Tuesday

July 29, 2014

July 29, 2014

Total # Posts: 26,897

**algebra**

welcome

**algebra**

multiply each term by 2x(x+1) 6x - 2(x+1) = x(x+1) 6x - 2x - 2 = x^2 + x x^2 +3x + 2 = 0 (x-1)(x-3) = 0 x = 1 or x = 3

**Calculus1**

it would be a combination of the chain rule and the product rule, doing it as a single power the way I did it was easier as a product rule - chain rule for that term ..... x√x = x x^(1/2) derivative: x (1/2) x^(-1/2) + (1)x^(1/2) = x/(2√x) + √x = x/(2√x...

**Calculus1**

yes, of course, silly me, the exponent on the last one was 3/2

**Calculus1**

I would rewrite as h(x) = 3x^(1/2) - x^(3/2) h ' (x) = (3/2) x^(-1/2) - (2/3) x^(1/2) = 3/(2√x) - (2/3) √x

**Algebra**

it will hit the ground when the height h(t) = 0 -16t^2 + 144 = 0 16t^2 = 144 t^2 = 144/16 = 9 so t =√9 = 3 after 3 seconds

**Pre calculus**

welcome

**Pre calculus**

PS-3PQ = (-10,4) - 3(2,5) = (-10,4) + (-6,-15) = (-16,-11) magnitude is √((-16)^2 + (-11)^2) = √377

**Algebra**

since you want the height horizontally from the starting height, and that height was 5.4 metres, -.06x^2 + 9.6x + 5.4 = 5.4 the 5.4 drops out, so x(-.06x + 9.6) = 0 x = 0 , the starting time or x = 9.6/.06 = 160 it will land after 160 m

**Geometry**

let the chord AB = 2x then the diameter = 2x+2 or the radius = x+1 This allows me to draw a right-angled triangle with sides x and 9 and hypotenuse x+1 (x+1)^2 = x^2 + 9^2 x^2 + 2x + 1 = x^2 + 81 2x = 80 x = 40 AB = 80 check: diameter = 82 is 41^2 = 40^2 + 9^2 ? LS = 1681 RS =...

**Algebra II**

rowing speed in still water ---- x mph speed of current ------------- 2 mph time to go 50 miles with the current = 50/(x+2) time to go 25 miles against current = 25/(x-2) the two times are the same, so ... 50/(x+2) = 25/(x-2) 50x - 100 = 25x + 50 25x = 150 x = 6 speed in still...

**slope**

y = 3x - 7 straight line with slope of 3 and y-intercept of -7 http://www.wolframalpha.com/input/?i=y+%3D+3x+-+7

**Pre-calc**

What are we doing with this hyperbola ?

**Math help**

look back at your previous post of this

**Math**

let the slant height of one side be h then using (1.2)base x height 1980 = (1/2)(35.4)h h = 3960/(35.4) = 111.8644 = appr 111.86 m this can't be. According to the given dimensions on the webpage, the base is about 35 by 35 and the height is 21.6 m, for a slant height of 27...

**calculus**

let the two equal width be x let the single side by y xy = 600 y = 600/x cost = 20y + 30x = 20(600/x) + 30x d(cost)/dx = -12000/x^2 + 30 = 0 for a min of cost 30 = 12000/x^2 x^2 = 400 x = 20 the two equal sides are 20 yds each, and the long side is 600/20 = 30 yds.

**Word problem**

the x of the vertex is -b/(2a) = -184/(-32) = 5.75 seconds plug that into the function h(5.75) = 16(5.75^2) + 184(5.75) + 20 = 549 ft

**Finance**

monthly rate = .041/12 = .00341666.. let the effective annual rate be i 1 + i = (1 + .00341666..)^12 1+i = 1.0417783 i = .0417783 or appr 4.18%

**PRE CALC**

using the standard notation: term(20) = a + 19d = 27 and a = -11 -11 + 19d = 27 19d = 38 d = 2 the common difference is 2 check: term(2) = a+19d =-11 + 19(2) = -11+38 = 27

**calculus**

I see that C(1990) is given as 271.9 What are you asking?

**Equations**

did it, look back

**trig**

after 1 hours, one ship has gone 25 km, the other 15 km make a sketch, let the distance between them be x straigh-forward case of the cosine law x^2 = 25^2 + 15^2 - 2(25)(15)cos 60° = .... you do the arithmetic. (I got appr 21.8 km)

**Algebra Question~!**

To be a factor, the division has to be exact, that is, the remainder must be zero works that way with numbers, works that way in algebra.

