Wednesday

January 28, 2015

January 28, 2015

Total # Posts: 28,761

**Calculus**

change y = 2^x to ln y = x ln2 now take derivative: dy/dx / y = ln 2 dy/dx = y ln2 = ln2 (2^x)
*September 28, 2014*

**math**

number of children --- c number of adults ---- 155-c 5.3c + 8.7(155-c) = 1137.7 5.3c + 1348.5 - 8.7c = 1137.7 -3.4c = -210.8 c = 62 So 62 children tickets were sold on Friday
*September 28, 2014*

**algebra 1 question**

you can't just write things down . I hope nobody showed you how to solve equations that way. remember, "whatever you do to one side of the equation you must do to the other 3/2 x - 4 = 16 Add 4 to both sides 3/2 x = 20 multiply both sides by 2 3x = 40 now divide both ...
*September 28, 2014*

**Math quick question!**

12a^2-5a-2m^2 = (3a -2m)(4a + m) If we add 1 m to the end of each length and width area of garden including path = (3a-2m+2)(4a+m+2) So area of path = (3a-2m+2)(4a+m+2) - (3a -2m)(4a + m) I will let you do the expanding and simplifying sub in a = 6 into your answer for the ...
*September 28, 2014*

**pre algebra**

let the radius be r 2πr = 16π r = 8 so the height is 4 inches and the radius is 8 inches. SA = 2 circles + a rectangle = 2πr^2 + 2πrh = 2π(8)^2 + 2π(8)(4) = ....
*September 28, 2014*

**Calculus Maxima/Minima**

Let the time passed since the truck went through the intersection be t seconds Make a diagram Let the distance between them be D ft I see that D^2 = (40t)^2 + (120-30t)^2 = 1600t^2 + 14400 - 720t + 900t^2 = 2500t^2 - 7200t + 14400 2D dD/dt = 5000t -7200 but at a minimum of D...
*September 28, 2014*

**trigo**

use cos 2A = 1 - sin^2 A or cos t = 1 - 2sin^2 (t/2) 2sin^2 (t/2) = 1 - 1/3 = 2/3 sin^2 (t/2) = 1/3 sin (t/2) = 1/√3 , since you want quadrant I, we use only the positive result
*September 28, 2014*

**trigo**

after doing what ?
*September 28, 2014*

**Math Homework**

1. keep in mind that both f(x) and g(x) would be undefined for x=0 so even though g/f = (1/x) / (1/x^2) = x the final function would still be undefined (actually it would be indeterminate) for x = 0 so the domain is : set of all real numbers, x ≠ 0
*September 28, 2014*

**Pre-Calculus**

How did you get -3 ? (f-g)(x) = 4 - (2x-1) = 4 - 2x + 1 = -2x + 5
*September 28, 2014*

**Pre-Calculus**

if f(x) = 2x-5 and g(x) = 4 then (f-g)(x) = 2x-5 - 4 = 2x - 9 Do #2 in the same way
*September 28, 2014*

**geometry**

Don't you just have a nice right-angled triangle? You should recognize 5-12-13 as one of the common ones with integer lengths, if not AC^2 = 5^2 + 12^2 = 169 AC = √169 = 13
*September 28, 2014*

**Fractions**

1. area of each piece = 8.5(11) = 93.5 inches^2 2. no definite answer since we don't know the dimensions of the larger piece. e.g. it could be 20 by 50, or 25 by 40 , or 16 by 62.5, or .....
*September 28, 2014*

**math**

Using the simple interest formula I = PRT 6 = 100(R)(2/52) R = 6(52)/200 = 1.56 or 156 % per year (in the Middle Ages, they would have been burned at the stake for usury)
*September 28, 2014*

**math**

let the side of the smaller square be x let the side of the larger square be y 4x/4y = 1/5 x/y = 1/5 y = 5x area of larger = 250 y^2 = 250 y = √250 = 5√10 then 5x = 5√10 x = √10 perimeter = 4x + 4y = 4√10 + 20√10 = 24√10 or appr 75.9 m
*September 28, 2014*

**Geometry**

This is a more difficult problem than it first appears. Here is a complete solution to your problem using a radius of 10 Change the appropriate numbers to suit your solution http://www.analyzemath.com/Geometry/circles_problems.html
*September 28, 2014*

