loan at 2.8% --- $ x loan at 4.5 % ---- $ 31000-x solve for x .... .028x + .045(31000-x = 1024.40 times 1000 28x + 45(31000-x) = 1024400 etc
Just noticed a typo (sticking 3 key) <taking the first 3 I got: a = 5.5 , b=-12.5 , c = 12> should say: taking the first 3 I got: a = 53.5 , b=-12.5 , c = 12 btw , I did not show how I solved those 3 equations in 3 unknowns, I used a webpage for that http://www.1728.org/...
I did the usual analysis and found the first differences to be 145, 250, 358, and 465 and the second differences to be 105, 108, and 107 which appear to be relatively constant at appr 106, so I suspect a quadratic. let N = ad^2 + bd + c, where d is the number of days, and N is...
So the punch contained 1 gal of fruit juice and 1 gal of ginger ale, for a total of 2 gallons percentage of fruitjuice = 1/2 * 100% = 50% I have no clue how they get 25%, did you check the wording of the problem?
66 2/3 of 39 = (200/3)(39) = 7800/3 = 2600
If you have consecutive values of x, like in both your cases, in general if the first differences in the y's are constant, you have a linear function if the 2nd differences in the y's are constant, you have a quadratic function, (as your case above) if the 3rd differen...
I took first differences and got 2.8 , 8.4 , 14, and 19.6 second differences yielded: 5.6 , 5.6 , 5.6 which tells me that the relationship is a quadratic function. so let y = ax^2 + bx + c, giving us 0 = c 2.8 = a + b + c 11.2 = 4a + 2b + c we know c = 0 so if we double the 2n...
sinhx = (e^x - e^-x)/2 and coshx = (e^x + e^-x)/ , by definition. then: 5coshx + 3sinhx = 4 5(e^x + e^-x)/2 + 3(e^x - e^-x)/2 = 4 5e^x + 5e^-x + 3e^x - 3e^-x = 8 8e^x + 2e^-x = 8 times e^x 8 (e^x)^2 + 2 = 8e^x a quadratic, let a = e^x 8a^2 - 8a + 2 = 0 4a^2 - 4a + 1 = 0 (2a - ...
The correct answer to your question is: It is a quadratic equation. If you want the solution ... it factors: (3x-1)(3x + 2) = 0 x = 1/3 or x = -2/3
from sin 2x = 1/2 2x = π/6 or 2x = π-π/6 = 5π/6 x = π/12 or 5π/12 but the period of sin 2x is π so we get 2 more solutions: x = π/12 + π = 13π/12 or x = 5π/12 + π = 17π/12 in [ 0 , 2π] x = π/12 , 5π...
Math - PreCalc (12th Grade)
First of all , I am sure you meant: s(t) = 2t^2 + 3t s(2) = 2(4) + 3(2) = 14 s(4) = 2(16) + 3(4) = 44 total distance = 44-14 = 30 m total time = 4-2 seconds = 2 seconds average velocity = total distance / total time = 30 m/2 seconds = 15 m/s
Math - PreCalc (12th Grade)
very similar to http://www.jiskha.com/display.cgi?id=1395410253
Math - PreCalc (12th Grade)
Use you "sense" of numbers to see what happens to the fractions as n gets larger. (I think your last term should read 15/(3n^2) or else it becomes large as n gets large) e.g. look at 5/n suppose n = 100,000, then 5/n = .00005 , which is close to zero suppose n = 1,00...
Math and Music
Perhaps you will find it fascinating to see the relationshipe between music and the Fibonacci Numbers and the Golden Ratio ( google Fibonacci numbers to see thousands of webpages, here is probably one of the best: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fi...
interest = 2000(1.0155)^20 - 2000 = 720.37 or "appr" $ 720
Math - PreCalc (12th Grade)
spread = 5-2 = 3 if cut into n pieces, each base = 3/n endpoint of 1st rectangle = 2 + 3/n endpoint of 2nd rectangle = 2 + 2(3/n) ... endpoint of kth rectangle = 2 + k(3/n) = 2 + 3k/n f(2+3k/n) = 2(2 + 3k/n) + 1 = 5 +6k/2 I see you have two other questions above that follow th...