**Calculus Help Please!!! Check**

looks like you are using Newton's Formula for Cooling properly.

**Derivatives**

write it as: G(t) = 5200 (1+12e^(-.52t)^-1 G ' (t) = -5200(1+12e^(-.52t) )^-2 (-.52)(12)e^(-.52t) = + 32448 e^(-.52t) / (1+12e^(-.52t) )^2 I got a positive instead of your negative.

**kaylah - math**

kaylah, you can't draw a triangle with 2 sides parallel !!

**math**

Can you draw a 4-sided figure with 2 lines parallel ?

**Equation help 2 questions**

You state the equation as a function, so to speak of real number solutions makes no sense. There are an infinite number of solutions, any ordered pair satisfying the equation would be one. You probably want the solution to -4x^2 + 7x - 8 = 0 in both cases, it depends on the va...

**Math**

t(1) = 1/3 t(n) = 3term(n-1) , n>1

**Calculus Help**

I can add more rats!! last step: dx/dt = -6( csc^2 (π/3)) (-π/3) = -6((4/3)(-π/3) = 24π/9 km/min = 8π/3 km/min (which is Steve's answer)

**Calculus Help**

At a time of t min after the plane passed over the tracking telescope, let the horizontal distance be x km Let the angle of elevation be Ø Make a sketch, I get cot Ø = x/6 x = 6cotØ dx/dt = -6 csc^2 Ø dØ/dt when Ø = π/3 and d&Osla...

**Calculus Help Please!!!**

given : dr/dt = 40 cm/s A = πr^2 dA/dt = 2π r dr/dt case 1: when s = 1, r = 40 dA/dt = 2π(40)(40) = 3200π cm^2/sec case 2: when s = 3, r = 3(4) = 120 cm dA/dt = 2π(120)(40) = 9600π cm^2/sec case 3: ... your turn .....

**math**

multiples of 5 and 8 from 1 to 110 : either 40 or 80 so prob of your event = 2/100 = 1/50

**algebra 2**

subtract them : 30y^2 - 96x = 192 5y^2 = 32 + 16x back into the first: 16x^2 - (32+16x) = 64 16x^2 -16x - 96 = 0 x^2 - x - 6 = 0 (x-3)(x+2) = 0 x = 3 or x = -2 if x = 3, 5y^2 = 32+48 = 80 y^2 = 16 y = ± 4 if x = -2 5y^2 = 32-32 = 0 y = 0 so we have 3 points: (-2,0) , (3...

**Math**

ignore the 2nd part of my answer to the above, the numbers don't even match. I cut and pasted from a previous solution but the numbers were not even the same Also note that even though 263 is a solution, it is one of an infinite number. But it said to find "a number&q...

**Math**

look up "Chinese Remainder Theorem" and you will find many pages for this kind of problem You will have to know how to do arithmetic in "modular arithmetic" , and this forum is not suitable to teach you that. I just worked out the above problem using that m...

**Equation help**

you must have a typo, since all your terms are positive. Your rock will continue to rise higher and higher. I was expecting the square term to be negative. so I will assume that -.04x^2 + 1.3x + 56 = 0 (y is zero when it hits the ground) times -100 4x^2 - 130x - 5600 = 0 x = (...

**math**

number of boys --- 2x number of girls --- 5x after 12 new boys number of boys = 2x+12 girls , still 5x (2x+12)/(5x) = 4/9 18x + 108 = 20x 108 = 2x x = 54 So now the number of boys = 2x+12 = 108+12 = 120

**math**

your data just has to be entered here http://davidmlane.com/hyperstat/z_table.html

**Math**

forgot the link http://www.jiskha.com/display.cgi?id=1329034595

**Math**

looks like yours, just input 20 instead of the 60

**Algebra II**

number from A ---- x number from Bx+6000 solve for x: .04x + .03(x+6000) = 880

**Math**

did it here .... http://www.jiskha.com/display.cgi?id=1396401662 give your posts a bit of time. You reposted this with only about 20 minutes in between. If tutors are online they may be answering somebody else's question while yours is waiting.

**Combinations Algebra Readiness**

you should know these w definitions nCr = n!/( r!(n-r)! ) nPr = n!/(n-r)! 6C3 = 6!/(3!3!) = 20 6P4 = 6!/2! = 360 On most scientific calculators both of these functions are built-in on mine they are found below the 5 - key and the 6-key to do 6C3 enter 6 2ndF 5 3 = to get 20 Ho...