**Pre-Calc**

f(x) = 3x^2 + 2x + 4 whatever replaces x, replace it in the algebraic expression f(♠) = 3♠^2 + 2♠ + 4 f(☂) = 3☂^2 + 2☂ + 4 f(2) = 3(2)^2 + 2(2) + 4 = 20 follow the same pattern: f(a+h) = 3(a+h)^2 + 2(a+h) + 4 = 3(a^2 + 2ah + h^2) + 2a + 2h...
*September 27, 2014*

**quanta tive skills and reasoning**

N(math) + N(psych) - N(math AND psych) = N(math OR psych) 140+85-65 = N(math OR psych) = 160 (the 250 did not enter the picture unless you want to note that 90 took neither math nor psych )
*September 27, 2014*

**Math plz help.**

1, correct 2. correct 3. F 4. B 5. A 6. C
*September 27, 2014*

**Algebra**

number of ounces of $1 stuff --- x 4(40) + 1(x) = 2.2(40+x) solve for x, you should get x = 60
*September 27, 2014*

**Pre-Calc**

Wow , that would be overkill, but anyway .... first of all , it is very difficult to write it in matrix form in this format, so you would have the matrix 3 2 2-4 multiplied by the column matrix x y = 14 4 I will assume you know how to find the inverse of a 2by2 matrix, and how...
*September 27, 2014*

**Pre-Calc**

I would double the first then add that to the 2nd to get 8x = 32 x =4 sub into the first: 12 + 2y = 14 2y = 2 y = 1 x=4, y =1 check by subbing those values into both equations, they should work
*September 27, 2014*

**Calculus**

the whole problem becomes trivial when you realize that (0,0) does not lie on y = lnx If you recall your properties and definition of logs, you know that we can only take logs of positive numbers, that is, ln (0) is undefined. Your method is correct until you come to the point...
*September 27, 2014*

**Math. I have a question.**

2l+2w=800 l+w=400 so he can build an infinite number of such rectangles as long as the length + width = 400 e.g. 1 by 399 2 by 398 3 by 397 ... .1 by 399.9 .01 by 399.99 etc if you allow sides with non-integer values.
*September 27, 2014*

**algebra**

shortest side --- x each of the other sides --- 3x x + 3x + 3x = 126 7x = 126 carry on ....
*September 26, 2014*

**algebra**

amount of $8 coffee --- x amount of $ 4 coffee -- 60-x 8x + 4(60-x) = 5.25(60) 8x + 240 - 4x = 315 4x = 75 x = 18.75 lbs
*September 26, 2014*

**Trigonometry**

8% = 8/100 = .08 so tanØ = .08 Ø = 4.57 = 4.6° to the nearest tenth
*September 26, 2014*

**math**

You don't define what your x is, so your equation makes no sense to me. The left side of your equation has units of distance, while your right side is speed, thus it is gibberish. If x is the time needed the distance covered by the slower car = 15 + 50x the distance ...
*September 25, 2014*

**Math URGENT QUICK QUESTION**

9-6x-3x^2 notice the common factor of -3 = -3(x^2 + 2x - 3) = -3(x + 3)(x - 1) x^2 - 8x + k If we have 1x^2 at the front, then the sum of the roots equal the coefficients of the middle term, and the product of the constants. so x^2 - 8x +7 ?? two numbers that have a sum of -8 ...
*September 25, 2014*

**calculus 1**

According to your answer of a positive dy/dt, the laddder would be sliding UP the wall. Since the ladder is sliding away from the wall along he ground, dx/dt should be +4 ft/sec which would make dy/dt = -3 ft/sec, showing that y is decreasing, thus sliding DOWN the wall as ...
*September 25, 2014*

**algebra**

let the distance be x nautical miles x/12 + x/10 = 8.8 times 60 5x + 6x = 528 x = 48 n miles. check: one way = 48/12 = 4 hrs other way = 48/10 = 4.8 , for a total of 8.8 hrs
*September 25, 2014*

**Calculus I**

A function is even if f(-a) = f(a) a function is odd if f(-a) = -f(a) f(a) = a^3(a^3) + a^3 = a^3(a^3 + 1) f(-a) = -(a^3)(a^3) - a^3 = - (a^3)(a^3 + 1) notice that abs(a^3) is always positive So what do you think? You might try it with numbers, e.g. f(2) = 8(8) + 8 = 72 f(-2...
*September 23, 2014*

