.

KE=(1/2)mv² =(1/2)*0.1822*4.6² =1.9276 =1.93 (3 significant figures) To calculate the uncertainty, we do a partial differentiation with respect to m and v, and multiply by the maximum errors of δm=0.00005kg and δv=0.05 m/s. δKE=(1/2)v²δm+...

Algebra 2
Write the equation as y=a cos(b(θ))+k For a max=4,and min=-4, k=0, and a=4, so y=4cos(b(θ))) Period = 2π/b if period = 2π/3, then b=3, and the equation reads: y=4cos(3θ) Pick your choice betwen A and D, unless there is a typo.

You may want to check the equation to see if there is a typo. I expect it to read: h=-16t²+v_0 t since the object is thrown straight upwards, while gravity (downwards) is indicated negative. If it is fired straight upwards at an initial speed of 800 ft/s, the initial velo...

Not counting the mitred joints, you will need 4(13"1/8)=4*13" + 4(1/8)=52"1/2

Business Math
Cash discount practices vary. Some expect full payment within the specified date to qualify for the discount, some will discount the paid amount. I assume the latter given the nature of the question. 3/20 means 3% discount on amount paid within 20 days, and the remainder due o...

Algebra 2 - Use parentheses
The expression as is when evaluated according to the BEDMAS rules would be equal to: sin2θ - cosθ since the division is done before the subtraction. The expression should have been written sin2θ/(1-cosθ) in which case = (1-cos2θ)/(1-cosθ) =(...

The y-intercept is the value of y when x=0. (0,2) => y-intercept=2 The x-intercept is the value of x when y=0. (4,0) => x-intercept=4.

algebra/can you see if I am on the right track
You have completed the first part of the correct answer, but you forgot the 3 numerals. So 456730*10^3

By mental calculations: Reverse number by adding 18 means the digits differ by 2, 13,24,35, etc. 13/31 does not work, 4*4+3=19 24/42 does not work either, 6*4+3=27 35/53 4*(5+3)+3=35 works. The pair of numbers would be 35 and 53. By mathematics. Let x and y be the two digits 1...

If k is the spring constant in N/m, and if the initial length is the natural (stress length), then energy=work done =(1/2)kx² joules where x=stretching in metres =15.9cm=0.159 m

Math functions help
a) correct b) put (x+1) instead of x in f(x), f(x+1)=1-2(x+1)=1-2x-2=-2-2x c) g o f(x) (reads g of f(x)) means g(f(x)) =g(1-2x) =(1-2x)²+1 =1-4x+4x²+1 =2-4x+4x² =2(1-2x+2x²) d) f-1(x) the inverse of f(x). follow the following steps to find the inverse. 1. w...

quadratics math
Let h=height base, b =h+4 Area of triangle =bh/2 =(h+4)h/2 or h(h+4)/2 = 48 Solve for h. h²+4h-96=0 (h-12)(h+8)=0 h=12 or h=-8 (reject negative root)

euclidean geometry-missing diagram
Please describe diagram or post a link. If ABC form a triangle, and X,Y are mid-points of AB and BC, then mXY = mAC÷2 Reason: ΔBXY~ΔBAC SAS mXY=mAC÷2 corr. sides proportional

math quadratic equations
A. correct B. look for two numbers m,n such that mn=2*15=30, and m+n=13. m and n are therefore 10 and 3. 2x²+10x + 3x+15 =2x(x+5) + 3(x+5) =(2x+3)(x+5) C. y-intercept: correct. X-intercept=zeroes. Factorize y=x²-3x-4=(x+1)(x-4) to get the zeroes. The vertex is locate...

60 rpm = 60 revolutions / minute = 60 revolutions / 60 seconds = 1 revolution / second = 1 hertz (Hz) So what is 45 rpm in Hz? Orbital time is the shortest time for any point on the record to come back to the previous position, which is the same as the time it takes to make on...

It would be easier to set references. In this case, I would set t=0 when B starts pursuit, at which time A would be ahead by 25 m/s *2 s = 50 m. For distance reference, I would set B's initial position as zero. This means that A's position as a function of time, A(t) =...

7th math
You need to know the scale. Divide the dimensions by the scale to get the drawing dimension. For example, for a scale of 1:500, 120 m /500 = 0.24 m = 24 cm 400 m /500 = 0.80 m = 80 cm and so on. Familiarity with units conversion is a definite asset in these problems.

All students have equal probabilities of being picked (random). Number of possible successes (picking an A-student) = 24 Size of Ω (sample space)=237 Probability of success = 24/237, a little more than 10%.

First set up equation for each house to put together a system of 3 linear equations. You can then solve by the method you have learned. Finally post your answer for checking as necessary. I will start the setting up of the equations. Let M=pluMber's hours E=electrician'...

Isolate variable by transposition: 5t²=520 Divide by the coefficient of t² t²=520/5=104 Take square-root on both sides: t=±104=±10.2 (approximately)

Hmm... I would think expected profit (oil)=415000-25000=390000 expected profit (gas)=145000-25000=120000

Geometry (Checking)
See your original post.

Business mat
b=3 after you subtract 7x from both sides.

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