Sunday
April 20, 2014

Posts by MathMate


Total # Posts: 9,948

Calculus - please check my work
Any point on the plane will satisfy the equation. Since there are three variables x,y and z, you can fix any two variables and solve for the third. Example: Assuming arbitrarily y=6, z=6 => 5x+4(6)-3(6)=6 5x+24-18=6 5x=0 x=0 So (0,6,6) is a point on the plane.

Calculus - please check my work
All correct, well done!

algebra math
31=3 32=9 33=27 34=81 35=243 ... So we conclude that 3 raised to any power divisible by 4 ends with a 1. Similarly, 3 raised to any power "divisible by 4 minus one", such as 3, 7, 11, ... ends with a 7. Can you figure out the answer for 3^59 (noting that 59=4*15-1)?

math
Whenever transcribing fractions, do not forget to insert parentheses around numerator AND denominator. The posted expressions do not evaluate into what you wanted to do. 1. Factor numerator and denominator. Reduce expression by cancelling common factors. Evaluate remaining exp...

Calculus
What do you want to do with the equation? Do you need to differentiate the right-hand-side? Treat it as a product of cos(3x) and sin³(x) and within each, use the chain rule. dy/dx=-3sin(3x)sin³(x)+cos(3x)*3cos²(x) and simplify.

Integral calculus
To show the results, we assume F(x)=∫f(x)dx then ∫f(x)dx from 0 to a is F(a)-F(0) and ∫f(x-a)dx from 0 to a is F(0)-F(0-a) =F(0)-F(-a) =-F(-a)+F(0) For the two to be equal, we require: F(a)-F(0) = -F(-a) + F(0) or F(a)-F(-a) = 2F(0) Which is not generally true. So ...

geometry
For the top eight, how many choices are there for the top? How many are left for the second? ... How many choices are there for the last? Use the multiplication rule to calculate the total number of ways for the top eight list. The award list can be similarly calculated, excep...

algebra 2
tan(35°) = height of pole / shadow length. Solve for height of pole.

trig
Use the laws of scalar multiplication of vectors: A=(x,y) aA=(ax,ay) u=(10,5) -u=(-10,-5) -3u=(-30,-15)

probablity
3R,6B,3W for a total of 12 marbles. P(R)=3/12

maths
I believe somewhere in the question says a and b are rational numbers. What are your thoughts? If you have no idea, review your notes on the terms on the right-hand side.

Math - parentheses missing
I think you mean: 4/(x-2) - 7/(x^2-4) = 1 Assume x≠2 and x≠-2, factorize and multiply by common factor: (x+2)(x-2)[4/(x-2) - 7/((x-2)(x+2)) = (x+2)(x-2) 4(x+2)-7=x²-4 => x²-4x-5=0 (x-5)(x+1)=0 Guess you can take it from here.

Math
7 ft = height 24 ft = length of shadow Angle with horizontal (ground) = tan-1(7/24) I will let you do the calculator part.

statistic & probability
Men: Jeff, Lyle, Norm, Paul Women: Karen, Maria, Olivia Number of arrangements of 4 men : 4!=24 Number of arrangements of 3 women : 3!=6 Number of arrangements for men first followed by women = 24*6=144

statistics
Given probability distribution (pdf): x 1 2 3 4 5 6 7 p(x) .04 .05 .08 .26 .39 .16 .02 Since ∑p(x) for x=1 to 7 =1.0 we conclude that: p(0)=0 p(1)=0.04 ... p(7)=0.02 p(8+)=0 (a) P(x=4)=0.26/1=0.26 (b) P(x>4) =P(5)+P(6)+P(7)+P(8+) =0.39+0.16+0.02+0 =0.53 (c) P(x≤5)=P(...

Algebra
Area of rhombus = product of diagonals /2 = M*N/2 where M,N are lengths of the diagonals.

Maths
Hint: write equation as: tan(a)=(x²-y²)/(x²+y²) Cross multiply to eliminate denominators: (x²+y²)tan(a)=(x²-y²) Implicitly differentiate both sides (2x+2yy')tan(a) = 2x-2yy' Group terms and express y'(=dy/dx) in terms of x, y...

