Monday
April 21, 2014

Posts by MathMate


Total # Posts: 9,948

Maths
Use the property of intersecting chords PA*PB=PC*PD In this case the chords intersect outside of Γ. Also, if T is the tangent to Γ passing through P, then PA*PB=PC*PD=PT²

math
Trade discount = $679.95*0.30

trig
So on the Cartesian plane, it is in the fourth quadrant, with x-y as (900,-500). Atan(-500/900)= -29° approximately. So the bearing is S61°E.

Calculus
Use substitution, p=sin(x), dp=cos(x)dx I=∫ydx =∫cos(x)(2sin(x)-1)^6dx =∫(2p-1)^6 dp Substitute again, u=2p-1, du=2dp I=∫u^6 (dp/2) =u^7/7 ÷2 + C Now back substitute u=2p-1=2sin(x)-1 I=(2sin(x)-1)^7 /14 +C

Math/ Algebra
Rewrite the equation in symmetric form x/a + y/b = 1 where a and b are the x- and y-intercepts respectively. y/2 -3x/5 = 1 can be rewritten as: x/(-5/3) + y/2 = 1 Identify the intercepts and graph accordingly.

Math
15/20/20 is a successive discount of 15%, followed by 20% on the discounted price, and finally another 20% of the doubly discounted price. For example, $1000 with a trade discount of 15/20/30 would have a final discounted price of $1000*(1-0.15)(1-0.20)(1-0.30)=$476 So the tra...

Math/ Algebra
See http://www.jiskha.com/display.cgi?id=1369451313

Math
p=probability of scoring (success) = 0.8 q=probability of not scoring (failure = 0.2 Assuming the probability does not change over time and is independent of previous results, then we can apply the binomial distribution: P(7+ out of 8) =8C7*0.8^70.2+8C80.8^8 =0.34+.17 =0.50 (a...

statistics
Ah! I see it now. "y (in tens of thousands of dollars)" That might be the culprit.

statistics
Did you put $5.13 or 5.13?

Statistics
There are different ways to find the regression line. Do you know which one you are supposed to use? It should be around y=-0.6x+310. Try to calculate the coefficients and we can check you answer. Do specify the method, and work details if you can.

statistics
If you are working on the computer, you have to get the answer exactly right. It asked for the answer to 2 decimal places. If you put three (3.625), it could mark you wrong. On the other hand, there are two ways to round it to 2 decimal places. Most people round it up when it ...

Math - please help
The height is 280 ft. Distance from apex to mid-point of base = 356.1 ft = slant height. Area of one side = (1/2)base*slant-height then choose the correct answer.

Calculus
Let f(x)=sqrt(1+6x) then f'(x)=3/sqrt(6*x+1) and f'(0)=3 Thus the slope of the curve is 3 at x=0. f(0)=1 means that the tangent to the curve passes through (0,1)=(x0,y0). So the linearization is y=Ax+B =Slope(x-x0)+y0 =3(x-0)+1 =3x+1 Identify A and B for your answer.

Maths
For x near 1, you can use linearlization, which is f(x)=f'(1)(x-1)+f(1) =(1/8)x+f(1) Therefore, within the errors of the linearization, f(x)-f(1) = (x-1)/8 (approximately)

geometry - missing information
To scale or not, we don't get to see it. So we depend on you to describe the figure.

please answer simple stat any tutor
Think of the test as μ1>μ2 Is the solution of μ1 on the left, right or both sides of μ2?

algebra
slope of line y=(2/5)x+7 is (2/5) Slope of line perpendicular to it is -(1/slope)=-5/2.

Frenchhhhhhhhhh
All the cases are direct objects, so you need to replace them by le/la or les (not "des")depending on whether the nouns you are replacing are in singular or plural, and masculine or feminine. There is an extra caution in French is that the pronouns of direct objects ...

Frenchhhhhhhhhh
Replace by what?

Algebra - clarifications required
y=2x=1 is not an equation of a line. Please clarify the typo.

