Friday

January 30, 2015

January 30, 2015

Total # Posts: 28,784

**Calculus 1**

I drew a circle and placed the woman at point A. She wants to go to point B, clearly where AB is a diameter. Label the centre as O. Pick a point P on the circle so that she will row from A to P, and then walk along the circumference from P to B I labeled AP = x and arc PB as a...
*December 13, 2014*

**Algebra**

from the 2nd: 4x = 20 - 3y x = 5 - (3/4)y plug into the 1st: 5x - 7y = -18 5(5 - (3/4)y) - 7y = -18 25 - 15y/4 - 7y = -18 -43y/4 = -43 y = -43(-4/43) = 4 x = 5 - (3/4)4 = 2 (substitution would have been my last choice in the methods to solve this, I would have used elimination)
*December 13, 2014*

**AP CaLC. AB**

Here is a solution to your problem, with sides 6 and 12 I suggest you print out the solution and change the constants to yours. I suggest you are careful that your base of x, and height of y are consistent with the x and y in the solution https://www.math.ucdavis.edu/~kouba/...
*December 13, 2014*

**AP CaLC. AB**

Where do x and y enter the picture ??
*December 13, 2014*

**Algebra**

strange question, clearly 9x^2 - 12x + 4 = 49 (3x - 2)^2 = 49 3x - 2 = ± 7 3x = 2 ± 7 3x = 9 or 3x = -5 x = 3 or x = -5/3 so I guess they just wanted the 2nd line .
*December 13, 2014*

**math**

This implies that either 4, 5 or all 6 will pass prob = C(6,4) (.6)^4 (.4)^2 + C(6,5) (.6)^5 (.4) + C(6,6) .6^6 I get .54432
*December 13, 2014*

**math**

arggh, go with Damon's factoring of the last part Whatever made me think that 2x5 = 16 ?????? It's clearly 2 x 8
*December 13, 2014*

**math**

your expression definitely needs brackets to make sense (n^2-4)/(n^2-2n) * n/(n^2+10n+16) = (n+2)(n-2)/(n(n-2) ) * n( (n+2)(n+5) = 1/(n+5) , n ≠ -2 , 0, 2 , -5
*December 13, 2014*

**math**

another way: find the intersection line of the two planes add the two equations, 4x -3y = 10 y = (4x-10)/3 pick any "nice" value of x let x = 1, y = -2 in the 2nd equation: 3 + 2 + z = 4 , z = --1 --> point (1,-2,-1) let x = 10, y = 10, in the 2nd 30 - 10 + z = 4...
*December 13, 2014*

**math**

year 1 = 19000 year 2 = 19000(1.04) year 3 = 19000(1.04)^2 .. year 10 = 19000(1.04)^9 I somehow expect that "they" want you to add them up. It would be a GS, with a = 19000, r = 1.04 , n = 10 BUT, from an actuarial point of few monies cannot just be added up unless ...
*December 13, 2014*

**Algebra 1**

y = |x-2| why not just take some simple values of x and see what points you get, then plot them 0,2 1,1 2,0 3,1 4,2 ... -1,3 -2,4 -3,5 .. can you see the pattern ?
*December 13, 2014*

**Algebra**

t2 = a + d = 2 t9 = a + 8d = 30 subtract them 7x = 28 d = 4 in a+d=2 a + 4 = 2 a = -2 t15 = a + 14d = -2 + 14(4) = 54
*December 13, 2014*

**#4 easy geometry**

x-17 + 24-x + 3x-40 + x+1 = 42 4x = 74 x = 18.5 , so the sides are 1.5 , 5.5, 15.5 , and 19.5 how about doubling each side, creating a "similar" quadrilateral, (angles won't change) 3 , 11 , 31 , and 39 , mmmh, what do you know about sides of a parallelogram ? #5...
*December 13, 2014*

**easy geometry**

1. In a rhombus, the diagonals bisect each other at right angles. So you have 4 congruent right-angled triangles with sides 5 and 12, and the hypotenuse is the side of the rhombus. s^2 = 5^2 + 12^2 (You should recognize that Pythagorean triple, if not, remember it) Find the ...
*December 13, 2014*

**Probability**

To get a plain cookie: we could have (1,P) or (2,P) prob (1, P)= (1/2)((30/40) = 3/8 prob (2,P) = (1/2)(20/40) = 1/4 prob(plain cookie) = 3/8 + 1/4 = 5/8 (checking: prob(1,C) = (1/2)(10/40) = 1/8 prob(2,C) = (1/2)(20/40) = 1/4 note 3/8+1/4+1/8+1/= 1 , check! ) could have ...
*December 12, 2014*

