Wednesday
July 23, 2014

Posts by MathMate


Total # Posts: 10,590

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...

math
If you suspect that the rule is a straight line, y=mx+b then find the slope using m=(y2-y1)/(x2-x1) Substitute m and (x1,y1) into the equation to find b. Verify that the rule applies to all the points.

mathe
Not familiar with how bonds work. Here's a try. Assuming the bond is issued for 30 years, then, and the current yield is x*100%. 1000=78.5(1+x)^30 1+x=(1000/78.5)^(1/30)=1.08852, or current yield is 8.852%

algebra
You can use the same reasoning as the answer to your previous post.

math
The roots p,q, of the equation ax²+bx+c=0 have the properties that: p*q = c/a p+q =-b/a Check each of the solution sets above, c/a=-3.5 If p*q ≠ -3.5, then p and q are not solutions to the equation. If p*q = -3.5, then check if p+q = -b/a=2.5. If both conditions are sa...

solve the equation - typo
We will use a lemma that states: logax = loga²x² The proof of the lemma is left to you as an exercise, if it was not already covered in your course.

solve the equation
Given log14x+49 - log196x = 1 We will use a lemma that logax=loga²=x² Since 196=14², we write above as log14x+49 - log14²x = 1 Then log14²(x+49)² - log14²x = 1 Rewrite using laws of logarithm: log14²(x+49)²/x = 1 Using the alternate...

math
Let A be the top of the pyramid, B = centre of pyramid at ground level P=position of first observation (angle=20 deg) Q=position of second observation (angle=10 degrees) Then PQ=189 feet and APQ is a triangle where APQ=10° AQP=180-20=160° Consequently PAQ=10 deg by ang...

ap calculus
Assuming the function is x(t)=(ln(t))^2 then t has a vertical asymptote at x=0. which explains why the domain of x(t) is set at x>0. To find the maximum, we need to find x'(t)=0 where x'(t)=2ln(t)/t and x'(t)=0 at t=1. Check if maximum or minimum by finding x&qu...

Calc
To find the absolute maximum of a function within a finite domain, you can do: find f'(x) and equate to zero to find the relative maxima and minima. In this case, f'(x)=0 at x=1 and x=3. By checking with f"(x) or otherwise, you will find that x=1 is a minimum, and...

question still incomplete
Please complete "the table".

Trigonometry
I am curious how you find the probability of divisibility of palindromes by 4 using the sine law. Can you kindly show your work?

Trigonometry
What is the probability, i.e. a and b?

Trigonometry
What is your answer? Did you use the sine law?

Not trigonometry
There are 900 5-digit palindromes, from 10001, 10101 , 10201, 10301, ... to 99899, 99999. Out of these 900 palindromes, divisibility is determined by the last four digits, namely 00, 01, 02, ...99. The probability of divisibility by 4 for digits of 00 to 99 is 1/4. So a=1, b=4...

incomplete question
It seems that you have been copying the question in a rush. It says the probabilities are given in a given table which you have not posted.

algebra 2
The function does not have rational roots, as it does not factor. If you graph the function, you will find approximate values (3 of them) of the real roots. One of them is positive, and two are negative. To locate them without graphing, you can find f'(x) and equate to zer...

job related
If the slope is 9 inches per foot (run), then the roof is 15" per foot run. I suppose rake factor is the ratio of roof length to rise, which works out to 1.25 in this case. The roof area (for one sloping face) is therefore (15"/9")*10'*30' long = 500 sq....

Math - correction
Correction in an intermediate step (only): ... =M((1+i)^n-1)/(1+i-1) =M((1+i)^n-1)/i

Math
Use the compound interest formula: P=$3690 i=0.21/12=0.0175 n=17 M=amount of monthly payment Amount after 17 months (without payment) = A(1+i)^n Value of his payments at the same interest rate =M+M(1+i)+M(1+i)^2+...+M(1+i)^(n-1) =M((1+i)^n-1)/(1+i-1) =M(1+i)^n/i Equate the two...

Critical Points
Inflection point at (2,3) means f"(2)=0 => f"(x)=6x+2a = 0 at x=2, or a=-6(2)/2=-6 Since f(2)=3 (from given point (2,3) ), we conclude that: f(2)=c+2b-16=3 or 2b+c=19 ....(1) We also know that there is a critical point at (1,5), so f'(1)=0, or b=9 Substituting...

Minimum on a Closed Interval
Note: -3/2 is not in [1,2], so it cannot be the correction solution.

Minimum on a Closed Interval
On a closer look, the first equation f(x)=1/(x sin(πx)) is undefined at x=1 and x=2, so probably not what you want. For equation 2, f(x)=(1/x) sin(πx) you would find f'(x)= (%pi*cos(πx))/x - sin(πx)/x^2 equate f'(x) to zero to find the minimum, and solv...

Minimum on a Closed Interval
Is the function f(x)=1/(x sin(πx)) or f(x)=(1/x) sin(πx) [ as written ]?