**Algebra**

√(y+3) - 4 = 5 what about it? are we solving for y? √(y+3) = 9 square both sides y+3 = 81 y = 78 test it.

**Math!!!**

4/100 = x/80 100x = 320 x = 3.20 or take .2($4) = $ .80 after discount, cost = $ 4.00 - .80 = $3.20

**Calculus Help Please!!!**

done http://www.jiskha.com/display.cgi?id=1396400942 are you switching names???

**Calculus Help Please!!!**

Use the product rule to get f ' (t) = -(t^2 - 32)/√(64-t^2) = 0 for a local max/min t^2 = 32 t = ±4√2 f(±4√2) = 0 f(-1) = -1√63 f(8) = 8(√0) = 0 there you go, you got your f(t)'s what do you think? Here is your graph, notice ...

**MATH UGH WORD PROBLEM**

capacity of tank = π r^2 h = π(100^2)(40) = 400000π number of gallons = 7.5(400000π) = appr .....

**Calculus Help!**

see http://www.jiskha.com/display.cgi?id=1396388805

**not - trigonometry**

Why are you calling this trig ? assuming his first deposit is NOW end of 1st year: 1000(1.06) + 1000 = 2060 end of 2nd year: 2060(1.06) + 1000 = 3183.60 ... end of 5th year: .......... = 6637.09 fill in the rest using your calculator

**algebra**

first one: add them, 2y = 6 y = 3 sub into the 2nd: (could have used the 1st, makes no difference) 2x - 3 = 1 2x = 4 x = 2 so x=2, y=3 do the 2nd one by adding them, follow my example

**math..help again**

look back at your previous post of this same question

**Math- urgent**

1st number --- x 2nd number --- y "The second of two numbers is five more than the twice first." ---> y = 2x+5 "the sum of the numbers is 44" ---> x+y = 44 x+y = 44 x + (2x+5) = 44 x + 2x + 5 = 44 3x = 39 x = 13 1st is 13, 2nd is 31 check: is 31 five ...

**Math**

area of whole thing is 120x60 = 7200 ft^2 so half of that is 3600 ft^2 make a sketch showing the first run area of 1st run = 120x4 + 120x4 + 52x4 + 52x4 = 1376 leaving 2224 make a sketch of the remaining rectangle which is 112 by 52 area of 2nd run = 112x4+112x4+48x4+48x4 = 12...

**Math**

ummmhhh, how many sides does a hexagon have ?

**trig**

I assume you want the distance traveled along the hypotenuse, d, then sin30° = 5000/d d = 5000/sin30 d = ... if you want the horizontal distance traveled , x tan30 = 5000/x x = 5000/tan30 = ...

**Urgent Calc Help!!! Thanks!**

f ' (x) = x( xe^((−x^2)/98)(-2x/98) + e^((−x^2)/98) = e^((−x^2)/98) ( -x^2/49) + 1) = 0 for a max/min -x^2/49 +1 = 0 x^2 = 49 x = ± 7 evaluate f(7) f(-7) f(-6) f(14) and determine which is the largest and which is the smallest

**Calculus**

f ' (t) = -8sin t + 2(4 cos t) = -8sint + 8cost = 0 for a max/min 8sint = 8cost sint/cost = 1 tant = 1 t = 45° or 225° or t = π/4 , t = 5π/4 -->(outside our domain) so evaluate f(0) f(π/4) f(π/2) and determine which is the largest and which i...

**Calculus Help Please!!!**

so it the same way you were just given in your previous post. Let us know what you got

**Calculus Help Please!!!**

looks like we both messed up in the f(x) calculations should be f(4) = 2(64) - 3(16) - 72(4) + 7 = -201 f(-3) = 2(-27) - 3(9) - 72(-3)+7 = 142 end-values: f(-4) = 2(-64) - 3(16)( - 72(-4) + 7 = 119 f(5) = 2(125) - 3(25) - 72(5) + 7 = -178

**Calculus Help Please!!!**

f ' (x) = 6x^2 - 6x - 72 = 0 for a local max/min x^2 - x - 12 = 0 (x-4)(x+3) = 0 x = 4, or x = -3 f(4) = 2(64) - 3(16) - 72(4) + 7 = -201 f(-3) = 2(-27) - 3(9) - 72(-3)+7 = 115 end-values: f(-4) = 2(-64) - 2(16)( - 72(-4) + 7 = 135 f(5) = 2(125) - 3(25) - 72(5) + 7 = -178 ...