**Algebra**

Let the amount of the 4.50 coffee be x lbs 7.5(20) + 4.5x = 5(20+x) solve for x
*September 22, 2014*

**math**

questions in 2nd test --- x so 48/x = (1/2)(24/25) 48/x = 24/50 24x = 2400 x = 100 There were 100 problems check: 1st test = 24/25 = 96% 2nd test = 48/100 = 48% , which is 1/2 of 96%
*September 18, 2014*

**Algebra 2**

use brackets please (x/4 - 4/x) / (1 - 4/x) = (x/4 - 4/x) / (1 - 4/x) * (4x)/(4x) , actually multiply by 1 =(x^2 - 16)/(4x-16) = (x+4)(x-4)/(4(x-4)) = (x+4)/4 , x ≠ 4
*September 18, 2014*

**Algebra 2**

(5√7)/(√6) = (5√7)/(√6) * √6/√6 = 5√42/6 A good idea is to check your answer with your calculator evaluate the original, then evaluate your simplified answer, you MUST get the same answer.
*September 18, 2014*

**math**

let the original fraction be a/b equation #1: (a - 3)/b = 1/2 b = 2a - 6 equation #2: (a+5)/(b+7) = 3/4 4a + 20 = 3b + 21 4a - 3b = 1 sub in #1 4a - 3(2a-6) = 1 4a-6a+18 = 1 -2a = -17 a = 17/2 b = 2(17/2)-6 = 11 our fraction is (17/2)/11 = 17/22 When we check with 17/22, we ...
*September 18, 2014*

**science/math**

your numeral answer is correct (actually -7/3) As I noted in an earlier post, since it asks for the skater's "acceleration" and he slows down to a stop , your answer should be expressed as a negative so a = -2.3
*September 18, 2014*

**science/math**

I get 2.571 , which would be 2.6 correct to one decimal place
*September 18, 2014*

**science/math**

correct, assuming the runner starts from rest your answer should be in m/s^2
*September 18, 2014*

**science/math**

your of acceleration should be 8 m/s^2 your answer is correct
*September 18, 2014*

**Math**

did you mean y = -.25x + 5 ? several ways to do this, here is a way that is simple to understand Let's take two points on the line x = 0, y = 5 ---> (0,5) x = 4, y = 4 ---> (4,4) when we reflect across the x-axis, the x values stays the same, but the way values ...
*September 18, 2014*

**science/math**

Here is my mathematical approach physics has nice formulas for this v = at + c when t = 0, v = 25 so 25 = 0+c c = 25 then v = at + 25 when t = 10 , v = 6 6 = 10a + 25 10a = -19 a = -1.9 Whenever you see the word deceleration (things slow down) you can expect a negative result...
*September 18, 2014*

**Algebra1**

divide by -3 |2x+6| = 4 so 2x+6 = 4 OR -2x -6 = 4 ---> 2x = -2 , x = -1 or ---> -2x = 10 , x = -5
*September 17, 2014*

**math**

speed of plane --- x speed of wind ---- y 3927/(x+y ) = 7 ---> 7x + 7y = 3927 3437/(x-y) = 7 ----> 7x - 7y = 3437 add them 14x = 7364 x = 526 then but subbing in x - 526 into either equation y = 34
*September 17, 2014*

**Analytic Geometry**

divide by 9 x^2/(1/9) + y^2 = 1 a^2 = 1/9, a = ±1/3 b = ±1 so we have an ellipse with the major axis as the y-axis vertices: on x-axis ( 1/3,0) , (-1/3 , 0) on y-axis (0,1) , (0,-1) foci: c^2 + (1/3)^2 = 1^1 c^2 = 1-1/9 = 8/9 c= ± (2√2)/3 this will ...
*September 17, 2014*

**Linear Algebra**

t1(1,1) + t2(1,-1) = (13,-12) (t1,t1) + (t2,-t2) = (13,-12) (t1+t2 , t1 -t2) = (12, -12) so t1+t2 = 13 t1-t2 = -12 add them 2t1 = 1 t1 = 1/2 subtract them 2t2 = 25 t2 = 25/2 b) using he results of above replace 13 with x1 and -12 with x2 and repeat my steps
*September 17, 2014*