Steve's answer and mine seem to contradict each other, but we defined x differently. Steve defined x as his usual time, so the answer of 7.5 is correct for his usual time I defined x to be the usual speed, and got x = 2/15 so to go 1 km would take 1/(2/15) = 15/2 = 7.5 , t...
usual speed --- x km/h time at usual speed to go 1 km = 1/x hrs time at 3/4 his normal speed = 1/(3x/4) = 4/(3x) 4/(3x) - 1/x = 2.5 times 3x 4 - 3 = 7.5x 7.5x = 1 x = 1/7.5 = 2/15 km/h
r^2= 7^2 + (-3)^2 = 58 r = √58 since (7,-3) is in IV, cosØ = 3/√58 secØ = √58/3 cotØ = -7/3
Unless the x term had a coeffecient of zero, then of course you wouldn't count it, so 5a + 10b = 0 ---> a = -2b and 45/2 a^2 + 45b^2 = 90 (45/2)(4b^2 + 45b^2 = 90 90b^2 + 45b^2 = 90 135b^2 = 90 b^2 = 90/135 = 2/3 b = ±V2/√3 if b = +√2/√2 then a ...
(1+ax/2)^10 + (1+bx)^10 = (1 + 10(ax/2) + (10)(9)/2 (ax/2)^2 + ... ) + (1 + 10bx + (10)(9)/2 (bx)^2 + ...) = 2 + (5ax + 10bx) + (45/4) a^2 x^2 + 45b x^2 + .. = 2 + (5a+10b)x + (45/2 a^2 + 45b^2)x^2 + ... first term matches your given, but the 2nd only contains first degree x ,...
roughly plot the points to see that you have a rectangle of base = 30 height = 2 area = 2x30 = 60 square units
term 11 = a+10d = 8+10d term 7 = a + 6d = 8+6d (8+10d)/(8+6d) = 5/8 64 + 80d = 40 + 30d 50d = -24 d = -24/50 = -.48 check: term 11 = 8 + 10(-.48) = 3.2 term 7 = 8+6(-.48) = 5.12 5.12 : 3.2 = 512 :320 = 8 : 5
Physics question - I NEED HELP PLEASE
need rules of physics here. volume of water if trough is full = (1/2)(3)(5)(8) = 60 cubic metres from here on it is physics
boys --- 4x girls ---- 5x 4x+5x = 54 take over....
distance at 15 km/h --- x distance at 18 km/h ---- 136-x x/15 + (136-x)/18 = 8 multimply each term by 90 6x + 5(136-x) = 720 6x + 680 - 5x = 720 x = 40 distance at 15 km/h is 40 km distance at 18 km/h is 136-40 or 96 km check: 40/15 = 2 2/3 hrs 96/18 = 5 1/3 hrs , for a total ...
(1/8) of what number is 3 ?
yup! sloppiness on my part
I assume that you want the derivative, since you titles your post that way. if y = x^2cosx-2xsinx-2cosx dy/dx = (x^2)(-sinx) + 2x cosx - 2x(-cosx) - 2sinx + 2sinx = -x^2( sinx) + 4x( cosx) etc if needed
Not so fast .....
Since each flower needs 1 square foot, the flowers planted along the circumference will not have a complete square foot. To illustrate, take a grid paper, and draw a circle with radius 7. we will need x^2 + y^2 = 49 you only have to look at 1/4 of the circle and look at the nu...
y = (e^-x) (cosx)^2 (x^2 + x + 1) take ln of both sides ln y = ln e^-x + ln (cosx)^2 + ln(x^2 + x + 1) = -x + 2 ln(cosx) + ln(x^2 + x + 1) now differentiate y' / y = -1 + 2(-sinx/cosx) + (2x+1)/(x^2 + x + 1) = -1 - 2tanx + (2x+1)/(x^2 + x + 1) y' = y(-1 - 2tanx + (2x+1...
for any quadratic function f(x) = ax^2 + bx + c the x of the vertex is -b/(2a) sub that x value into the function to get the y of the vertex, so n(x) = -.3x^2 + 9x + 15 x of vertex is -9/(2(-.3)) = 15 n(15 = -.3(225) + 9(15) + 15 = 82.5 ticket sales will peak on day 15 and the...
TC = 5/9 (TF 32) TF = 9/5 TC + 32 , converts between TF and TC TF is temperature in archaic Fahrenheit, TC is temperature in Celsius I + PRT, interest = principal x rate x time for simple interest D = R x T , distance = rate x time
yes , the x-intercepts are 0 and 4, respectively confused about your second reply, the vertices are indeed (0,0) and (0,4) <<I mean 0 for -2x^2. Sorry about the 4, I didn't mean to put that. >> , don't even know what that is supposed to say. see, http://www...