**Math**

PV = 5 e^-.03 + 5 e^-.06 + ... + 5 e^-(10(.03)) I see a GS with a = 5 e^-.03 r = e^-.03 n = 10 PV = a(r^n - 1)/(r-1) 5 e^-.03( e^-.3 - 1)/(e^-.03 - 1) = appr 43.85 million dollars
*December 12, 2014*

**College math 100**

white ribbons --- x blues ---------- x-2 reds ----------- x+3 form the equation and continue
*December 12, 2014*

**Math**

5 Σ 4(3/4)^k k=0 = 4(3/4)^0 + 4(3/4)^1 + 4(3/4)^2 + 4(3/4)^3 + 4(3/4)^4 + 4(3/4)^5 = 4[ 1 + (3/4) + (3/4)^2 + (3/4)^3 + (3/4)^4 + (3/4)^5 ] The part in the brackets is a GS with a = 1 , r = 3/4 and n = 6 = 4 ( 1( (3/4)^6 - 1)/(3/4 - 1) =4 (729/4096 - 1)/(-1/4) = -16(-3367...
*December 12, 2014*

**Math**

no 1/2 * 6 + 9^2 - (18/6) = 3 + 81 - 3 = 81
*December 11, 2014*

**math**

In a true scale , the units of the terms are the same, and thus the units would cancel 8 cm : 1000 m = 8 cm : 100000 cm = 1 : 12500 behold the beauty and simplicity of the metric system Had this been 1000 yards and 8 inches, it would be a lot messier.
*December 11, 2014*

**algebra**

Where did you get a kitten to weigh 1.5 kg ?? 4x+4x= 10 8x=10 x = 1.25 kg so each kitten weighs 1.25 kg and the cat weighs 4x or 4(1.25) = 5 kg check: does the cat weigh 4 times as much as a kitten what is 4(1.25) ? = 5, check! what is the total weight of the 4 kitten and the ...
*December 11, 2014*

**algebra**

kitten --- x kg cat ------4x kg 4(x) + 4x = 10 take over
*December 11, 2014*

**math**

It asked for the ratio which cannot just be one number. Ratios express the relationship between 2 or more items so 180:20 = 9 : 1
*December 11, 2014*

**math**

3000 ??? Are you just guessing wildly ??? what is 180 : 20 ?
*December 11, 2014*

**Geometry**

make a sketch. You will be able to construct similar triangles. Remember that for two similar triangles, corresponding sides are in the same ratio
*December 11, 2014*

**Math**

see http://www.jiskha.com/display.cgi?id=1418350095
*December 11, 2014*

**Calculus**

take the derivative using the product rule f ' (x) = x(3)(1-2x)^2 (-2) + (1-2x)^3 sub in the x of the point(1,-1) f ' (1) = 1(3)(1)(-2) + (-1) = -7 which will be the slope of your tangent Now you have the slope of -7 and a point (1,-1) Use your favourite method of ...
*December 11, 2014*

**Math**

(-3) - (-8) = -3+8 = +5 to add to negatives will always yield a negative. could you have two debts, add them up and suddenly have a profit ???
*December 11, 2014*

**Math**

Let two of the sides be x ft each let the other two sides by y ft each xy = 310 y = 310/x cost = 3(2x) + 3y + 14y = 6x + 17y = 6x + 17(310/x) = 6x + 5270/x d(cost)/dx = 6 - 5270/x^2 =0 for a min of cost 6 = 5270/x^2 6x^2 = 5270 x^2 = 878.333.. x = √878.333 = appr 29.64 ...
*December 11, 2014*

**Math**

No, you cannot just add two sums of money if they are not in the same time slot, unless you totally ignore the compound interest. amount = 1000( 1.07^10 - 1)/.07 * (1.05)^8 + 1000( 1.05^8 - 1)/.05 = $29,962.30 You must be able to analyse my equation and it should make sense to...
*December 11, 2014*

**4th**

could be 1,8 2,7 3,6 4,5 5,4 6,3 7,2 8,1 prob(1,8) = (1/10)(1/10) = 1/100 each of the remaining cases has the same prob so prob = 8(1/100) = 8/100 = 2/25
*December 11, 2014*

**Math-Calculus**

For hours ??? Slope of the given line is 1/2 so the slope of the line through (-2,1) and perpendicular to it must be -2 equation of that perp. y = -2x + b, with (-2,1) lying on it, thus ... 1 = -2(-2) + b -3 = b y = -2x - 3 solve the two equations to get the required point -2x...
*December 11, 2014*

