Friday
August 29, 2014

Posts by MathMate


Total # Posts: 10,658

math (incomplete)
"mike runs for 5 of an hour " Please clarify 5 (what) of an hour, it could be 5%, 5 minutes, or one-fifth, ...
December 25, 2012

math
tom, chris, charls, TIM, lorra, lindy: please do not use different aliases. A[]B = A^B-(A+B) for 3[]4, substitute A=3, B=4, rewrite the equation as: 3[]4=3^4-(3+4)=81-7=74 You can do the same for 7[]9. If you wish, you can post your answer for checking.
December 25, 2012

ctu
Calculate the present value of the investments using the compound interest formula over the past 10 years, or n=120 periods (t) at interest rate of i=0.0384/12=0.0032 per period. The monthly payment P=$625 per period, and therefore PV = present value FV = (i.e. future value ...
December 24, 2012

maths
Should read: y"=0+2sec(x)*(-1/cos²(x))(-sin(x)) =2sec²(x)tan(x)
December 24, 2012

maths
y=x+tan(x) y'=1+sec(x)^2 y"=0+2sec(x)*(-1/cos²(x))(-sin(x)) =sec²(x)tan(x) => cos²(x)y"-2y+2x =2cos²(x)sec²(x)tan(x)-2(x+tan(x)+2x =2tan(x)-2x-2tan(x)+2x =0
December 24, 2012

maths
There is no diagram posted, and not enough description to give a defined question. I am adding the following guesses. Check if they are correct. If they are not, post the complete description. AMB is a straight line such that AM=MB. Semicircles are drawn with AB,AM and MB as ...
December 24, 2012

maths
From the familiar sin(A+B)=sin(A)cos(B)+cos(A)sin(B), and sin(A-B)=sin(A)cos(B)-cos(A)sin(B) Add both equations to get sin(A+B)+sin(A-B)=2sin(A)cos(B) .....(3) But 2x=3x-x 4x=3x+x, so substitute A=3x, B=x into equation (3) and simplify to get your answer.
December 24, 2012

Calculus
Roll's theorem applies to a continuous interval. So to answer the question, you will first need to look for discontinuities in the given rational function. You will get the hint by searching for at what point(s) the denominator vanishes (i.e. becomes zero).
December 23, 2012

Math
Let x=mAB then mBD=x+1 Since mAB=5, we apply Pythagoras Theorem to get (mBD)²=(mAB)²+(mAD)² All of the measures are either know or can be expressed in terms of x. Solve for x.
December 23, 2012

maths
See Derrick's post: http://www.jiskha.com/display.cgi?id=1356307353
December 23, 2012

math
Will be able to provide help when we see the figure, or when the figure is described in detail.
December 23, 2012

math
Without log, you only have to multiply 1.0 by 0.9 as many times as need to get a product of 0.05. I get 0.052 after multiplying 28 times and 0.047 after multiplying 29 times. So the answer is between 28 to 29 doses.
December 23, 2012

math
7*7=49 8*8=64 So the square root of 51 is between 7 and 8, in fact, approximately 7.14. What is the integral part of 7.14?
December 20, 2012

Stat
Look up a normal distribution table, such as: http://www.math.unb.ca/~knight/utility/NormTble.htm Look up P(Z<2.35), which gives you 0.9906. We now need to subtract P(Z<-1.5) to get P(-1.5<Z<2.35). For this, we need to make use of the fact that the normal ...
December 14, 2012

French
Un beau travail! Je n'ai pas terminé la lecture, mais je vous conseille de vérifier certains aspects: 1. Le genre, ex. un beau-père. 2. sujet et objet, ex. quelque chose qui changeait... 3. les virgules, ex. et mon beau-père qui s'appelle ...
December 14, 2012

calculus
all sides infinite! There are no constraints, so there is no limit to the length of the sides.
December 13, 2012

maths --plse help me..
Look at the coefficients as 1 -3 3 7 They add up to 8, so x=1 is NOT a factor. Now change the sign of the coefficients of the odd powers (x^3 and x): -1 -3 -3 7 They add up to zero, so x=-1 is a factor. We do a synthetic division, or a long division to get: (x^3-3x^2+3x+7)/(x+...
December 13, 2012

algebra
From the coefficients of the equation, you would have to figure out that x represents the number of quarters, and y=number of nickels. The x-intercept means the number of quarters required if y=0 (no nickels used.)
December 12, 2012

Algebra
Let x=weight of ground pork in kg then 8-x=weight of ground beef. total weight = 8 kg therefore 5.50x + 4.75(8-x) = 5.10 * 8 Solve for x.
December 12, 2012