**math**

I gave it to you ... instead of y I have "cost" instead of x I have "n" y = mx + b <-----> cost = (1/10)n + 5

**math**

I will assume that your given ordered pair (10,6) is of the type (number , cost), then cost - 6 = (1/10)(number -10) cost = (1/10) number -1 + 6 cost = (1/10)n + 5 so if n = 25 cost = (1/10)(25) + 5 = 7.5 units of cost (you gave no units)

**calculus and vectors**

Add the 2 equations ... 6x + y = 6 y = 6-6x let x = 0 , y = 6 2(0) + 4(6) + z = 5 --> z = -19) we have a point (0,6,-19) on the line of intersection let x = 1, y = 0 2(1) + 4(0) + z = 5 --> z = 3 and (1,0,3) is another point on that line So a direction vector of that lin...

**Algebra II**

just plug in your value: 24.2 = √(19.6 h) √h = 24.2/√19.6 h = (24.2/√19.6)^2 = 29.88 m or I know from physics that h = 4.905 t^2 gives you the height from which an object was dropped after t seconds , and v = 9.81 t gives you the velocity after t second...

**maths geometry**

let the distance of the shorter chord to the centre be x x^2 + 15^2 = 25^2 x^ = 400 , x = 20 let the distance between the longer chord and the centre by y y^2 + 24^2 = 25^2 y^2 = 49 , y = 7 so x+y = 27 the chords are 27 cm apart

**Algebra**

the way you typed it would be r = (2√5) L or did you mean r = 2√(5L) major difference between the 2 formulas, please clarify.

**math**

let the 3 numbers be a , b, and c, in order of size, c is the largest a+b+c = 36 c = 2a b = (a+c)/2 = (a+2a)/2 = 3a/3 back into the first a+b+c = 36 a + 3a/2 + 2a = 36 times 2 2a + 3a + 4a = 72 9a = 72 a = 8, then c = 16, and b = 12 Our 3 numbers are 8, 12, and 16 (all informa...

**Math**

your answeres are correct so far. for the increasing/decreasing part, find dy/dx I got (-c((ax+b) + a(cx+d))/(cx+d)^2 = (ad - bc)/(cx + d)^2 since the denominator is always ≥ 0 we only have to look at the top for the function to increase , dy/dx > 0 ad - bc > 0 for...

**Algebra 1**

Didn't know baskets were worth 4 point, did you mean 2 or 3 points? I will assume that. number of 2-pointers ---x number of 3-pointers --- 9 2x + 3(9-x) = 22 2x + 27 - 3x = 22 x = 5 so 5 two-pointers and 4 three-pointers check" 5(2) + 4(3) = 22

**math**

Same structure as the one I just did for you. Try it, let me know what you got.

**math**

amount(1.03)^5 = 5(125000) I got $ 539,130.49

**statistics**

plug in your data here .... http://davidmlane.com/hyperstat/z_table.html to get .4013

**Math**

prob(spade facecard, then king) = (3/52)(4/52) = 3/676

**math**

3sin = 1.2 sinØ = .4 (set your calculator to RAD) Ø = .41152 or π-.41152 which is 2.73008 but you wanted from 0 to 4π so add a period , or 2π, to each of the above answers Ø = .41152 , 2.73008 , .6947, and 9.01326

**trig**

I drew a circle, and a vertical radius of 12 m In 40 s, it rotates 360°, so in 5 sec it rotated 45° let the vertical position from the centre be y cos45 = y/12 y = 8.485 m so he is 12-8.85 or appr 3.5 m high after 5 seconds

**Math**

just translate the English into Math, 4x - 6 = 2x + 4 then solve for x

**Algebra**

y-5 = -5x + 10 5x + y = 15

**math**

We will need to find the sides angle P = 180 - 60 - 75 = 45° let PQ=x , QR = y , PR = z x/sin75 = y/sin45 = z/sin60 let's assign an arbitrary value of y = 1 to our smallest side using x/sin75 = 1/sin45 we get x = .1.366025 using 1/sin45 = z/sin60 z = 1.224745 so sum of...

**Math**

ways to choose 5 of the 6 multiple choices = C(9,5) = 126 number of ways to choose 2 of the 6 essay questions = C(6,2) = 15 number of ways to answer the test = 126x15 or 1890 ways

**Finance**

I have now answered 2 of these kind of questions for you. Exactly where are you finding difficulties with these? Do you know the 4 basic formulas we have to use for these ?