Statistics
Events: A=no error B=with error P(AAA)=(48/59)*(47/58)(46/57)

math
Please specify what you are required to do. This is an equation with two unknowns, which has infinite solutions. It could also be the representation of a function 2x+3y=9 which reduces to y=(9-2x)/3. It could also be a straight line with slope -2/3 and y-intercept of 3.

math
Hint: Draw a Venn diagram to fill in all the numbers, starting with the last (2 liked all sports) and work backwards. I find 17 students in all. Not too sure how the question is supposed to be interpreted: 1. how many students liked tennis and no other sport or soccer and no o...

statistics
If we have 1000 people, of which exactly two are MEN. Can we claim: "If any two persons are picked at random, at least one of the two would be a woman." What does that tell you? Now back to the above problem: "If any two persons are picked at random, at least on...

subset
A subset B of a given set A is a set in which all members of B are contained in A. If one member or more in A does not belong to B, the B is a proper subset of A. Example: A={cups, glasses, plates} B={cups} C={glasses, forks} then B is a subset of A, and C is NOT a subset of A.

statistics
For the first pick, we need a green out of 8 balls. For the second pick, we need a yellow out of 7 balls. For the last pick, we need a red out of 6 balls. By the multiplication rule, the probability is P(G,Y,R)=(1/8)(1/7)(1/6) I'll leave it to you to do the arithmetic.

Statistics
The experiment consists of 10 bernoulli (either true or false) experiments over one week. The probability of success p is 0.3 (so failure, q=0.7) The probability does not change throughout the week. This is a binomial distribution, where the probability of r success out of n t...

math 2 - incomplete question
We don't see a question.

calculus
Please check the function for typo, since f(x,y)=e^(-x²) is independent of y. Assuming no typo, the region R is bounded between x=0 and x=1, and y=0 and y=x. So the integegration dy from 0 to x dx from 0 to 1. I=∫∫ye^(-x²)dy dx =∫xe^-x² dx =1/2-e^(-1...

statistics-normal distribution
μ=575 σ=50 z1=(550-575)/50=-0.5 z2=(650-575)/50=+1.5 From normal distribution tables, find the probability between z=-0.5 to z=+1.5.

Algebra III
Last digit:0 or 9 (2 choices) second to fourth digits, 4 choices each. Total number of four digit odd integers =4*4*4*2 =128 (these include 9999 and 0009, etc.)

probability
A=sum is odd B=sum is 5 or less P(B)=|{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)}|/36 =10/36 P(A∩B)=|{(1,1),(1,3),(2,1),(2,3),(3,2),(4,1)}|/36 =6/36 P(A|B)=P(A given B) =P(A∩B)/P(B) =?

Math
The question as it is is not very clear. I will restate it the way I understand it. If the restatement is incorrect, please give the corrected version. "Given f(x)=x²+3x-5 on [-1,3] show that f(x)= 10 exists without solving for x." We first note that f(x) is a p...

Calc
If y=tanx-2cosx y'(x)=sec²(x)+2sin(x) So what is y'(π/3)?

algebra 1b
Price*(1-discount)=$3200 discount = 0.125 Solve for Price.

algebra
Assume DC current where voltage is constant. P=EI P=180 w E=120 v Solve for I (answer in ampères)

quadratic equations
6^2-8+41 =36-8+41 =28+41 =69 If it is a quadratic equation, the unknown (usually x) is missing, and something should appear on the right hand side.

algebra
What is (4/3)π(8/2)³ ?

algebra 1
-7p3(4p2 + 3p - 1) =(-7p3)*4p2 + (-7p3)*3p - (-7p3)*1) =-28p^5 - 21p^4 + 7p^3

math - missing data
You have probably a table of numbers to do this problem. Without it, there is not much you can do. Also, do you actually mean lower and upper quartiles?

math
Kinetic energy at velocity v Ek(v)=Kv² Since Ek(20)-Ek(15)=10 j = K(20²-15²)=175K we solve for K to get K=10/175 Ek(12)=(10/175)*12² j =8.2 j.