**Algebra 1**

4x^2 - 1 It is essential that you recognize and memorize the difference of squares pattern for your factoring skills
*September 17, 2014*

**math**

let the shortest be x inches let the longest piece be x+39 let the other piece be (1/2)(x+39) x + x+39 + (1/2)(x+39) = 132 don't like fractions, so multiply everybody be 2 2x + 2x + 78 + x+39 = 264 5x = 147 x = 29.4 inches shortest is 29.4 inches longest is 68.4 inches ...
*September 17, 2014*

**Pre-Calculus**

3 strikes ... 1. slope AB = (2-0)/(-2-3) = -2/5 slope CD = (4+1)/(-1+3) = 5/2 So perpendicular 2. slope AB = (1+3)/(1-4) = -4/3 slope CD = (1+3)/(2-5) = -4/3 so parallel 3. slope EG = (2-0)/(-3-2) = -2/5 so slope of perpendicular is 5/2 Looks like somebody has some serious ...
*September 14, 2014*

**ccs trigo**

info missing
*September 14, 2014*

**Math**

looks like Damon lost about $10,000 interest should have been $9,998.80
*September 13, 2014*

**maths**

I disagree with your reasoning. I read it that she spent 2/5 of her pocket money on a necklace so she spent 6 on a necklace So far she has spent 5 + 6 or 11 leaving her with £ 4 or 1/3 + 2/5 = 11/15 leaving 4/15 (4/15)(15) = 4
*September 13, 2014*

**Math**

looks like y = x^3 for x < 0 , y = -x^3 for x ≥ 0 to me
*September 12, 2014*

**Pre-Calculus**

I agree with your choices
*September 12, 2014*

**Algebra 3-4**

time of burn of 2nd stage = x seconds time of burn of 1st stage = x+28 x + x+28=152 2x = 124 x = 62 2nd stage takes 62 seconds 1st stage is x+28 = 62+28 = 96 sec
*September 12, 2014*

**Algebra**

Sam, did you not see Steve's reply? why not try some values? e.g. let a = 4, b = 5 then 2ab= 2(4)(5) = 40 a^2 + b^2 = 16 + 25 = 41 so what do you think?
*September 12, 2014*

**Algebra**

let's assume that the silo will be totally filled including the hemisphere. radius of cylinder and hemisphere is 15 let the height up to the hemisphere be h ft πr^2 h + (1/2) (4/3)πr^3 = volume π(15)^2 h + (2/3)π (15)^3 = 10800 225πh + 2250π...
*September 12, 2014*

**College Algebra**

rate of current --- x mph let the distance each way by y miles so upstream distance: y = (24/60)(5-x) downstream distance y = (16/60)(5+x) but they are both equal to y, so 24(5-x)/60 = 16(5+x)/60 times 60 24(5-x) = 16(5+x) 120 - 24x = 80 + 16x -40x = -40 x = 1 So the current ...
*September 12, 2014*

**Algebra 1**

amount of 10% solution ---- x L amount of 60% solution ---- 200-x L .1x + .6(200-x) = .5(200) times 10 x + 6(200-x) = 5(200) x + 1200 - 6x = 1000 -5x = -200 x = 40 check: .1(40) + .6(160) = 4+96 = 100 which is 50% of 200L
*September 12, 2014*

**math**

2=1(1+.127/2)^2t , where t is half-years (2t is years) 2 = (1+.127/2)^2t log2=log (1+.127/2)^2t by the rules of logs ... log2=2t log(1+.127/2) 2t = log2/log(1.0635) 2t = 11.26 So it would take about 11 1/4 years or 11 years and 3 months
*September 11, 2014*

**math**

The amount of salt stays the same .20(110-x) = .12x times 100 20(110-x) = 12x 2200 - 20x = 12x 2200 = 32x x = 68.75
*September 11, 2014*

**math**

distance to island --- n miles x/11 + x/10 = 4.2 times 110 10x + 11x = 462 x = 22 nautical miles
*September 11, 2014*