**Finance**

PV = 10000(1 - 1.08)^-10)/.08 + 20000(1 - 1.08^-30)/.08 (1.08)^-10 = 171391.45 or pretend you are gettting 20,000 for 40 years - the 10,000 for the first 10 years = 20000(1 - 1.08^-40)/.08 - 10000(1 - 1.08^-10)/.08 = 171391.45

**Finance**

150000 =PAY( 1 - 1.07^-20)/.07 solving for PAY, I got $ 14,158.94 Balance owing after 7 years = 150000(1.07)^7 - 14158.94( 1.07^7 - 1)/.07 = $ 118.335.46

**math**

I will assume you meant: log3 (2x + 5) = 1 then 2x+5 = 3^1 2x = -2 x = -1 If otherwise, let me know

**survey math 140**

Number of ways to select 5 of 19 is C(19,5) = 19!/(5!14!) = 11628 most calculators have that function built-in look for something like nCr

**algebra**

James, I gave you a detailed solution yesterday for the same question on the assumption that your symbol was supposed to be ≥ You later told me that it was to be ≤ So why don't you just switch all the conditions e.g. all the domain that worked before, now will ...

**Math**

I am guessing that P(number < 2) is supposed to mean probability that the number is less than 2 What number ???? Are you tossing a die ? confirm

**calcules**

let base be x by x let the height be y x^2 y = 8 y = 8/x^2 SA = base + 4 sides = x^2 + 4xy = x^2 + 4(8/x^2) = x^2 + 32/x d(SA)/dx = 2x - 32/x^2 = 0 for a minimum of SA 2x = 32/x^2 2x^3 = 32 x^3 = 16 x = cuberoot(16) = appr 2.52 then y = 1.26 the base is 2.52 by 2.52 and the he...

**Algebra 2**

same idea as before, factor first, then divide, restrict what you divided by Again, I am putting in the brackets, they are extremely important here h(x)=(x^2-9)/(x^2-4x+3) = (x+3)(x-3)/(x-1)(x-3)) = (x+3)/(x-1) , x ≠ 3

**Algebra 2**

I have a feeling you meant: (49X^6+7X^7)/(28X^8) take out a common factor = 7x^6( 7 + x)/(28x^8) now divide = (7+x)/(4x^2) now we divided top and bottom by a variable. If that variable is zero, we just divided by zero, which is a mathematical no-no. so we have to state a restr...

**algebra**

I have a strong feeling you meant (x-4)(x+2)/( (x-3)(x+5) ) ≥ 0 I good and fast way is to look at the graph of y = (x-4)( (x+2)/(x-3)(x+5) ) http://www.wolframalpha.com/input/?i=y+%3D+%28x-4%29%28x%2B2%29%2F%28%28x-3%29%28x%2B5%29%29 It shows the graph to be above the x-...

**Geometry**

You are missing one of the dimensions of the floor, its length Once you have that, Cost = 105 ( 33 * 1/2 * ??)/27 units of money where ?? in your length we divide by 27 since there are 27 cubic feet in 1 cubic yard If the concrete is sold in whole cubic yards, you will have to...

**ALGEBRA**

the t of the vertex of your parabola is -b/(2a) = -20/-32 = 5/8 at t = 5/8 h = -16(25/64)+20(5/8) + 6 = 12.25 nope!

**math**

avg rate of change = (23500 - 8750)/(8 = ...

**Math**

treat it as two ordered pairs (t, c) where t is temperature and c is consumption so we have (90,220) and (76, 178) slope = (220-178)(/(90-76) = 42/14 = 3 so: c-220 = 3(t-90) c = 3t - 270+220 c = 3t - 50 check: if t = 90, c = 270-50 = 220 if t = 76, c = 228 - 50 = 178

**Math**

no, 26x^2 ≠ x√26 Whatever made you think so. let x = 4 26(4^2) = 26*16 = 416 xV26 = 4√26 = appr 20.4 is 416 = 20.4 ???? However, you could write 26x^ as (x√26)^2

**Math**

Imagine "opening up" a cylinder, what would you get? 2 equal circles + a rectangle whose length is the circumference of the circle and whose height is the height of the cylinder. so SA = 2π(6^2) + 2π(6)(20) = 72π + 240π = 312π = appr 980 No w...

**Math**

I assume you pick a card, then throw the die primes from 1-10 : 2,3,5,7 , so 4 of them primes on a die: 2 3 5, so 3 of them prob(2 primes) = (4/10)(3/6) = 1/5 prob(not 2 primes) = 4/5 odds in favour of getting two primes = (1/5) : (4/5 = 1 : 4

**2nd question - math help!!**

(x+y)^2-x-y = (x+y)^2 - (x+y) = (x+y)(x + y - 1)

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