Algebra - clarifications required
1. slope = 15/12 2. slope = -5/4 3. slope = ? (two equal signs, so the sign of the slop could go either way. Please clarify.

pre calc
If sin(x)=-3/5 in Q3, then cos(x)=-4/5 (using cos²(x)=1-sin²(x)) Similarly, cos(y)=5/13 in Q1 means sin(y)=12/13 sin(x-y)=sin(x)cos(y)-cos(x)sin(y) =-3/5*5/13 - (-4/5)*12/13 =(-15+48)/65 =33/65

Math
Yes, it's correct. 2 gals must be added (and well agitated).

Math (Probability)
The size of the sample space of the last throw is 20*20=400. Out of the 400 outcomes, Bret needs those where his throw is 11 or more than Shawn's, namely: (12,1),(13,1),(14,1)...(20,1) (13,2),(14,2)...(20,2) ... (19,8),(20,8) (20,9) There are ∑(i), i=1,9 outcomes. Can ...

math
One cup is 240 ml 1 table-spoon is 15 ml. So 1 cup = 16 table-spoons How table-spoons are in 16 gals? This equals how many cups?

Math
Certainly, if the father has a foot-length equal to 150% of that of Aaron.

Physics
Use the definition of a Coulomb. There are 11 ampères of current 10 minutes = 600 seconds. Can you now figure it out?

math
Let E=age of Mr. Edwards. (E+15 + E/3+15) = 86 Solve for E.

Pre-Calculus
Draw a right triangle with XY vertical, and a base AX of 200 ft. The angle XAY=25 degrees. Use the definition of tangent(A)=tangent(25°)=XY/AX Solve for XY.

7th Grade Math
Volumes are (linear ratio)³ and areas are (linear ratio)²

probability
There were 40 outcomes, of which 6 were spinning a 2. Experimental probability = 6/40 = 3/20.

7th grade math help :)
You're welcome!

7th grade math help
Assuming one must make a single choice in each group, so it is a three-step experiment. choices for group 1 = 2 choices for group 2 = 3 choices for group 3 = 2 Total number of outcomes in the sample space is therefore the product of the choices in each group (step).

physics
v0=5.5 m/s v1=0 m/s F=160 N m=80 kg Use Newton's second law, F=ma a=F/m=-2 m/s-2 (deceleration) Use: (v1^2-v0^2)=2aS So S=(v1^2-v0^2)/2a=30.25/4=7.5625 m

Physics
F=>M2=>F1=>M1 On the frictionless table, both will have an acceleration a. Draw the free-body-diagrams (FBD) and conclude that M2.a = (F-F1) M1.a = F1 using Newton's second law. Solve for F1 and a. Part (b) can be found in a similar way.

calculus
Steve is right. Whenever you transpose a fraction from a book to a single line to post, you need to insert the implicit parentheses. In this case, I believe it is 1000 = 10,000(1 − (5/[5 + e^−0.001x]))

calculus
p = 10,000(1 − (5/5 + e^−0.001x)) for p=1000, 1000=10000(1 − (5/5 + e^−0.001x)) 5/(5+e^(-0.001x)=0.9 e^(-0.001x)=5/0.9-5 take log -0.001x = log(5/0.9-5) x=-1000 log(5/0.9-5) =587.8, say 588 (b) can be done in a similar way.

Math 208
Let x be the amount he invested at 6%. Then x-1400 is the amount he invested at 5%. Total interest after 1 year x*0.06+(x-1400)*0.05=172 0.11x=172+1400*0.05 0.11x=242 x=2200 Check 2200*0.06+800*0.05=132+40=172 ok.

programming - C++ or Java?
The instructions are quite clear as to what to do. I suggest you read through your teacher's notes or instructions and give an attempt. Programming is learned by actually writing and compiling code. Copying or reading alone will not help you solve your next problem. You...

Physics
Speed of sound in sea water depends on the temperature and salinity. At 25 degrees and 35 ppt salinity, the speed of sound is approximately 1551 m/s. So divide 19000/1551 to give the time in seconds it takes.