You talk about equations, but show no equation. You must have meant the equations to be y = -2x^2 and y = -2x^2 + 4 You are asking for the axes of symmetry but instead state the vertices. You were correct that the vertices are (0,0) and (0,4) respectively. so the axes of symme...
Did you not notice that for every increase of 20 in the x's there is a decrease of 20 in the y's so the slope is (45-65)/(30-10) = -1 so y = -x + b using x=10, y = 65 65 = -10 + b b = 75 y = -x + 75
the formula you want is cos a + cos b= 2cos((a+b)/2) * cos((a-b)/2) so cos 5w + cos 2W = 2cos(7w/2) * cos(3W/2)
I did this one last year http://www.jiskha.com/display.cgi?id=1362104847
first even : x 2nd even : x+2 now do it like the others
Andy, I have done quite a few for you now. Give this one a try, let me know what you get.
done, look back to your earlier post of this
done , look back
we don't really need the amount at first rate: 2 = 1 e^(.05t) ln2 = .05t t = 13.86 ---> the doubling time at 2nd rate: 2 = 1 e^(.1t) you finish it.
1st number ---> x 2nd number -- > x+1 3rd number --> x+2 x+x+1+x+2 = -204 3x = -207 x = -69 largest is -67 or let the 3 numbers be (x-1) , x , (x+1) x-1 + x + x+1 = -204 3x = -204 x = -68 largest number is -68+1 = -67 notice that in my second solution, the equation wa...
what does (2/9)x = 24 sound like to you?
looks like (3/8)b = 14
The ones digit is 5 less than 10. ---> xx5 The tens digit is 2 more than the ones digit -- x75 it must be less than 200 so it is either 175 or 75
I have now answered several question for you of this type. This is the easiest of the bunch Your turn ! let me know what you got
amount = 100 (1/2)^(t/5730) b) 59 = 100 (.5)^(t/5730) .59 = .5^(t/5730) ln .59 = (t/5730) ln (.5) t/5730 = ln .59/ln .5 = .76121314 t = 4361.75 yrs
time from 1992 to 2010 = 18 years Denmark: pop = 5.2 e(18(.001)) = appr 5.29 million Chad: pop = 5.2 e(18(.025)) = 8.2 million when is 10 = 5.2 e^(.025t) 1.923077 = e^ .025t .025t = ln 1.923077 t = 26.16 years or in appr 26 years or in 2018 (in 2010 it was 12.7 million)
let t=0 correspond with the year 1850 then 1900 ---> t = 50 then 1950 ---> t = 100 population = a( e^(kt) ) , where a is the initial population and t is the number of years since 1850 23,191,876 = a e^0 a = 23,191,876 then: 62,947,714 = 23,181,876 e^(50k) 2.715384812 = e...
what is 123(81) - 492(9) + 813 ?
let's eliminate the parameter t from x = e^t lnx = t then y = (lnx)^2 - 3 to be concave up, the second derivative must be positive y' = 2(lnx)(1/x) y'' = 2lnx (-1/x^2) + (1/x)(1/x) = (-2lnx + 1)/x^2 x^2 is always positive so -2lnx + 1 > 0 lnx < -1/2 ----&...
cos y = x - y -sin y dy/dx = 1 - dy/dx dy/dx - siny dy/dx = 1 dy/dx(1 - siny) = 1 dy/dx = 1/(1 - siny) to have a vertical tangent, the slope of that tangent must be undefined, that is, 1 - siny = 0 sin y = 1 y = π/2 or y = -3π/2 or 5π/2 if y = π/2 , then co...
by intuition, it must be 8 oz or the amount of salt must stay the same, so .02(16) = .04(16-x) .32 = .64 - .04x .04x = -.32 x = 8
y=1000 sin (2t) +400 sin(anything) lies between -1 and +1 so the smallest value of sin(2t) is -1 so the smallest value of y = 1000(-1) + 400 = -600 But, it would make not make any sense to have a negative population, so my answer would be zero
I will assume I am looking at two different ones 1. -1< 3+2x<11 2. 1 x >-3 or 5x-1>19 #1. -1< 3+2x<11 subtract 3 -4 ≤ 2x < 8 divide by 2 -2 < x < 4 all real numbers between -2 and 4 #2 1 x >-3 or 5x-1>19 -x > -4 or 5x >...
