Thursday
July 24, 2014

Posts by MathMate


Total # Posts: 10,590

math
Ratio required: (54-30)/(30-26) =24/4 =6/1 Weight of 26% alloy:210*(6/7)=180 oz Weight of 54% alloy:210*(1/7)=30 oz

Calculus - linearization
Since the exact increase can be calculated readily by π(r2²-r1²) =π(44.4²-44²) =35.36π I assume you are working on linearization in calculus. Let A(r)=πr² A'(r)=2πr Approximate increase in area =A'(r)Δr =2πr*Δr =2&...

heeeeeeeelp math
Given ΔABC, A=20° B=80° => C=80° => isosceles triangle with base BC=x. Let E=mid-point of BC, then ΔAEC is a right triangle right-angled at E EC=x/2 By definition of cosine, AC=(x/2)/cos(80°) =x/(2cos(80°)) Consider ΔADC, AD=x (given...

heeeeeeeeeeelp math
The way I interpreted the question is that she does not move at all if she rolls doubles. After rereading, it looks like that when she rolls doubles, she moves the token before rolling again, and on the third double, she advances it to 36. If this latter interpretation is corr...

heeeeeeeeeeelp math
Solve using a probability tree. First calculate the outcomes with distinct rolls for a sum of P(x)=30/36. For simplicity, the probability is multiplied by 36 to use integers. sum=x 36*P(x) x*36*P(x) 3 2 6 4 2 8 5 4 20 6 4 24 7 6 42 8 4 32 9 4 36 10 2 20 11 2 22 Sums of 2 and 1...

Math
One kilogram is equivalent to 1000 grams. So 4.86932 kg = 4.86932*1000 g = 4869.32 g To round to the nearest gram, we draw a vertical line at the decimal point: 4869 | 32 if the first digit after the | bar is 5 or over, we add one to the number before the bar. Otherwise we do ...

Physics
There is probably a typo: ...east at 4.0m/s for 0 seconds. should probably read ...east at 4.0m/s for 30 seconds. Sum up all the individual displacements to get the overall displacement. Let +x=east, +y=north, then (dx,dy) =(-2*15+0+4*30, 0+3*20+0) =(90, 60) =108.17 in directi...

Math Calculus
The domain of the function is all Real, except for those two points which will result in a zero in the denominator, and hence f(x) will not be defined. One of these points is x=7. The roots can be deduced from the numerator of f(x). One of the roots is x+1=0, or x=-1. Vertical...

C++ debugging
If you need to debug a programme, it would help more if you specify: 1. object of the programme 2. language (C++ in this case) 3. What does not work: - does not compile? (error message?) - does not run ? (error message?) - does not give proper answer (logical error) - loops in...

math 3
Add three times the second equation to the first to get: (10+15)x=-16+66 25x = 50 x=2 Substitute x=2 into the second equation to get: 5(2)+2y=22 2y=22-10=12 y=6 Now substitute x=2 and y=6 into the first equation to check solution 10(2)-6(6)=-16 so solution is correct.

math
As Reiny pointed out, we do not use tables for the past 40 years, so we can only guess what's shown in the tables. My guess would be that the factor is the ratio of future/present values, namely: 1.005^48=1.270489 Note: compound interest is calculated as: future value=pres...

Statistics
Your reasoning and calculations are correct. So the probability of getting a prime number as the sum is 15/36.

Stats
An even number is any of 2,4,6,8,10,and 12 (within the sample space above). So the probability of throwing a sum equal to an even number is the sum of the corresponding probabilities, namely: 1/36+3/36+5/36+...1/36.

math
By trial and error, I get: 11^3+(-5)^3+(-6)^3=990 If we assume the largest integer is N such that N(a,b)=a^3-b^3-(a-b)^3 =3ab(a-b) The likely candidates are: 990=3*11*5(11-5)... a,b,c = 11, -5, -6 993=3*331 996=3*332=3(4*83) 999=3*333=3(9*37) All of which cannot be reduced to ...

probability
The experimental probability of multiple births is #of multiple births/total # of births =(68339+1337)/3612258 =1.9% (approx.) Check my arithmetic.

compound interest math
calculate the compound interest on an investment of $45,000 at 6% interest compounded quarterly fro 3 years Formula for compound interest: A=P(1+i)^n A=amount at the end of n periods (future value) P=amount invested (present value) i=interest per compounding period. 6% per ann...