Math
Basically you cannot. A bar graph puts different numbers into the same class, and so there is loss of information. If you have a problem in hand, post the data (if they are not too numerous) and we can appreciate better the problem in hand.

Calculus
Parentheses are implicit when it is printed in fraction form. If it is printed as a fraction, your post is linearizing it (put on a single line) and it is necessary to insert parentheses around all numerators or denominators which contain more than one term.

Calculus - clarifications required
Could you please insert parentheses to clarify the question? 10x-3/5x+6x could mean (10x-3)/(5x+6x) [??] 10x -(3/5x) + 6x [??] [(10x-3)/5x] +6x [??} etc.

Algebra - clarifications required
Jamila, please clarify what SR stands for. Is it a monetary unit, or is it an abbreviation for some term?

calculus
Find derivative with respect to x: y'(x)=dy/dx=6x-5 Evaluate derivative at x=3: y'(3)=6(3)-5=13

Algebra
Using calculus, it would be finding dy/dt and equating to zero to solve for t. Since it is algebra, you could complete squares: y=-4.9(t-7)²+49*4.9 =-4.9(t-7)²+240.1 which means that the maximum height of 240.1 m at t=7.

math
You can take the average, namely [(1+2)/8]2 = 3/16 If you want just ANY fraction between, you can add the numberators and denominators: (1+1)/(8+4)=2/12 = 1/6

Computer Science
Depending on the complexity of the game, it takes proficiency in the language, which means lots of late nights leaning and practising programming on different projects. In short, you have to like it so that it is not work, but fun.

please hurry
It is almost impossible to show the calculations here because the proportional font used here makes it difficult to line up calculations. You can look up an example at the following link: http://www.homeschoolmath.net/teaching/square-root-algorithm.php

maths-formula
Sorry mate, this expression does not have rational factors.

Physics
Since it is an elastic impact, we can equate energies.

Probability
Only question left is how Andrew found a fair 10 sided die. Platonic solids have 4,6,8,12 and 20 sides!

Probability
Use a probability tree to find that the overall probability of winning is [∑(i²)/100]/10] for i=1 to 10 =385/1000 which should be simplified to an irreduceable fraction a/b. The sum of a+b is then 277.

maths
Subdividing a pizza according to the number of people, getting change after paying for a purchase, finding unit price of items in a grocery store to compare unit cost, checking that the restaurant bill is correct, calculating tip, counting money after a withdrawal, finding the...

Algebra
See http://www.jiskha.com/display.cgi?id=1369047938

Algebra
See http://www.jiskha.com/display.cgi?id=1369047938

French-SraJMcGin
Watch spellings of "Sacré-Coeur", as pointed out by Mme Sra. The proper name seems to be "La Basilique du Sacré Coeur"

math
This equation is separable, so dy/dx = 6xy dy/y = 6xdx Integrate both sides, log(y)=3x²+C1 y=Ce3x² y(0)=40 -> C=40 therefore y=40e3x²

geometry
Draw a rhombus, and mark one side as 24 cm, and one of the diagonals as 24 cm long. Then the half diagonal is 12 cm. Since the diagonals of a rhombus intersect at right angles, we have a right-triangle with hypotenuse 14 cm, with one side as 12. The other half-diagonal is ther...

Geometry - incomplete?
You are probably missing a diagram or figure. x has not been mentioned in more than one place in the question.

advanced algedra 2
Substitute y=x² a) y²-9y+18 =(y-6)(y-3) and put back y=x².

Mathematics
θ=133 rpm = 133*2*π/60 radians/s Speed = rθ=40/100 m *θ =1.7733π m/s =5.571 m/s (approx.)

math please hurry
Assuming the code uses English alphabet, Choices for first letter: 26 Choices for second letter: 26 Choices for third letter: 26 Choices for digit: 10 Total number of codes = product of all 4 choices.