**math**

I suspect a typo
*September 11, 2014*

**math**

done, look for your other post
*September 11, 2014*

**math**

done, look for you other post
*September 11, 2014*

**Trig**

Make your sketch, label the person nearest the obelisk as A and the person's position as B Top of obelisk as P and its bottom as Q. Look at triangle PAB angle B = 44 angle PAB = 180-65 = 115 then angle APB = 21 by the sine law: AP/sin44 = 25/sin21 AP = 25sin44/sin21 In the...
*September 10, 2014*

**math**

400 m in 1min, 32 sec = 92 seconds so 100 m in 92/4 or 23 seconds you did not specify what rate we are talking about m/s or s/m or ...
*September 10, 2014*

**Math**

Using trig: let the speed be x km/h after making your diagram, x^2 = 10^2+3^2 - 2(10)(3)cos 135° = 151.426... x = 12.3 km/h angle: using the sine law: sinØ/3 =sin135/12.3055 sinØ = .17238... Ø = 9.9266.. direction angle would be S (45-9.93)° E ...
*September 10, 2014*

**Math Problem (please help)**

rate = 8.12/115.99 = .070006035 but since the $8.12 was most likely rounded off to the nearest cent, I would say it was .07 or 7% so y = .07x so when x = 530.50 y = .07(530.50) = $37.14
*September 10, 2014*

**Math!**

mmmhhh, let's see if 2 hours make sense. to go another 2 hours at 55 mph, would take you another 110 miles, but you already went 275, so you went 110 + 275 or 385 miles. Looks like you stood up your friend. Why not just solve the simple equation given??? 55h + 275 = 440 ...
*September 9, 2014*

**Math**

2[4(9-7)+1]/3 = 2[4(2)+1]/3 = 2[8+1]/3 = 2[9]/3 = 18/3 = 6
*September 9, 2014*

**Math Problem (please help)**

I = kA when A = 4250, then I = 106.25 106.25 = k(4250) k = 106.25/4250 = .025 I = .025A
*September 9, 2014*

**Math - Finding the Equation**

(g∘f)(x) = g(f(x) ) = g(x+2) = -(x+2)^2 + 2(x+2) - 3 = -x^2 - 4x - 4 + 2x + 4 - 3 = -x^2 - 2x - 3 (g∘f)(-2) = -4 + 4 - 3 = -3 or f(x) = x+2 f(-2) = -2+2 = 0 then g(f(-2)) = g(0) = -0+0-3 = -3
*September 9, 2014*

**7th grade math**

let x be that fraction a/b so (5/6)/x = 1/4 then by cross-multiplying x = 4(5/6) = 20/6 = 10/3 so your fraction a/b = 10/3 check: (5/6) ÷ (10/3) = (5/6)(3/10) = 15/60 = 1/4 My answer is correct You should always check your answer in similar ways if possible
*September 9, 2014*

**Math Problem (please help)**

A fraction can only be zero if its numerator is zero so x^3 - 64 = 0 difference of cube factoring .... (x-4)(x^2 + 4x + 16) = 0 x = 4 or x = (-4 ± √(16- 64) )/2 x = 4 or x = -2 ± 4√3 i so the graph should cross the x-axis only once, at x = 4 ...
*September 9, 2014*

**Math**

1 p(1.045)^20 = 30000 p = 30000/1.045^20 = 12439.29 2. same method as #1 3. amount = 100(.5)^(15/25) = 65.98 g
*September 9, 2014*

**math help**

odd numbers differ be 2 let the first of the odd numbers be x then the next two odds are x+2, and x+4 x + x+2 + x+4 = 435 3x = 429 x = 143 so the largest is x+4 = 143+4 = 147
*September 9, 2014*

**Math**

so you want 40+39+38+...+1 or 1+2+3+...+39+40 a = 1, d = 1 for n=40 sum(40) = (40/2)(first + last) = 20(1+40) = 820
*September 9, 2014*

**Math**

total distance fallen = 16t^2 , where t is in seconds after 1 second --- 16(1)^2 = 16 after 2 seconds --- 16(2^2) = 48 after 3 seconds --- 16(3^2) = 144 Where did you get your data from, it certainly is not from this earth. But .... ignoring the silliness of your data, you ...
*September 9, 2014*