Math
Divide the number by 6 repeatedly until no remainder remains. The final quotient together with the successive remainders is the number in base 6. Example: Convert 256 to base 6: 256/6=42 R4 42/6=7 R0 So the base 6 number is 704 Convert 15203 to base 6: 15203/6=2533 R5 2533/6=4...

Math
§9=3 §3=1 Is §1 ∈ Z? where Z=set of integers, and ∈ ≡ "is in"

Mathematics-please help quick!!
Perimeter = 2(Length + Width),so length = (perimeter)/2 - Width =(16x+8y)/2 - (5x-2y) =8x+4y - (5x-2y) = 3x+6y

ALGEBRA
Each voter of the Borda count gives 1 point to the least favoured candidate, 2 for the next, until N points for the most favoured candidate out of N. (a) With five candidates, each voter gives 1+2+3+4+5=15 points for a total of 15*70=1050 points. (b) and (c) can be solved simi...

algebra
You have got: 3a+6=4a but we know that 3a =3a So subtract one equation from the second, 3a+6-3a = 4a-3a which gives 6 = a

Mathematics-please help!
Two vertices are on the same vertical line, namely x=2, for (2,1) and (2,7). This is the base of the triangle with length 7-1=6. The height of the triangle from point (-2,3) to x=2 is 2-(-2)=4. Area of triangle = (1/2)base*height = (1/2)6*4 = 12

Math
You can look up a normal distribution table to find that the z-score for the lower 30 percentile is z=-0.475. Use Score = μ+σz to get the raw score. Remember that the value of z is signed.

maths and statistics
Total cost = total fixed cost + unit cost*quantity C(Q)=75+5Q

probability, not geometry
If they are all equally likely to win, the fair price is the expected value of the prize, namely ∑xP(x) where x=winning for a particular outcome, P(x) is the probability of outcome x. and the summation is summed over all possible outcomes. The possible outcomes are: $50 (w...

math :)
You're welcome! Note: If it is a trick question, the height of the ball on the eighth bounce is zero!

math
Angie's right. The ball needs to fall down after the 7th bounce, i.e. we stop counting after the 8th down arrow, to the sum 19.84, we need to add 0.96. This is actually a summation of a geometric series of common ratio r=0.9, and initial value of 2.0. The total (up and dow...

precal
Assuming there is no typo in the question, we have to solve: 4=2cos(pi/6t-2pi/3)+4 the 4 on each side cancel out, so the equation becomes: 2cos(pi/6t-2pi/3) = 0 Divide by 2 on each side to get: cos(pi/6t-2pi/3) = 0 cos(x)=0 when x=(k+1/2)π, k∈Z (i.e. k is an integer). ...

PHYSICS
It is more accurate to work with fractions. The above calculations are correct except for minor rounding errors. We also have to assume that the car started from rest, which was unfortunately not mentioned in the question. If (2/3) had been used in place of 0.67, we would have...

physics
See Elena's response at: http://www.jiskha.com/display.cgi?id=1339176192

medu
Exact simple interest means we count the number of days in the year (some say it is 365, leap year or not) to do the calculation of simple interest. Ordinary simple interest is based on the banker's year of 12 months of 30 days, or 360 days a year. This is equivalent to a ...

maths
This is a problem in number theory and related to the Chinese remainder theorem. I do not know at what level you're working on. However, this problem is probably made to be solved without the use of advanced theory. Here's an approach that you can apply to other proble...

physics
See also response at: http://www.jiskha.com/display.cgi?id=1339176192

math multiply and simplify
What is -9s-4s?

math multiply :)
You're welcome!

math multiply
Correct.

Math add the polynomials
"...so answer is 5a²b4"

Math add the polynomials
I mean this is correct: "ahh so the 7ab cancels because of the -7ab so answer is 5a²b4."

To Adriana:
Your answer is correct.