Math
Check for type, I believe the question should read: (8/(sqrt(x)-3)) - (48)/x-9) =(8(sqrt(x)+3)/(x-9)- 48/(x-9) ... multiply top & bottom by sqrt(x)+3 =(8sqrt(x)-24)/(x-9) =(8(1/2)/sqrt(x)) / 1 ... diff. top and bottom, de l'hôpital's rule =4/3

math
4x4x4x4 =4^4 =(2^2)^4 =2^(2*4) =2^8

Discreet math
If you need a proof of the proposition/identity, please first double check the expressions. [(pvq)^(p=>)^(q=>)]=>r[(pvq)^(p=>)^(q=>)]=>r Not sure if something is missing where expression is indicated in bold. Perhaps there are other problems.

Math :)
You're welcome!

Math
Typo corrections: Area of square PRSQ - Area of ΔPDQ - area of sector RPD - Area of sector SQD. Note that sectors RPD and SQD have central angles of (90-60)=30°.

Math
We will describe the problem as follows. Two circles A,B of equal radii (r=30') are centred at P, Q, distance r apart. Points R and S on circles A, B are such that RS form a common tangent to both circles. Hence PRSQ form a square of side r. Arcs are drawn with centre P an...

devry
Divide total cost by the number of miles driven to get the average cost per mile, $773.02 / 180 miles = ? $/mile

Physics (Stress & Strain)
Area = lw (correct) =1cm x 2.5 cm =0.0100 cm x 0.025 cm =0.00025 m² (remember, length 8.1 does not come into the calculation of cross section area) Stress =force (in N)/area (in m²) =150000/0.00025 Pa =6×10^8 Pa =6×10^5 mPa =600,000 mPa Strain =deformatio...

Algebraic Fractions
6x/(12x) would be simplified just like an ordinary (numeric fraction). Look for common factors in the numerator and denominator to cancel out, separately for numeric values and variables. For the numeric part, the HCF is 6 and for variables, it is x. So divide both numerator a...

Physics (Stress & Strain)
Correct!

Physics (Stress & Strain)
Stress = force / area Load is 87500N which is just a force. You need to divide the force by the area resisting the tensile stress. Factor of safety is then ultimate stress / stress under load

Physics (Stress & Strain)
Do not forget to multiply by 10^-4 when converting cm² to m² Here we are talking about shear stress, which is dependent on the thickness and the circumference of the hole, not the area. Surface area which resists shear force is similar to the lateral surface area of ...

math - please check question
There must be a typo, because the cheapest ticket is $7, which when multiplied by 1275 gives 8925, much higher than the revenue of $2490. Assuming total of 275 tickets sold. x=number of adult tickets 275-x=number of children's tickets Then 12x+7(275-x)=2490 Solve for x to ...

Physics
So is it 30 m/s or 35 m/s? Let the initial velocity be u m/s, which remains constant while it is airborne. Time to drop down 1.5 m vertically with g=9.81 m/s^2 is given by S=(1/2)gt^2 or t=√(2S/g)=√(2*1.5/9.81)=0.553 s Horizontal distance covered before touching gr...

Math 61 part 2
To solve this category of problems where you need the area/centroid of a region bounded by two curves, you need to first find TWO intersection points of the two curves by equating y1(x)=x^2 and y2(x)=2*x+3. The intersection points are at x=-1 and x=3, with y2(x) above y1(x). T...

How do I solve for this??
H (joules) =ΔT*m*Q where H=energy required (joules) ΔT=change in temperature (°C) m=mass (g) Q=specific heat in j/°C/g So heat gain =12.67 °C * 100 g * 4.180 j/°C/g =5296 j

physics
non-zero and constant.

math
Find the slope of the line that joins (0,-1) and the centroid of the parallelogram which is (8.5,4), or the mean of all the coordinates.

Physics
See: http://www.jiskha.com/display.cgi?id=1372082354

Physics
See: http://www.jiskha.com/display.cgi?id=1372082354

Math
Since 31^2=961<1000, and 32^2=1024>1000 we can have a maximum of 31 pairs of numbers whose product would be less than 1000. So the maximum number of runners would be 62.

Physics (Stress & Strain)
When you see a factor of safety over 10, it would be a good idea to check your calculations. Watch out for units conversions for areas and volumes. In converting 6.5 cm² to m², you must multiply by the (linear factor)², namely 0.01². The area is therefore 6...