Geometry
If centre has (6,8) and one end of the diameter has (4,2), add Δx and Δy to the centre to get the other end of the diameter, namely, (Δx,Δy) = (6-4, 8-2) = (2,6) So the other end of the diameter would be (6+2,8+6)=(8,14). Check: the mid-point of the dia...

math
It could be a rectangle (or any other shape). Use L and W to represent the length and width. Use the area and perimeter formula to construct 2 equations and consequently solve for L and W. The solution consists of integers.

geometrY!
Given: Let r=AE:EB Draw a diagram of the parallelogram ABCD. Insert E on AB. Extend DE to join CA at F. (The above is as given by the question). Examine the triangles FAE and DBE. Show that they are similar noting that FA is parallel to DB. Therefore the ration FE:ED = AE:EB S...

math
Correction: 4/52=1/13

math
Note: the above answer assumes no replacement of cards. If the question assumes with replacement, then drawing a queen from a full deck has a probability of 13/52=1/13. In a 4 step random experiment, the probability of getting a queen at each of the four steps is given by (1/1...

math
A standard deck of cards has 4 queens, one from each of the four suits (Spade, Heart, Diamond and Club). Therefore the event Q of drawing 5 queens does not exist in the sample space Ω. Therefore probability P(Q) of drawing 5 queens is zero.

maths
I think we are missing information here. AB=AD, and ∠BAD=90° mean that BD is a diameter, and hence ∠BCD=90°. Also, AB=AD means that ∠ABD=∠ADB=45°. However, we do not know anything about ∠DBC or ∠BDC, just that they are complementary. So &Del...

Math
Assuming nobody shares the medals, 8 choices for the gold, 7 choices for the silver, 6 choices for the bronze. Use the multiplication rule.

Math
Use same method as the runners.

Math
1 inch = 25.4 mm (exactly) so 1/16" = (1/16)*25.4 = 1.5875 mm Can you round to the nearest 0.1 mm?

math
((x-12)÷ 7) + 23 = 32

math
Let the number be x. Difference of his number and x = (x-12) "divide the difference of his number and 12 by 7, and then add 23, the result is 32" (x-12)\÷ 7 + 23 = 32 Can you solve for x?

Computer
If you are using Windows 7, disk management is under: Control Panel -> Administrative Tools -> computer management -> storage -> disk management.

Allegbra
Use the quadratic formula to get a=-0.01 b=0.06 c=5.9 x=(-b±sqrt(b²-4ac))/(2a) 3±sqrt(599)

algebra 1
graphing tabulation substitution elimination comparison Cramer's rule Gauss methods inversion iterations (such as Gauss-Seidel method)

algebra
1. Expand expressions 9w+3=6w-12 2. Group like terms and isolate unknown on the left 9w-6w = -12-3 3w = -15 3. Solve for unknown. ... Can you take it from here?

Math
Fencing means putting up a fence around the perimeter. For a lot of 37.5 by 24.8, the perimeter would be 2(L+W)=2(37.5+24.8) linear metres. The height of the fence is not mentioned, so the answer should be in metres in length.

math
If you notice that numbers with the required property has two pairs of factors, for example, for 12, we have 2*6, 4*3. Which means that numbers divisible by 4 are more likely to have this property. Can you find them?

math
Check: Divide (-36) by 2 to see if you get back 18.

Math
Use the Gauss method: 60+61+62...+70+71...+80 80+79+78+..+70+69...+60 Add the two lines, you will get the sum 140 21 times. So half the sum is 70*21=1470.

calculus--please help!!
Hint: by definition H(x)=(fog)(x) = f(g(x)) what would be the appropriate functions f(x) and g(x) such that f(g(x))=(3x+2)^6?

FUNCTIONS 11
t(1)=-2 t(2)=5 t(3)=-10 ... Hint: compare 2,5,10,17,26 and 1,4,9,16,25.... The sign can be achieved by multiply by the factor (-1)^n

chemistry
Hint: again, start by balancing the "H".

chem
Hint: How many "H" is on the left side, and how many are on the right?

math
Hint: Can you find g if f(x)=x^6 ?

Information Technology (2 Qs)
Hints: 1. Cache is the fastest memory (aside from registers, which is not on the list). 2. By what data go from memory to the CPU and vice-versa? Does a human have access directly to the memory?

Math
Approximate a year to 50 weeks, with 12 miles each week, it would be 600 miles a year. 624 is within 10% of 600 miles, so it is reasonable that they job 624 miles a year.

statistics
There are 52 cards in a deck. There are 26 red suits, and 2 black kings for a total of 28 cards which are either red or a king. Can you find the probability?

math
4x^2-81 can be written as (2x)^2-9^2, then apply the identity a^2-b^2=(a+b)(a-b) to factorize the expression.

Math
The area of a square is the square of one side. So the length of a side is the square-root of the area, i.e. Side = sqrt(64x^2)=8sqrt(x^2)=8x.

design of rc structure
What kind of help do you need? Is the water tank in RC? Most water tanks in North America are in steel and supported over steel columns, which also gives resilliance when subject to earthquakes. 200kL is basically 200 m³. It could be a cylinder of 6.5m diameter by 6m high....

Probability
The problem satisfies the following conditions: -the experiment is a Bernoulli experiment (i.e. each trial has one of two outcomes) - the probability of each trial is known remains constant throughout the experiment - each trial is independent of the others. This indicates a b...

design of rc structure
Here are some ideas to investigate and comment. Working stress is generally more conservative. It does not take into account of the post-yield behaviour of the reinforcing steel. Ultimate stress caters to both strenth and serviceability requirements separately. If properly des...

Probability
I assume that each of the sixteen events has two outcomes of S, namely P(s1,s1), P(s1,s2).....P(s4,s4). By the multiplication rule, and assuming that the two outcomes are independent, we have P(s1,s1)=P(s1)P(s1)=0.5*0.5;=0.25 .... P(s4,s4)=P(s4)P(s4)=0.125*0.125=0.015625 Note:...

math
1. The closest is J, which should read (M-6)/3 2. a=b-2, then b-a=2 what should be (b-a)^4?

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