Math add the polynomials
You need to find the like terms, for example, a²b4 and 4a²b4 are like terms. You can add them together to make 5a²b4. So a²b4+4a²b4=5a²b4 Like terms must have the same variables each raised to the same power. We can add like terms by adding the co...

geometry
Coordinates of mid-point M between points P1(x1,y1) and P2(x2,y2) is M((x1+x2)/2, (y1+y2)/2)

maths
The general solution to the equation ax^2+bx+c=0 is, using the quadratic formula: α=(-b+√(b²-4ac))/2a, and β=(-b-√(b²-4ac))/2a From there, expand α²+β² to get (b²-2ac)/a² I will leave parts (ii) to (iv) for you as...

math
This is the same as the formula for borrowing money and repaying a monthly amount. Let P=principal n=number of months it will last y=interest rate, compounded monthly at y/12, (use 0.10 for 10% per annum) x=monthly spending then p(1+y/12)^n=x((1+y/12)^n-1)/(y/12) Unfortunately...

math
f(x) can be factored as f(x)=-(x+6)(x-1) and x-intercepts mean zeroes of the function. Can you take it from here?

Math
"1billion meters of hail" Do you mean 1 billion m³ of hail? We can calculate how many hailstones there were before they melted. What does melting (and the density of ice has to do with the problem? Please recheck the exact wording of the question.

Algebra 1B--Check Please!
#2 is not correct. You can follow the steps above and try again.

Algebra 1B--Check Please!
I assume you have not done calculus before. To find the axis of symmetry of a polynomial of second degree (quadratic), we only have to complete the squares, which will then give the coordinates of the vertex in the form V(h,k) where y=a(x-h)²+k and a is another constant. ...

math
A=4B, B=3C, so A=12C, B=3C A+B+C=12C+3C+C=1600 16C=1600 C=100 Therefore A get 12C=12*100=?

geometry
Expected value for a probability distribution is E(x)=∑xP(x) In this case, P(200)=1/1000 P(50)=2/1000 P(other prizes)=0/1000 Calculate E(x)

math
If 200<n<300, then the first digit must be 2. That leaves 4 digits for each of the remaining digits for a total of m=1*4*4*4 numbers. If there is no limitation, the number of all possible (distinct) numbers is N=4^4. The probability that a number formed by the digits 1,2...

Algebra 1B :)
You're welcome!

Algebra 1B
GCF of two numbers means that the GCF divides each of the two numbers. 1. 25a3b4 does not divide one of the two numbers, so it is not the GCF. 2. a²b is correct. 3. 2ab³ is correct.

math
I suppose what you mean by a perfect trinomial is a perfect square, in which case c has to be a perfect square in such a way that 25x^2-40x+c = (5x-4)^2 Can you find c?

Advance mathematics
The coefficients are: 1 -1 -10 -8 which do not add up to zero. So (x-1) is not a factor. If we change the sign of the odd powers, we get: -1 -1 10 -8 which adds up to zero. So (x+1) is a factor. Divide x3-x2-10x-8 by (x+1) to get x²-2x-8 and factorize to find the other ze...

PHYSICS
Gain in potential energy =mgh =200kg*9.81 m/s²*5m =9810 N-m equals work done in hoisting the piano.

Physics :)
You're welcome!

Physics
y(t) = 8.4 sin(14t) m v(t)=dy/dx = 8.4*14 cos(14t) m/s max. v(t) occurs when cos(14t)=1, or max v(t)=8.4*14=117.6 m/s

Physics
Use conservation of momentum for inelastic collisions (when both masses travel at the same final speed in the same direction): m1u1+m2u2=(m1+m2)v Here m1=0.009 kg u1=to be found m2=1910 kg u2=61 mph (m1+m2)=1910.009 v2=55 mph So 0.009u1+1910*61 = (1910.009)(55) Solve for u1 u1...

Physics :)
You're welcome!