Statistics
Convert to z-score using (X-μ)/σ where X=89 or 121, σ=15, μ=105. Look up normal distribution table to find probability enclosed between these two z-scores.
December 12, 2012

geometry
The sum of exterior angles of all polygons (including triangles) is 360° Can you find the third exterior angle?
December 12, 2012

maths --plse help me..
L(ab): (0,-1,-1)+(4u,6u,2u) L(cd): (3,9,4)+(-7v,-5v,0) If they intersect at P, then corresponding x,y,z values match, hence 2u-1 = 0 => u=2.5 where P=(0+4*2.5, -1+6*2.5, -1+2*2.5)=(10,14,4) For line L(cd), we have P(3-7v, 9-5v, 4+0v) => 3-7v=10 => v=-1 or 9-5v=14 =>...
December 12, 2012

algebra
Andrea, which continent are you on? In USA, 1 billion = 10^9, and I think in UK and France, 1 billion = 10^12. This makes a big difference.
December 12, 2012

algebra
Formula for continuous interest: A=Pe^(rt) take log on both sides and solve for r: r=ln(A/P)/t where A=4300000000,P=0.93,t=1000 You should get around 2.2%, ASSUMING banks do not round interest deposits to the nearest cent. If they deposit interest every two months and round ...
December 12, 2012

maths --plse help me..
p/p=1
December 12, 2012

maths --plse help me..
By symmetry, we conclude at least one solution is x=y=z. Assume p=x=y=z, then 1/p^2=p/p+1=2 Can you solve for p?
December 12, 2012

math
We know that 3*3=9 4*4=16 so square-root of 11 is between 3 and 4. Can you now choose the piece from which to cut?
December 12, 2012

math
Let the smaller even integer be n. The larger is then n+2. The problem says "smaller added to five times the larger is 58" which translates to n+5(n+2)=58 Solve for n (smaller even integer)
December 12, 2012

Mathmatics
First simplify given expression 2a+6b-3(a+3b).... first remove parentheses =2a+6b-3a-9b .... group like terms =2a-3a +6b-9b .... sum like terms =-a-3b =-(a+3b) Square expression [-(a+3b)]^2 .... ^2 means raise to 2nd power =(-1)^2 (a+3b)^2 =(a+3b)^2 .... use identity (x+y)^2=x...
December 12, 2012

math
We have a cube of 6 cm broken into 216 cubes (of 1cm cubed), meaning each face is divided into 6x6=36 small squares. The interior cube that has no paint therefore has a size of 4 cm cubed, or 64 cubic cm. The cubes that have paint on two sides would be the middle four along ...
December 12, 2012

annual interest
12000*0.05=600 12000*0.07=840 Proportion at 5% = (840-760)/(840-600)=1/3 Proportion at 7% = (760-600)/(840-600)= 2/3 (or 1-1/3=2/3) (1/3) of 12000 = 4000 at 5% (2/3) of 12000 = 8000 at 7%
October 28, 2012

math
For each large print, he sells small prints. For the three prints, he makes 45+2*20=85$. Rent = 510 He must sell 510/85=6 sets of three prints, or 6 large and 12 small prints to break even.
October 28, 2012

Discrete Mathematics
Think of the case of 4 people for 3 different posts, and if any one person can hold zero, one, two or three posts. There are 4 choices for the president, 4 choices for the secretary, and 4 choices for the treasurer. Invoking the multiplication rule, there is a total of 4×...
October 28, 2012

Physics
The package was released 82 m above ground. With no air resistance, and acceleration due to gravity = 9.81, time it takes is 82 = (1/2)gt² t=sqrt(2*82/9.81) = 4.089 s. During this time, the helicopter has travelled 96 m horizontally, therefore Velocity of helicopter = 96/...
October 28, 2012

Math
Normalize! Calculate Z=(X-μ)/σ where Z = Z score found in standard normal distribution tables X = value of random variable, the diameter of 5.45 inchs μ = mean diameter of population, 5.52 inches σ = standard deviation of population, 0.46 inch. Look up a ...
October 28, 2012

algebra
First step: divide each equation by the common factors, i.e. first equation by 7, and second equation by 5. x + y = 11 4x- y = -7 Afterwards, use elimination to solve for x and y. Hint: there will be fractions in the answers.
October 28, 2012

math calc 2
Hint: Think of the difference in potential energies of the initial and final positions of the chain.
October 28, 2012