**Precalculus**

Profit = Revenue - Cost subtract the two functions and simplify you will have a quadratic with a negative x^2 term, so it opens down, thus there will be a max find the vertex of that parabola
*December 11, 2014*

**Maths**

tan18° = 55/x take over
*December 11, 2014*

**Precalculus**

the y-intercept is 4, so the height is 4 the x-intercept is 4/3, so the base is 4/3 area = (1/2)base x height = (1/2)(4)(4/3) = 8/3 square units
*December 11, 2014*

**Precalculus**

let side parallel to river be y let the other two sides be x each 2x + y = 1000 , ----> y = 1000-2x area = xy = x(1000-2x) = 1000x - 2x^2 if you know Calculus..... d(area)/dx = 1000 - 4x = 0 for a max of area 4x =1000 x = 250 y = 1000-2(250) = 500 so max area = xy = 250(500...
*December 11, 2014*

**Algebra !**

a + (b/100)a = 12 a( 1 + b/100) = 12 a - (b/100)a = 8 a( 1 - b/100) = 8 divide the top equation by the last one (1+b/100)/( 1 - b/100) = 12/8 = 3/2 2 + 2b/100 = 3 - 3b/100 times 100 200 + 2b = 300 - 3b 5b = 100 b = 20 back in a(1-b/100) = 8 a(1 - 20/100) = 8 a(1 - 1/5) = 8 a(4...
*December 11, 2014*

**Math**

If I were you , I would go with Ms Sue's answer of 5/16 since often lawyers don't tell the truth. btw, Ms Sue's last line is 16/16 - 11/16 = 5/16
*December 11, 2014*

**algebra**

short side ---- x each of other sides (must be isosceles) ---- 3x x + 3x + 3x = 112 I will let you finish it
*December 11, 2014*

**algebra**

v = -6000t + 70000
*December 11, 2014*

**Algebra 1 Ohio 8th grade standards**

since in the form y = mx + b, the slope of the line is m so for your line y = (1/2)x + 1, the slope is 1/2 But for perpendicuar lines, their slopes are opposite reciprocals of each other, so the slope of your new line must be -2/1 or -2 and the new equation must be y = -2x + b...
*December 11, 2014*

**Math**

"How much must they deposit NOW" isn't that present ? PV = 5500( 1 - 1.02^-20)/.02 = $89932.88
*December 11, 2014*

**math**

let the number of boys be 7x and the number of girls be 4x 7x - 4x = 21 3x = 21 x = 7 so there are 49 boys and 28 girls for a total of 77
*December 11, 2014*

**algebra**

so you have 2 ordered pairs of the type (brownies, cost) , (2000,1500) , (4000, 2000) slope = (2000-1500)/(4000-2000) = 500/2000 = 1/4 using the 2nd point, ... cost - 2000 = (1/4)(brownies - 4000) 4 C - 8000 = B - 4000 B - 4C = -4000 (checking if 1st point satisfies ... LS = ...
*December 11, 2014*

**Precal**

Assuming exponential decay amount = a e^(kt) where a is the initial amount, and t is number of years .8 = 1 e^(250k( ln .8 = ln e^(250k) ln .8 = 250k k = ln.8/250 after 600 years ? amount = 1 e^(600ln.8/250) = .5853 or appr 58.5% for half-life ? .5 = e^(ln.8 t/250) ln.5 = ln.8...
*December 11, 2014*

**Math**

7r + -5 = 7r - 5
*December 11, 2014*

**math**

normal rate: adult --- 14 child ---- 8 for holiday: adult -- 28 child -- 5/4(8) = 10 The rest of your post is quite confusing. What part of December is a school holiday in Malaysia?
*December 11, 2014*

**math**

How about this ? (5/6 - 2/3 + x)/3 = 1/4 1/6 + x = 3/4 x = 3/4 - 1/6 = 7/12 I agree with Damon, the wording is rather ambiguous.
*December 11, 2014*

**Sixth Grade Math**

you want the ratio of L : W to remain at 8 : 5 so 42/W = 8/5 8W = 210 W = 210/8 = 26.25 check: 42/26.25 = 1.6 = 8/5 Of course the ratio could have been expressed in more than one way, but whichever way you choose, the cross-product has to end up as 8W = 210 Looking over your ...
*December 11, 2014*