Physic (Stress & Strain)
Both are numerically correct. In #2, you divide m by m, hence no units.

math
This is similar to a previous question. I believe it would do you good to plot the scatter diagram and calculate the regression line according to the formula. Post again if you have difficulties. For your information, the regression coefficient a is between 0 and 0.2, the cons...

statistics check :)
You're welcome!

statistics check
I got it from summing (y-yBar)^2, and I had yBar=24.3.

statistics check
SE² is given by: [ Σ(y-yBar)^2 - [Σ(x-xBar)(y-yBar)]²/Σ(x-xBar)² ] /(n-2) I get: Σ(y-yBar)²=258.1 Σ(x-xBar)(y-yBar) = -168.7 Σ(x-xBar)²=296.9 n=10 to get se²=20.28

math
A=P[(1+i)^n -1]/i => P=Ai/[(1+i)^n -1] =1000000*(0.08/12)/((1+0.08/12)^480-1) =286.45023 per month.

Please help me solve
See http://www.jiskha.com/display.cgi?id=1372073330

Please help me solve
Multiply the temperature difference by the calorimeter constant to get the energy in joules.

Phil103 Informal Logic
I think you would be more productive if you read Chapter six before you attempt these exercises. For example: ~p∨q reads as not p or q, with the "not" applying to p only.

Strength of materials
You have posted a number of questions without your input, and most of all, without the accompanying diagrams, nor the descriptions to replace the diagrams. If you believe that we can imagine what the loading is like, you are mistaken. I suggest you concentrate on one particula...

Physics (Stress & Strain)
Area 10.5cm²=10.5*10^(-4) m² Load = 5550 N Stress =load/area =5550/(10.5*10^-4) Pa =5285.714 kPa Strain: 1.1mm/1.9 m =1.1*10-3 m / 1.9m =0.000 579 (no units)

math
This is an exponential function of the form y=ae^x Substituting x,y values (20,45)into the equation, 20=160*e^(45k) take logs on both sides and solve for k k=-(1/45)ln(8) =-0.04621 So the mathematical model becomes: y(t)=y0*e^(-0.04621t) t=time in hours y0=initial mass y(t)=ma...

Physics
2 grams of hydrogen occupies 22.4 litres, so 18000kg=18000*1000 g will occupy 18000000/2*22.4 L =9000 m³ (at STP)

maths
See: http://www.jiskha.com/display.cgi?id=1371992237 If you do not agree with the response, please post and explain.

maths
The problem we have on hand is: Maximize |xy| subject to: f(x,y)=0 where f(x,y)=2y^2+43x^2y-6xy+5y+2x^2+48x-174.3 To solve the problem, we will solve for the extreme values of xy, and choose from the extreme values the largest value of |xy|. To do this, we would use Lagrange m...

physics
Use kinematic equation v^2-u^2=2as v=0 (at 0.8m above floor) u=unknown a=-9.81 s=0.8 u^2=√(2*9.81*0.8)=15.696 u=4 m/s approx.

business math
We do not know if it is simple or compound interest. Since compounding frequency is not mentioned, we assume it is simple interest. The simple interest formula: Future value = present value(1+ni) n=number of years, i=annual interest So 4,370.91 =PV(1+3*0.03) => PV=4,370.91/...

statistics
This is a binomial distribution of n=240 trials with probability of success p=0.17 and of failure q=1-0.17=0.83. Mean=np=40.8 variance = npq=33.864 Std dev = √(33.864)=5.82

math
Divide by two until the remainder is 0 or 1. The corresponding quotients will give the powers of 2 to make up 2000. 2000/2=1000 R0 1000/2=500 R0 500/2=250 R0 250/2=125 R0 125/2=62 R1 62/2=31 R0 31/2=15 R1 15/2=7 R1 7/2=3 R1 3/2=1 R1 So 2000 in binary notation is 11111010000 or...

maths
Assuming 74.2 cm of pressure refers to the mercury column. Under standard temperature and pressure (273.15°K, 100 kPa=760.06 mmHg), the gas constant is: 62.364 L mmHg K−1   mol−1 molecular mass of N2=2*14.0067=28.0134 So volume occupied ...

maths
The solution is given for AD. Are you able to calculate AD²?

maths
I assume the last sentence is "What is AD?" since AD2 does not mean much. Hints: Use cosine rule to find ∠A, in triangle ABC. A=arccos((20²+24²-22²)/(2*20*24)) =arccos(41/80) = 59° (approx.) Then Area of triangle ABC =(1/2)AB.AC.sin(A) =(1/2)*2...

phy
Do check your previous post for answers before reposting! See: http://www.jiskha.com/display.cgi?id=1371911866

Physics :)
you're welcome!