DBU
Z=(28-μ)/σ Look up the standard normal distribution table and look at the percentage for the left tail.
October 28, 2012

statistics/probability
Expected winning can be found by summing over all possible outcomes the product of winning and the respective probability. For outcome HH: winning=0.25 probability = 0.25 prodcut = 0.25*0.25=0.0625 Repeat for the 3 other outcomes, and add the 4 products together to get the ...
October 28, 2012

calculus
"The solid whose base is the region and whose cross-sections perpendicular to the x-axis are squares." means that z=2y but since y=2sqrt(1-x^2) (on the circle), so z=2sqrt(1-x^2) For example, at x=0, z=1, at x=1, z=0. The volume of the solid is then ∫∫∫dx...
October 28, 2012

Geometry
It is a quadrilateral.
October 28, 2012

HELP A.S.A.P. PLEASE: linear programming-maths
The objective function in this case is to calculate the profit. s=number of squash rackets (made and) sold. t=number of tennis rackets (made and) sold. From "The profit on each tennis racket and squash racket is $7 and $9 respectively" we can say that the objective ...
October 28, 2012

Geodetic Survey
Unless you're very experienced in the area, it would simplify your thought process by drawing a diagram as described by the question. Here is more or less what you should have: http://imageshack.us/a/img441/9503/1347673609.jpg You will need to solve for the height H using ...
September 14, 2012

Help with Calculating Probabilities
You can review your teacher's class notes, and the textbook, which should be self-explanatory. You are probably stuck with notations, which are usually described at the beginning of the notes or textbook. Probabilites are numbers between 0 and 1, and represent the ...
September 13, 2012

Linear Algebra :)
You're welcome!
September 9, 2012

Linear Algebra
The normal to this plane is normal to both lines, so the cross product of the direction vector of these lines will be the normal to the plane. Finally, find the equations of the plane passing through each of the given points. Both of them should give the same equation, ...
September 9, 2012

STATISTICS
"a grade less than 58 and greater thAN 110 " No student will receive this grade! Seriously, you probably mean "a grade less than 58 or greater thAN 110 " What can be done is to calculate the percentage of students who receive X, where 58≤X≤110. Given...
September 9, 2012

math
Hint: Since all the choices are independent, use the multiplication rule.
September 9, 2012

algebra 1 stat question
The maximum value is 70, which is (70-37.7)/14.01=2.3 standard deviations above the mean. You can calculate similarly for the smallest value of 15.
September 9, 2012

algebra 1
See response to: http://www.jiskha.com/display.cgi?id=1347171948
September 9, 2012

Linear Algebra :)
You're welcome!
September 8, 2012

Linear Algebra
To find the vector equation of M1, we need to find the direction along which it is moving, which is given by the difference of coordinates of B and A: BA=<7-(-3),10-(-10),-10-10> =<10,20,-20> We know that the speed (magnitude) is 3 m/s, so we normalize the ...
September 8, 2012

Calculus
Hint: Rational functions (where the denominator is a polynomial) have discontinuities when the denominator vanishes (=0). This is where we find vertical asymptotes.
September 8, 2012

math
Assuming no loss in the cutting, how would I would cut 3 strips of 32 cm long, each subdivided into 8 pieces of 15 cm wide. This will take care of 24 pupils. For the remaining 4 students, we cut in the direction, giving an extra length of 30 cm. with some waste. The total ...
September 8, 2012

math
The worst case is if you took out 34 brown, then 1 red, and 1 blue. After that, any colour goes! Can you work that out?
September 8, 2012

c/c++
Fun problem, a little different from most other standard ones. 11*24*23*22*21*20 12*25*26*27*28*19 13*14*15*16*17*18 Like that? You can iterate through with two variables, i,j so that if i=j, you switch directions. (note: C/C++ arrays are zero-based).
September 8, 2012

Math :)
You're welcome!
September 8, 2012

Math
We will assume that train A goes west at 72 km/h, and train B goes east at 54 km/h. We further assume that at time t=0, the two trains meat head to head, with the stationary observer at the head of train B, i.e. the engineer of train B. In 18 seconds, train B would have gone ...
September 8, 2012

Math
Hint: Distance = speed * time They have to have consistent units.
September 8, 2012

Math
The relative velocity between the two trains is 54+72=126 km/hr. The 18 seconds would be equivalent to the time it takes a train at 126 km/hr to pass a (stationary) lamp-post. Can you work out the length of the fast train? Hint: It's more than half a km long.
September 8, 2012

Programming in Python
Here's a tutorial with examples on Python input/output. http://docs.python.org/tutorial/inputoutput.html Study them and code accordingly. If you have difficulties, post your code for help.
September 7, 2012