**Math**

Oh well, that changes everything. Notice that your lines do not line up as you intended, that is a fault of this format. If the bar is above the .63 then clearly that is your answer
*December 11, 2014*

**Math**

7/11 = .36363636... , the 36 repeats Those are poor choices for answers. First of all A and B are the same answer, rounded to one decimal would be .4 rounded to two decimals would be .64 rounded to three decimals wold be .636 so none of the choices are correct.
*December 11, 2014*

**algebra2**

so the hypotenuse of your right-angled triangle is 102 (ignoring the slack in the line) let the height be h sin 54.9° = h/102 h = 102sin54.9° = ...
*December 10, 2014*

**calculus**

limit ( √(x^2 + 7) - 4)/( √(x^2 - 8) - 1) , as x --> 3 my first step always is to actually sub in the approach value, sure enough, I get 0/0 That means the "eventually" my expression should factor. multiply top and bottom by (√(x^2 - 8) + 1) I ...
*December 10, 2014*

**Math**

let the length of the large rectangle be y let each of the parallel divider sides be x so we have 4x + 2y = 940 2x + y =470 y = 470 - 2x Area of whole field = xy = x(470-2x) = 470x - 2x^2 d(Area)/dx = 470 - 4x = 0 for a max of Area 4x = 470 x = 117.5 then y = 235 and the ...
*December 10, 2014*

**Ap calc**

let the distance run by the running player be x from the line of scrimmage. Let the distance between them be d In my diagram, I have a right-angles triangle with fixed side of 30, the other side (x+2.5) and the hypotenuse d, so that d^2 = (x+2.5)^2 + 30^2 2d dd/dt = 2(x+2.5) ...
*December 10, 2014*

**math**

first part is simply 40 choose 5 = C(40,5) = 658008 b) The leader can be picked in 8 ways, and then we have to choose 4 more from 39 = 8 C(39,4) = 658008 Are you surprised that the answers are the same ?
*December 10, 2014*

**math**

225+75+200-50+125 + x = 895
*December 10, 2014*

**D J HIGH SCHOOL SOST GOJAL PAKISTANmaths trignometry**

Did you make a diagram ? On mine I labeled the top of the observation point A and its bottom as B The farter boat as P and the closer boat as Q So we have two right-angled triangles with the angle at P as 30° and the angle at Q as 45° in triangle AQB , tan 45° = ...
*December 10, 2014*

**Calculus**

amount at the beginning = 5000 amount after 20 years = 5000 e^(.04(20)) = 11127.70 evaluated the "average value" as defined in your text book or notes. I don't know how it was defined for your course.
*December 10, 2014*

**Math**

Question is not clear. How is the interest rate compounded? When are payments made? What is that payment?
*December 9, 2014*

**Math**

f ' (x) = 3x^2 + 12 which is clearly positive for any value of x you give me. So, yes, you are correct
*December 9, 2014*

**CAL**

Why do you keep switching names ? As you can see from the previous replies there is a max at x = 1 form 0 to 3 for x = 1 y = 3 - 25 + 60 + 1 = 39 so the max is (1,39) the graph I gave you confirms this
*December 9, 2014*

**Derivative Test**

I did most of this in the previous post Here is a picture of your graph http://www.wolframalpha.com/input/?i=plot+y+%3D+3x%5E5+%E2%80%93+25x%5E3+%2B+60x+%2B+1
*December 9, 2014*

**Math**

no, points consist of ordered pairs of two numbers. ±1 and ±2 are the x's of the points. I told you what to do with those x's above, please read it.
*December 9, 2014*

**Math**

I am sure you meant: y = 3x^5 - 25x^3 + 60x + 1 dy/dx = 15x^4 - 75x^2 + 60 = 0 for your critical values 3x^4 - 15x^2 + 12 = 0 x^4 - 5x^2 + 4 = 0 (x^2 - 1)(x^2 - 4) = 0 x^2 = 1 or x^2 = 4 x = ± 1 OR x = ± 2 sub in those values of x in the original to get the ...
*December 9, 2014*

**7th grade math**

why are you repeating the questions? btw , the very last one is correct
*December 9, 2014*

**7th grade math**

#1 - correct , all you had to do is multipy 1 1/4 by 3 , sinc 9 helpings = 3 x 3servings #2 5 cm <----> 1500 ft 1 cm < ----> 500 ft, that is a scale #3, no need to convert, if you use the same units in each fraction 2.5/4.25 = 50/x 2.5x = 212.5 x = 212.5/2.5 = 85 ...
*December 9, 2014*