Algebra
Since the title is "algebra", I assume calculus cannot be used. In this case, complete squares of P(x). P=-5(x-20)²+2200 which means that P(x) is at a maximum when x=20, and P(x)=2200.

advanced algedra 2
See: http://www.jiskha.com/display.cgi?id=1368991756

Geometry
Lateral surface area of a cone Al = πrL r=radius of base L=slant height. So Area of canvas = π(12.5)(26)

To GANDU MAN
Your geometry problem of yesterday has been answered. http://www.jiskha.com/display.cgi?id=1368886945

math
a^3=1/cos-cos = (1-cos^2)/cos=sin^2/cos b^3=1/sin-sin = (1-sin^2)/sin=cos^2/sin a^3/b^3=sin^2/cos * cos^2/sin=sin^3/cos^3 => a/b=sin/cos = tan (Hope you understand your own notations.)

statistics
μ=98.2 σ=0.62 Z(100)=(100-98.2)/0.62=2.903 Look up (normal) probabilities for Z=2.903 from tables (for people with temperatures below 100). Subtract from 1 to get probabilities of healthy person considered having a fever.

Mathematics
Assuming radiator reaches 120° between 0 and 4 minutes. Trying to solve: 120 = 6.2t² + 12t +32 or 6.2t² + 12t - 88 = 0 Use quadratic formula to get t=-4.8 or t=2.92 sec. Reject t=-4.8 because it is not within interval [0,4].

Algebra
1. The transformations are: e(O,2) : dilation about origin of 2 units t(0,5) : translation 5 units up r(y,-x) : rotation counter-clockwise 90° So (x,y)-> (2x,2y) -> (2x, 2y+5) -> (2y+5, -2x) So combining it all: (x,y) -> (2y+5, -2x) 2. Using Cramer's rule: ...

Physics
We are unable to help you solve the problem without guessing how the objects are configured. You can describe in detail how the objects are arranged, or post the diagram at an external site and post the link.

Math 4 questions
"at most" means ≤ "minimuum of" means ≥ "less than" means < "low of" means ≥ "high of" means ≤ You will be more likely to get an answer quickly if you show your attempts.

Algebra II Part 2
Thanks Steve, good thought!

Algebra II Part 2
use the identities: tan(x)=sin(x)/cos(x) cot(x)=cos(x)/sin(x) and sin(π/2)=1, cos(π/2)=0 sin(0)=0, cos(0)=1

ALGEBRA
Use compound interest formula: Amount = Principal * (rate)^n rate=interest rate per period n=number of periods compounded. Here rate = 1+ 0.07/2=1.035 number of periods = 3 years * 2 periods/yr principal=$7300 The question didn't say what's required.

Exponential modelling
Let the mathematical model be f(x)=ax^b where x=years past 1970. f(x)=population in millions Note: much better accuracy is obtained by shifting the origin to 1970, the closest possible. Substituting given data for 1970: 5.1=ax^0=a so f(x)=5.1x^b For 2004, 14.3=5.1(34^(b)) or ...

geometry
Area of annulus (area between circles of radii a and b) = π(a+b)(a-b)

geomerty
There are different ways to solve for the circumscribed radius, depending on which part of geometry you are working on. The most basic calculation taking advantage that the triangle ABC is equilateral is to construct a perpendicular bisector on side BC such that ABD is a right...

Trigonometry
If sin(α)>0, then 0<α<π. So α1 = asin(15/17)=1.0808 radians and α2 = π-α1.

French
While you're waiting for Mme Sra, you could make a review on the following: - If you abbreviate the church, you need to know what the omitted word (Basilique) is masculin or feminine. If you mean the official name of La Basilique du Sacré Coeur, then you should chan...

Algebra
Use the fact that the sum of the interior angles of a triangle is 180°. So x+(2x+24)+3x+48)=180. Solve for x.