Diff Eq
Differentiate y(t): y'(t)=3*2te^(t^2) = 6te^(t^2) Given y'(t)+p(t)y=0 => p(t)=y'(t)/y(t)=-2t The original DE becomes y'(t)-2ty(t)=0 If y(0)=y_0, then y'(0)-2(0)y_0=0 which is always true irrespective of the value of y_0, since y'(0)=6te^(t^2)≡0...
September 7, 2012

math
100 choose 4, or C(100,4) where C(n,r) is defined as C(n,r)=n!/[r!(n-r)!] Think of choosing the first number out of 100 choices. We can choose the next number from the remaining 99 numbers, then 98, then 97. By the rule of multiplication of a multi-step experiment, we have 100...
September 7, 2012

Computers
It appears there is a "write-lockout" command in the firmware. For more details, see: http://en.wikipedia.org/wiki/Floptical
September 7, 2012

math
Hint: Slope between two points = (Δy)/(Δx)
September 7, 2012

math
A vertical line has the form x=k, where k is the x-coordinate of all points on the line. The given point has an x-coordinate of 23, can you figure out the equation of the vertical line?
September 7, 2012

Maths
Looking from the side, the cylinder has an outline of a rectangle, of height 2x and width x. Since the cylinder is half-filled, at the point water touches the brim, there is as much water in the cylinder as there is air. So the water level divides the cylinder into two equal ...
September 4, 2012

Discrete Mathematics
a. C(n)=16+4n C(1)=16+4(1)=20 C(2)=16+4(2)=24 ... C(5)=16+4(5)=36 b. C(50)=16+4(50)=? c. 50 ∑ C(i) i=1 50 ∑ 16+4i i=1 16(50)+4sum(i) =800 + 4[ 50(1+50)/2 ] = 800+4(1275) = 5900
September 4, 2012

Math
Quadratic functions that have given x-intercepts x1 and x2 are given by the equation: y=a(x-x1)(x-x2) If a>0, the curve opens upwards, and if a<0, the curve opens downwards. |a| can be any value ≠0 depending on the location of the vertex or any other point on the curve.
September 4, 2012

Math
Standard quadratic function with given vertex (h,k) is given by: y=a(x-h)²+k where a can be found by substituting the values of any given point on the curve. Here, h=-2, k=5, so y=a(x+2)²+5 Now substitute x=0, y=9 and solve for a.
September 4, 2012

math
It is possible if we neglect the rounding of the cents. Ratio of prices is 1:2:4, and 1+2+4=7 So the prices are: $100*(1/7), $100*(2/7), $100*(4/7), or $14.29 $28.57 $57.14 Note that $14.29 has been rounded up half a cent, so $14.29>($28.57/2)
September 3, 2012

math
You're going to find the fifth root of 0.035? First, use the calculator. If you don't have one, calculate: Set x0=0.2 calculate x1=x0-(x0^5-0.035)/(5x0^4) Start with x0=0.55, and calcuate x1. Repeat by replacing x0 by x1 until the number stabilizes to the accuracy you ...
September 3, 2012

statistics
z-score = (X-μ)/σ μ=mean σ=standard deviation X=value of random variable (600)
September 3, 2012

physlcs
Acceleration has a unit of m/s². from 0 to 18m/s in 3 minutes</> is the same as 0 to 18 m/s in 180 seconds, which translates to 18m/s / 180 seconds or 0.1 m/s² A bicycle does better than that, haha!
September 2, 2012

Maths
Hint: Volume = area of base * height Knowing that 1 ml. of water occupies 1 cm³, then 400 cm³ = 40 cm² * height Solve for height.
September 2, 2012

Math
He needs to make 80%, so if he misses (100-80)=20%, he still passes. What is 20% of 35 items?
September 2, 2012

Math
Hint: cos(θ)=adjacent/hypothenuse (CAH)
September 1, 2012

Math
a number which is an easy multiple of 42 and less than 4452.
August 31, 2012

Math
4452-4200=252 (42*100=4200) 252/42=6 So the quotient is 100+6=106.
August 31, 2012

math
1.5*IQR=(49-28) IQR=21/1.5=14 So Q3=Q1+IQR=42 However, the median and Q1 should be recalculated after the outlier is removed.
August 31, 2012

Physics
For part c, you put average speed as 0.05 km/min, which is correct. Subsequently, as part 2 of (c), you did put average velocity as 0. Perhaps there was a confusion of the questions.
August 31, 2012