Physics
A=[5,-6.5] B=[-3.5,7] If A is perpendicular to C, then A.C=0, or C=[6.5k, 5k] (verify that A.C=0) If in addition, C.B=15, we have C.B=[6.5k,5k].[-3.5,7] =35k-22.75k =12.25k But C.B=15, therefore 12.25k=15, => k=15/12.25=60/49 Therefore C=[6.5k,5k] =[390/49, 300/49] Check my...

Physics
Ignore mass of balloon and basket. Consider 1 m^3 of hot air: mass, m = 0.93 kg net upward force, F =(1.29-0.93)=0.36 kg = 9.81*0.36 N =3.53 N acceleration = F/m = 3.53/0.93 m/s² = 3.8 m/s² Note: At this acceleration, air resistance is significant.

Maths
In the given case, since the given polynomial is of the fifth degree, you only have to try S=1,2,3,4 and up to 5. In fact: Let's factor the polynomial f(x)=n^5-17*n^3+16*n =(n-4)*(n-1)*n*(n+1)*(n+4) From this you will find the factors have the following properties: if n=0 ...

maths
Assume the equation has three roots a,b and c: then (x-a)(x-b)(x-c)=0 x³-(a+b+c)x²+(ab+bc+ca)x-abc=0 which means (a+b+c)=-3 (negative of coeff.of x²) (ab+bc+ca)=-7 (coeff. of x) Hence a²+b²+c² =(a+b+c)²-2(ab+bc+ca) =3²-2(-7) =9-(-14) =23

maths - incomplete
I'm afraid I do not make a lot of sense out of the the following definition: f(x2+1)1x√=x6x Kindly verify before and after posting your question.

Precal
5^(-t/2)=0.20 take log on both sides, (-t/2)log(5)=log(0.20) solve for t -t/2 = log(0.20)/log(5) t=-2log(0.20)/log(5)...isolate t =log(1/0.04)/log(5)...absorb -2 into log(0.2) =log(25)/log(5)... evaluate reciprocal =2... laws of logarithm, 25=5²

Math
The ordinary interest method is to calculate simple interest based on 360 days in a year. So interest=principal*(days/360)*rate 68.50=principal*(274/360)*6% therefore principal=68.50*(360/274)/0.06 =$1500

statistics
The answer should be a negative number as the numbers increase as x becomes smaller. The correlation coefficient lies between -0.2 and -0.3. Please post your equation for r again to see if it is interpreted correctly. Most of the time mistakes come from incorrect interpretatio...

statistics
What did you get using the given formulas 13.2 and 13.3?

math
Exact interest is based on a 365-day year. From June 30 to September 17, three months have passed. Both July and August have 31 days, while June has 30 days. So the duration of the loan is 30+31+31-3=89 days. Interest =Principal*(days/365)*0.10 =19000*(89/365)*0.10 =$463... do...

Algebra 2
Let y=kxz 98/3=k(2*7) k=98/3/14=7/3 Therefore y=(7/3)xz when x=7, z=3 then y=(7/3)*7*3=49

algebra - incomplete
I suspect you have missed out part of the question, such as: a) A∪B b) A∩B ... etc. Which is/are the "given set"?

Math Algebra 1A
I am not too sure what exactly your question is asking. If the time is elapsed since 1995, then you would subtract 1995 from the year in question. For example, 2004 is 9 years since 1995.

Physics
Assume a distance of d from the fulcrum. Take moments about the fulcrum: 350*2-540d=0 d=1.296 m

Physics
If I were to do the calculations, I would always work with stress, because ultimate stress is constant from problem to problem if the same material is used. It helps to spot errors, if any. Ultimate strength = 550 mPa. Stress under load = 64000/(7.6*10^-4) =84.2 mPa Now find t...