**Trigonometry**

Does this help ? http://www.wolframalpha.com/input/?i=plot+y%3D3cos%282x%29+%2C+y%3D-4sin%284x%29
*December 9, 2014*

**math**

by proper subsets I assume we would exclude the empty set So with the empty set there were 256 subsets for n elements, the number of subsets is 2^n 2^n = 256 but 256 = 2^8 so n = 8 and there were 8 elements in the set
*December 9, 2014*

**MATH HELP ASAP!**

Time = Interest/(principal x rate) = 550/(1000(.05) = 550/50 = 11 yup, its 11
*December 9, 2014*

**Pre-Algebra can you please help?!**

interest from simple interest = 400(.045)(3) = 54 interest fromt he compound account = 450(1.032)^3 - 450 = 44.60 total interest = 54 + 44.60 = 98.60 , which is D
*December 9, 2014*

**Math**

i = .05004/12 = .00417 n = 25(12) = 300 let the monthly payment be p p(1 - 1.00417^-300 )/.00417 = 292649 the monthly payment is $ 1711.48
*December 9, 2014*

**math**

I entered your date into this wonderful website http://davidmlane.com/hyperstat/z_table.html and got 21.19 %
*December 9, 2014*

**Math**

you are given 2 ordered pairs (5 , 1050) and (9,900) slope = (900 - 1050)/(9-5) = - 150/4 = - 75/2 N = (-75/2)C + b using (5,1050) 1050 = (-75/2)(5) + b 1050 + 375/2 = b b = 2475/2 N = (-75/2)C + 2475/2 or N = -37.5C + 1237.5 where N is the number sold and C is the price of ...
*December 9, 2014*

**math**

Don't know if they teach you algebra where you are. Think of the points being split into 9 parts, where Alan would get 2 parts, Gil would get 3 parts and Debbie 4 parts So for her 2 parts deb got 114400/4 = 28600 per part so the total number of points = 9(28600) = 257400 ...
*December 9, 2014*

**Math**

so treat your data as two ordered pairs (0,97000) and (6,109000) Just like in a normal x-y equation, slope = (109000-97000)/(6-0) = 12000/6 = 2000 using (0, 97000) , which would be the y-intercept y = 2000x + 97000
*December 9, 2014*

**Math**

g(x) = 15x + 9 - 9-12 = 3(5x+3) - 21 = 3 f(x) - 21 or g(x) = 15x + 15 - 15 - 12 = 5(3x +3) - 15 - 12 = 5 f(x) - 27
*December 9, 2014*

**Algebra**

I don't blame you for being lost, since the question is poorly worded. Since they started off my talking about linear equations, I had assumed that all the given points lie on the same straight line. But they do not. anyway... suppose we take the first two points (5,1) and...
*December 9, 2014*

**Euler's method help in Calculus?????**

This is tedious work I found an excellent youtube for you where they solve a problem very similar to yours. I assume your text or your notes contain the basic original formula for Euler's Method I suggest you pause the video at critical points and make the necessary ...
*December 9, 2014*

**math**

Let Sam's age 7 years ago be s let Tom's age 7 years ago be t So s+7 + t+7 = 27 s+t = 13 ---> t = 13-s "seven years ago, tomas was three years more than one-fourth as old as sam" --- t = (1/4)s + 3 13-s = (1/4)s + 3 times 4 52 - 4s = s + 12 -5s = -40 s = 8...
*December 9, 2014*

**Math**

how about 130 and 121 ? I would not count those starting with 0 e.g. 031 is a 2 digit number
*December 8, 2014*

**Math**

Larry , you are right and observant to catch my error. So just make the necessary changes here is a neat trick to make an inverse answer is correct (which I did not do) pick any "nice" x value and find y e.g. x = 0 y = (9-0)/(0-9) = -1 now put that into the inverse ...
*December 8, 2014*

**Math**

let y = (9-8x) / (10x-9) for the inverse, interchange the x and y variables ---> x = (9-8y)/(10y-9) 10xy - 9x = 9 - 8y 10xy - 8y = 9+9x y(10x - 8) = 9+9x y = (9+9x)/(10x - 8) f^-1 (x) = (9x+9)/(10x-8)
*December 8, 2014*

**General Calculus Question**

No, notice the highest powers are NOT the same, so my explanation is not valid. as x --> inf √(x^2 - 2x) ---> x e.g. pick x = 1000000 and use your calculator to see so the numerator ---> 3x^2 the denominator ----> x so the limit is inf.
*December 8, 2014*