Physics :)
You're welcome! Yes, velocity is a vector, so it is described by the magnitude (speed) and direction. The same goes for displacement, which is also a vector, and therefore is described by the magnitude and direction. Keep up the good work!
August 31, 2012

Physics
(a) we usually express car speeds in km/hour (b) Displacement = 10.3 km in direction 25° S of east Time = 18 min = 0.3 hour So velocity = 34.3 km/hr in direction 25° S of E. (c)Correct.
August 31, 2012

math
2*5280 = ?
August 31, 2012

Physics
Use the equations: S=vi*t + (1/2)gt^2 For 1st ball: 20=0+(1/2)gt^2 => t=sqrt(40/g) For 2nd ball: 20 = vi*(t-1) + (1/2)g(t-1)^2 vi = [20-(1/2)g(t-1)^2]/(t-1) =(20-(9.81/2)*(t-1)^2)/(t-1) =14.62 m/s downwards
August 31, 2012

calc 3
Trouble-free way to get resultant: resolve into x- and y-components and add. Wind is FROM N45W, which means that its direction is S45E. Take East = x, and North = y, the wind vector is then <40sin(45),40cos(45)> The velocity vector of the plane is <200sin(60),200cos(...
August 31, 2012

Math
Ratio of 40% and 25% solutions to form a 27% solution = 27-25 : 40-27 = 2 : 13 To make 54 litres, we need 54*(2/(2+13)) litres of 40% and 54*(13/(2+13)) litres of 25% solutions.
August 31, 2012

math
When you add (i.e. never need to borrow), you can calculate the integer and fractional parts separately, and carry if necessary. Integer part: 8+5-5=8 Fractional part: 9/10 + 3/4 find common denominator (=20) 18/20 + 15/20 =33/20 = 1 13/20 Carry the 1 to give 9 13/20
August 31, 2012

Algebra..
1. given slope, passes through origin: y=mx here m=3/2 2. given x-intercept=a, y-intercept=b y=-(b/a)x + b here a=4, b=-3 3. Given point (x0,y0) on line and slope m: y-y0=m(x-x0) (x0,y0)=(3,2) m=2 (coefficient of x in given line) 4. Given point (x0,y0) on line, and ...
August 31, 2012

math
Correction to one of the above lines: 12=a(0-24)(0+24)=-576a
August 31, 2012

math
x^2 means x squared, or x². If you just started with parabolas, it won't hurt to say what you've learned so far. Let's start over: We first assume the vertex of the parabola is at x=0. We know that y=0 at x=±24, or y=a(x-24)(x+24). We also know that y=...
August 31, 2012

math
Take the vertex of the parabola at x=0. Then the equation of the parabola (opening downwards) is y=12-ax^2 where a is a constant to be found. We know that y=0 at x=±24 (half span), so 0=12-a(24^2) => a=12/576=1/48 The equation of the parabola is therefore y=12-x^2/48...
August 31, 2012

Calculus
a. The conditions that f(x) must satisfy to have an inverse is: 1. f(x) must be a function 2. f(x) must be onto, i.e. ∀x ∈ dom f(x), f(x)=f(x1) <=> x=x1 condition 2 implies that f(x) must be strictly increasing or strictly decreasing. This can be satisfied if...
August 31, 2012

math
"Nine parts of the first piece are equal in length to 3 parts of the second piece. " means that each part of the second ribbon is three times as long as each part of the first, which also means that the number of parts of the second ribbon is one-third of the number ...
August 31, 2012

Math
6 3/5 - 2 4/5 (Note: 3/5 is smaller than 4/5) =5 8/5 - 2 4/5 (borrow a whole) =3 4/5
August 31, 2012

Math :)
You're welcome!
August 31, 2012

Math
They are each 13 and 20 km from the starting point, at an angle of 44 degrees. Solve the triangle by the cosine rule which gives the distance between the two: c²=a²+b²-2ab cos(C) where c=distance between bikers a=13km b=20km C=44°
August 31, 2012

trig
My calculator says sin(70°)=0.93969262
August 31, 2012

Algebra 1 or 2
Assuming no parentheses are missing, i.e. the question actually means: ((5x)/4) + (1/2) = x - (1/2) x=2 is not correct. To solve: (5x/4) - x = -(1/2) - (1/2) x/4 = -1 can you finish the solution?
August 31, 2012

Math
(A) x=13/4 means that the equation is valid only at x=13/4, and is not valid elsewhere. Would that be an identity or a conditional equation? (B) There was an arithmetical error on the last line: -7x+21+4x = 21-3x +21-3x = 21- 3x So after cancelling, we get 21=21 Would that be ...
August 31, 2012

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