**Algebra**

In all 3 questions you are using the same formula term(n) = a + (n-1)d 1. term(101) = x-y + 100(2x+y-3) = x-y+200x + 100y - 300 = 201x + 100y - 300 2. a=2 , d=4 2 + (n-1)(4) = 106 4n-4 = 104 4n = 108 n = 27 It is the 27th term 3. give this one a try yourself
*September 9, 2014*

**Math**

x^3 , when x = -3 = (-3)^3 = -27 btw, you meant to say "How would I write this ? "
*September 9, 2014*

**Math**

Ms Sue answered this a while back http://www.jiskha.com/display.cgi?id=1409874255
*September 9, 2014*

**algebra**

.6L + .2(200-L) = .5(200) solve for L
*September 9, 2014*

**math**

width --- x length --- 4x - 4 2x + 2(4x-4) = 62 solve for x
*September 9, 2014*

**MATH word prob!**

let the amount to be added be x gal .7x + .23(30) = .6(30+x) times 100 70x + 23(30) = 60(30+x) 70x + 690 = 1800 + 60x 10x = 1110 x = 111 gallons
*September 9, 2014*

**Math - Equation of the circle**

the centre must be the midpoint of the diameter which would give you (1, -4) so the equation must be (x-1)^2 + (y+4)^2 = r^2 sub in one of the points on the circle , I will use (-3,6) (-4)^2 + (10)^2 = r^2 r^2 = 16+100= 116 so (x-1)^2 + (y+4)^2 = 116 check by subbing in the ...
*September 9, 2014*

**Algebra**

r = (1/27) ÷ (1/81) = 3 so the series diverges, that is, the terms are getting larger. Think about adding terms that keep getting larger. Clearly the sum will get larger and larger and eventually become infinitely large. That is why for the formula Sum (infinite number ...
*September 9, 2014*

**Algebra**

correct
*September 9, 2014*

**Algebra**

Just looked at the first of the "Related questions" below, which I had answered in June, and realized that your _____ , meant that -243 was actually the second term I am pretty sure you can make the suitable adjustments. (your first term will be -260)
*September 9, 2014*

**Algebra**

a = -243 d = -226 - (-243) = 17 term(67) = a + 66d = -243 + 66(17) = 879 sum(n) = (n/2)(2a + (n-1)d) sum (27) = (27/2)(-486 + 26(17)) = -594 Here is a nice new part to the question: For which terms does the sequence switch from negative to positive ?
*September 9, 2014*

**Algebra**

strange question. since she uses 8 cups of water for 15 plants, each plant will get 8/15 cups of water. Where does the $35 water bill enter the picture ???
*September 9, 2014*

**Math**

1. correct in interval notation in standard notation: -7 < x < 7 - when written in this notation, the word "and" is used 2. |x| ≥ 7 x ≥ 7 OR -x ≥ 7 x ≥ 7 or x ≤ -7 so yes, you are correct ( I don't like the way you showed your ...
*September 9, 2014*

**math**

amount of weaker solution --- x L amount of stronger solution -- (600-x) solve for x .025x + .1(600-x) = .05(600)
*September 8, 2014*

**MATH HELP**

ummhhh loads after day 1 = 46-8 = 38 loads after day 2 = 38-8 = 36 ....
*September 8, 2014*

**math**

Preliminary decision: In the first equation, both terms are positive, so to get zero as a sum , one must be + , the other - That rules out #1 and #2. Try subbing in the other pairs.
*September 8, 2014*

**algerbra**

done, look at your other post of this same problem
*September 8, 2014*

**Calculus**

You did not say where your difficuly lies. Can you find the integral or do you already have that ?
*September 8, 2014*

**Calculus**

so area = integral (x^2 - mx + 1) dx from 0 to 5 = x^3 /3 - (m/2)x^2 + x from 0 to 5 = (125/3 - 25m/2 + 5) - (0-0+0) but this equals 11.3024 times 6 250 - 75m + 30 = 67.8144 -75m = -212.1856 m = 2.8291
*September 7, 2014*

**math**

expand first 4(2g + 104) - 96 = 504 + 6(g - 14) 8g + 416 - 96 = 504 + 6g - 84 collect like terms and simplify 8g + 320 = 6g + 420 terms on one side, constants on the other side 8g - 6g = 420 -320 2g = 100 g = 50
*September 7, 2014*

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