Physics
Required capacity of bar (in tension) =225kN*7 =1.575 MN Tensile strength = 231 MPa Area required =1.575 MN / 231 MPa =0.006818 m² =6818 mm² From πr²=6818 radius=√(6818/π) = 46.6 mm (or more)

Math
P²-0.037 = 0 P²=0.037 P=√0.037 Your calculator will give you the numerical value.

maths
A stimulating problem, combining probabilities with discrete mathematics. The question requires the probability of successively picking two balls of same colour be the same before and after adding 14 balls of a new colour. Initial situation: Assume there are n balls with k of ...

math - Tom Beth & Brad
Please do not use aliases, and do not repost within a short interval.

math
Let A = borrowed amount then A*(0.132)*2.5 years = 1320 A=1320/(0.132*2.5) =4000

Math (Trigonometry)
tan(θ)=1/4 => cos(θ)=4/√17, and sin(θ)=1/√17 Guess you can take it from here.

Calculus 2
Assume all measurements are in metres (since g is given as 9.8 m/s^2) The centre of gravity of the full tank is at 1.5/2=0.75 from the bottom. Work done is equal to the potential energy of the water at the spout (top) minus the potential of the full tank. Volume of tank, V=(&p...

math help
The probability is all the question wanted. If you have a more detailed question, kindly post. We do not generally follow all your previous posts.

math help
The probability of committing a type I error is the level of significance, α. See: http://www.cs.uni.edu/~campbell/stat/inf5.html

Algebra
Polynomials with all terms in even degree are even functions, and those with all odd degree terms are odd functions. For this purpose, a constant k can be considered as k*x^0, so it is even. A mix of even and odd degree terms is neithter odd nor even. Example: f(x)=x^6+x^2+4 i...

Physics
See your other post. Try to work with stress for comparison.

math
This has been posted many times, and answered more than once by different teachers. The solution to the system of algebraic equations are: (3,1),(1,3),(-2,4),(4,-2). The maximum value of |xy| is therefore 8.

math
The solution to the system of algebraic equations are: (3,1),(1,3),(-2,4),(4,-2). The maximum value of |xy| is therefore 8.

computer
It would be more helpful if you can indicate: 1. blank means black, white or blue screen? 2. What happened during the "booting" process, i.e. since the computer is turned on. Did you see any messages (whether you are able to decipher them or not). 3. Have you tried p...

math
This seems to be a programming challenge. While this can probably be worked out in mathematical terms, it is easily shown by exhaustive search that the 3-digit number is 199, where the minimum quotient is 199/19 =10.47 approximately.

diffirential calculus
Let the height be h (constant). First find radius in terms of V, volume. Volume, V = πr²h radius, r = √(V/(πh)) So the total surface area is obtained by substituting r in the following expression: A(total) =2πrh+2πr^2 =2π√(V/(πh))(√(V/(...

maths
obtained by adding the two vectors: (18,0)+(3cos(40),3sin(40)) =(18+3cos(40), 3sin(40)) =(x,y) The resultant speed R is obtained by |R|=sqrt(x²+y²)

Math
Let distance be D km, and the current be C km/h His speed is 8 km/h in still water. So his speed upstream is D/3.25=8-C and downstream, D/1.5=8+C Cross multiply each to get D = 3.25(8-C) D=1.5(8+C) Solve by comparison 1.5(8+C)=3.25(8-C) Isolate C 4.75C = 8(3.25-1.5) C=8*1.75/4...

maths - question incomplete
So far, ABC is just any triangle. The addition of the altitudes do not help. If it is further specified that BD intersects the segment AC at D, and CE intersects segment AB at E, and that BD and CE are equal, then it is possible to prove that triangles EBC and DCB are congruen...

statistics
A two-tailed test of a=0.05 is equivalent to two tests of a=0.05/2=0.025 for each for the upper and lower tails. So for |z|>1.96 has a=0.025 (two tailed) is equivalent to z>1.96 and z<-1.96. Ref: http://www.math.unb.ca/~knight/utility/NormTble.htm

math
Here m=7.50 / shirt b=set-up fee Since we know that 2450=7.5(300)+b => b=2450-7.50*300 =2450-2250 =200 So y=7.50x+200

Math
All good to me. For number 3, I am not sure if I understand the context of the question. I interpret it to mean what variable can adversely affect the accuracy of extrapolated data, in which case I choose independent variable. If an independent variable is chosen out of the ap...

maths
Distance travelled in one revolution = 2 × π × r where r is 3 cm. Distance travelled in 15 revolutions will be 15 time the above amount.

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