Multiplication
"what is 1250* 2987" Let's do this mentally: 1250*2987 =29870000*0.125 =29870000/8 = 3733750

math
Note: Segment lengths BA and AB assumed to be equivalent in the following proof. BN/sin(BAN)=BA/sin(BNA) (sine rule) => BA/BN=sin(BNA)/sin(45) AC/sin(CNA)=NC/sin(45) (sine rule) => AC/NC=sin(CNA)/sin(45) Since sin(BNA)=sin(180-BNA)=sin(CNA) BA/BN=AC/NC, or CN/NB =AC/AB=t...

mathematics
Use the standard form of a linear equation: y=m(x-h)+k where m=slope=-3 (h,k)=a point through which the line passes (9,7)

algebra
Conventional algebra: x=number of small cups y=number of large cups form the system of equations x+y=155 2x+3y=335 Solve the system for x and y. Quick way by substituting directly: Let 155-x=number of large cups 2x+3(155-x)=335 Solve the linear equation for x. Faster way by me...

Statistics
Use binomial probability because: probability is known and does not change over the experiment, outcome is binomial (success or failure), each step of the experiment is similar, p=0.25 n=10 P(r)=number of question correct =nCr(p^r)(1-p)^(n-r) nCr = binomial coefficient = n!/((...

algebra 2
g(x) = 4x^4 + 4x^3 - 11x^2 -12x -3 =x²(4x²+4x+1)-3(4x²+4x+1) =(x²-3)(4x²+4x+1) =(x+√3)(x-√3)(2x+1)² => g(x)=0 has roots ±√3,-1/2 (twice)

Probability
Sample space is the set of all possible outcomes. If you pick one single marble from a bag filled with blue and yellow marbles, the only outcomes are Y=yellow marble, and B=blue marbles. So Ω = {Y,B}

Stats
Price to play the game = $25 Sum/return 2/2 3/3 4/4 5/5 6/6 7/7 8/8 9/9 10/8 11/8 12/8 So the maximum return is $9 (if she throws a sum of 9), can never recover the $25 she pays to play. If she is the player, the recommendation is: "The expected valve of net gain is negat...

programming
Here we are pleased to provide help in debugging, review your pseudocode, etc. However, we expect you to give your input as to what you have learned, (Java, C++, i/o, hello world!, etc.), what your first draft would look, what difficulties you might be having. We can then help...

Statics
Assuming the crate is on a horizontal surface, so gravity is dedicated to the normal reaction N = 200 lb. force, and the 85 lb.force applied is used to overcome the static friction offered by the horizontal surface. Therefore the (resistive) force exerted by the horizontal sur...

math-incomplete
How much are you making in 2013? Since 2013 is half way between 2010 and 2016, in 2013, the salary is (28500+32000)/2 = 30250. You can also use the point of division formula.

calculus
Separate variables to get: dx/(1-x) = dy/y^2 Integrate each side and do not forget the integration constant.

Seth
Factor: 6(x^2+3x-4)=6(x+4)(x-1) So graph has zeroes at x=-4 and +1 Leading coefficient is positive, so minimum. A minimum is at x=(-4+1)/2=-1.5, which is also where the vertical line of symmetry intersects the curve. Minimum =(-1.5, f(-1.5)) = (-1.5, -37.5) The y-intercept is ...

FACTORIAL PRODUCT(ALGEBRA)
Count how many 2's there are in each of the factorials, 1! = none 2! = 1 3! = 1 4! = 2*4 => 3 5! = 2*4 => 3 6! = 2*4*2 => 4 7! ... 10!=2*4*8*2 => 8 Add all the numbers on the right to get N.

maths
Assuming the distances are measured at sea-level, then the altitude of the plane does not affect the distance between the two ships as long as they are navigating both at sea level. Since they form a right angled triangle with angle P, we can find the distance AB using Pythago...

Math
Correct. The formula used is 8C6*p^6*(1-p)^2 where p=0.6, 8C6=28.

statistics
Selected students means you are dealing with a sample from a population. The best you can do with a sample is to estimate the correlation coefficient of the population, or the correlation coefficient of the sample. See the formulas and examples from: http://stattrek.com/statis...

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