**General Calculus Question**

did you mean something like lim (4x^2 -2√x)/(3x^2 + 5√2x) of course it could only approach + inf , or else the root terms would be undefined. Other than that, the same rule applies the limit would be 4/3
*December 8, 2014*

**General Calculus Question**

as x ---> inf and the top and bottom have the same highest power, then those terms will determine the limit See my answer to a similar question by James at 11:06
*December 8, 2014*

**Math**

divide top and bottom by x^2 to get lim (7/x + 6)/(7 + 6/x) as x ---> inf both 7/x and 6/x ---> 0 so we are left with (0 + 6)/(7 + 6) = 6/7
*December 8, 2014*

**Math**

use your rules of logs logx + logx + logx = 3 log (x)(x)(x) = 3 log x^3 = 3 3logx = 3 logx = 1 or x = 10^1 = 10 check: What is log1010 ? isn't it 1 ?
*December 8, 2014*

**math**

you want your ball to be #7 AND black There is only one such ball prob (black and #7 ) = 1/10
*December 8, 2014*

**APCalculus**

lets look at your graph first of all http://www.wolframalpha.com/input/?i=plot+y%3D2sin%28x%29-cos%5E2%28x%29 clearly no vertical or horizontal asymptotes you had that, your y-intercept is correct symmetry: about each vertical line passing through a max or a min I disagree ...
*December 8, 2014*

**Math (Simplifying Fraction)**

= ( 1/x + 4/x^2) / (1 - 16/x^2) multiply top and bottom by x^2 = ( 1/x + 4/x^2) / (1 - 16/x^2) * (x^2/x^2) Since I am multiplying by 1, I am not changing the value of my fraction , simply its appearance = (x+4)/(x^2 - 16) = (x+4)/( (x+4)(x-4) ) = 1/(x-4) , x ≠ -4 (or ...
*December 8, 2014*

**APCalculus**

taking your typing at face value the way you typed it your domain is correct as a matter of fact: "I got some: domain: (-infinity, infinity) y-intercept: y=4 Vertical asymptotes: none Horizontal asymptotes: none Symmetry: y-axis F'(x): 2/3x^3-4x Critical numbers: x=0...
*December 8, 2014*

**Math**

you were right to factor it, but your second part is totally bogus I also think you placed brackets in the wrong place, probably should have been: 6/(x^2+5x+6) + 9/(x+3) = 6/( (x+2)(x+3) ) + 9/(x+3) we now need a common denominator which is (x+2)(x+3) = 6/((x+2)(x+3)) + 9(x+2...
*December 8, 2014*

**math**

ones digit --- x tens digit ---- 2x thousands --- 4x hundreds -----y x+2x + 4x + y = 19 y = 19-7x but x and y must be single digit positive integers. let x = 1, then y = 12 , not possible let x = 2, then y = 5 The number is 8542 let x = 3, then y = 19-21 = negative, no good ...
*December 8, 2014*

**Math**

(x-(1/x))/(1-(1/x)) = ( (x^2 - 1)/x) / ( (x-1)/x) = ( (x-1)(x+1)/x ) * (x/(x-1)) = (x-1)(x+1)/(x-1) = x+1 , x ≠0,1
*December 8, 2014*

**math**

I assume you mean: 25 = (748/7)^x take log of both sides log25 = log(748/7)^x = x log(748/7) = x(log748 - log7) x = log25/(log748-log7) get out your calculator and push some buttons I got appr .689
*December 8, 2014*

**Math**

1. cos^-1(sin(π/2) we know sin π/2 = 1 so cos^-1 (sin π/2) = cos^-1 (1) = 0 (because cos 0 = 1 ) 2. this one is easy, since arccos is the same as cos^-1 the answer is obviously 7π/2 However, they might just want a reduced answer since cos 7π/2 = cos 3...
*December 8, 2014*

**math**

Let the cost of John's 4 pencils and 3 erasers be x then the cost of Smith's 8 pencils and 6 erasers is 2x , notice twice as many cost of Smiths 3 pens --- y cost of John's 6 pens ---- 2y , notice twice as many pens Johns cost = 2y + x Smith's cost = y + 2x y...
*December 8, 2014*

**Calculus**

First we have to find their intersection to establish the boundaries. x^2 - 6 = 12 - x^2 2x^2 = 18 x^2 = 9 x = ± 3 so we have a closed region from -3 to +3 the height of the region for that domain = 12-x^2 - (x^2 - 6) = 18 - 2x^2 area = [integral] (18-2x^2)dx from -3 to...
*December 7, 2014*

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