Physics
(a) 4.9 l / 103 cm =4900 ml / 103 ml = 47.6 s (b) cross section area A = π2.1²/4 = 3.46 cm² Velocity = Volume/cross section area = 103/3.46 cm/s = 29.7 cm/s

calculus
Each cross section (from x=0 to x=1) is a square of side √x. So the total volume is the area of the square times dx, or A(x)dx V=∫ (√x)^2dx from x=0 to 1 =∫ xdx =[x²/2] from 0 to 1 = 1/2

computer
What kind of help do you need?

c0llege math
To do -7(2a-4) you only have to multiply -7 to the coefficient of 2 to get -14a-4

Physics
The idea is to calculate the pressure difference ΔP between the outside and the inside. Multiply ΔP by the area to get the force. One pascal = 1 N-m-2. Atmospheric pressure Pa= 100 kPa = 100*103 Pa Density of sea water = 1025 kg-m-3 = 1025*9.81 N-m-3 = 10.055*103 N...

linear programming
Given: Cost/Unit Labor Hours/Unit Clock $7 2 Radio 10 3 Toaster 5 2 Implicitly, all quantities produced daily are to be positive, so => c ≥ 0 r ≥ 0 t ≥ 0 The manufacturer has a daily production budget of $2,000 => 7c+10r+5t ≤ 2000 and maximum of 660 hours of ...

MATHS
Do a division of x^4-7x^3+17x^2-17x+6 by (x-3)(x-1)=x²-4x+3 to get x²-3x+2 as a quotient. Factor x²-3x+2, equate to zero and solve for x.

math
The standard quadratic equation in canonic form is f(x)=y=a(x-h)+k where (h,k) is the vertex. when a<0, parabola is concave down. So for Cohen, h=120, k=24, so f(x)=a(x-60)^2+24 However, we also know that y=0 at x=0 and x=120, so f(x)=x(x-120) Equate the two forms of f(x): ...

CALCULUS - HELP
Are you doing Calculus or pre-calculus? I believe that to solve for sin(x)=1/x requires numerical methods, such as Newton's method, or other approximation methods. You can also plot sin(x) and 1/x and see where they intersect or as approximations. See: http://img543.images...

CALCULUS - HELP
asin(a)-1=0 asin(a)=1 a=(2k+1/2)π where k=integer Use the graph of sin(x) to solve for a. Note: asin(a) does NOT equal 1/sin(a). asin(a)=x means sin(x)=a

CALCULUS
This would be more messy if you are looking for an explicit solution. You would solve for y as a quadratic equation, and verify that all solutions obtained from the equation are actual solutions. Most of the time, an implicit solution (where y occurs in more than one term or e...

CALCULUS
To separate: dy/dx = (2x+1) / (y+1) Cross multiply: (y+1)dy = (2x+1)dx To solve, integrate both sides (y^2/2+y) = (x^2+x)+C where C is an integration constant

Math
Fast way: Half of 545 = 272 must fall between two perfect sequres, namely 256 and 289, which means that the integers are 16 and 17. Standard way: Let x be one of the integers, then x+1 is the other. So that: x^2+(x+1)^2=545 2x^2+2x-544=0 x^2+x-272=0 (x+17)(x-16)=0 So x=16 or x...

Math
Convert equation to its canonical form by completing squares: h(x) = -0.0274x^2 + 1.34033x =-0.0274(x-24.46)²+16.3913 which means that the vertex is located at (24.46,16.3913). Determine if the vessel can goes through.

Calc
Yes, you're right. If we proceed with Cost = 6 w^2 + 8 w h we get: w=6 and h=9.

statistics
Total amount of prizes = 900+600+3*400+5*100 = $3200 Total number of tickets = 1000 expected value of prizes for each ticket sold =3200/1000=$3.2 What is the expected value of 5 tickets?

calculus
The square S is cut into 5 pieces by S2, namely the square S2, and 4 triangles at each of the four corners. If you flip each of the four triangles at the four corners about the sides of S2 so they go inside of S2, you will find that the sum of the areas of the four triangles e...

To Reiny: great minds...
Here we go again!

math-Probablity
Assuming: 1. he got indeed the 16 questions correctly. 2. the remaining 24 answers were random choices 3. there was exactly one correct answer 4. passing grade is 50% to each of the remaining questions then he will need 4 more correct answers to get 50%. Let p=probability of g...

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