The use of this page is more efficient and more accurate than using a standard normal distribution table, http://davidmlane.com/hyperstat/z_table.html for the prob(between 170 and 180) is gives .4772 for the prob( > 178) it gives .0548 multiply each of these by the 80 peopl...
This person has listed the number of school days of several countries http://norberthaupt.com/2012/04/20/school-days-around-the-world/ Not all countries are listed of course, e.g. he did not list my Canada, but I know that in Ontario the number of days is 195 on average.
Don't try to "create" fractions in this format, the spacing comes out all wrong. did you mean: 2x/(x+3) + 9/(x-3) - 36/(x^2 - 9) ?? if so, notice that x^2-9 = (x+3)(x-3) , so your LCD is (x+3)(x-3) give it a try
my goodness! I answered this same question for you earlier. All you have to do here is change the numbers. http://www.jiskha.com/display.cgi?id=1395018684
if those negatives are supposed to be exponents, write them this way: 6.3 x 10^-7 3.25 x 10^-12 both expressions are in scientific notation
I suspect a typo
ummh, that would be (0,0) You should know the properties of this , the simplest form of the equation of a circle.
done, check back on your previous post of this
I interpret (fg)(x) as (-6x-1)(4x^2) = -24x^3 - 4x^2
I bet you mean: f(x) = (x+10)^2 new equation: g(x) = (x+10 - 12)^2 = (x-2)^2
radius of each bubble = .005 m or (1/2) cm volume of each bubble = (4/3)π(1/2)^3 cm^3 so 1 million of them = 1000000(4/3)π(1/2)^3 = appr 523598.78 cm^3 = appr .5236 m^3 a bit over 1/2 cubic metre
2tanA+6=tanA+3 tanA = -3 so A must be in II or IV using tanx = +3 x = 71.565° so A = 180-71.564 = appr 108.4 or A = 360 - 71.565 = appr 288.4°
rate = 4760/34000 = .14 so .14(36000) = $ 5040
Make the rectangle sit on the diameter. Let its base be 2x and its height be y then x^2 + y^2 = 27^2 y = √(729 - x^2) area = 2xy area^2 = 4x^2y^2 = 4x^2(729-x^2) = 2916x^2 - 4x^4 d(area^2)/dx = 5832x - 16x^3 = 0 for a max of area (if area is the largest of all areas, the...
A variety of 9 different questions with no apparent effort shown by you, indicates that you just want us to do this assignment for you. Tell me what answers you obtained, and where you are having difficulty. Are you telling me that you can't do #2 ?
Just realized that I answered this same question back in 2011 http://www.jiskha.com/display.cgi?id=1306326095
Did you make a diagram? Did you not realize that the direction of the plane and the wind form a right angle ? How did you get 266.4 for the groundspeed ? (I got 241.86)
Math 2 questions
volume of 2 similar solids is proportional to the cube of their corresponding sides, so x/240 = 23^3/92^3 = (23/92)^3 = (1/4)^3 = 1/64 64x = 240 x = 3.75 the new volume is 3.75 ft^3 If I told you that the surface area of 2 similar solids is proportional to the square of their ...
number of chairs --- x number of tables --- 14-x 30x + 70(14-x) = 660 solve for x, pretty straightforward.
can u explain? 1 question
volume of pyramid = (1/3) area of base x height
i need yur help with this..
look at my answer to your first question here http://www.jiskha.com/display.cgi?id=1394926846 In calculating the area of the triangle, the height is not 15. make a sketch of the triangle to see that 15 is the hypotenuse.
quick way: for a given point (p,q) , the shortest distance from that point to the line Ax + By + C = 0 is |Ap + Bq + C|/)√(A^2+B^2) so we have (p,q) = (-4,-4) and line 2x - 2y + 3 = 0 distance =|-8 +8 + 3|/(4+4) = 3/√8 = 3/√8*√8/√8 = 3√8/8 =...
could be a very nasty equation but .... 3^x + 4^x = 5^x by inspection and recall, I know that 3^2 + 4^2 = 5^2 (did you recognize the 3-4-5 right-angled triangle) so x = 2 now suppose it had been 3^x + 4^x = 6^x look at Wolfram's solution http://www.wolframalpha.com/input/?...
Math help plz check my answers!
Surface area of a square pyramid usually just adds up the surface area of the 4 isosceles triangles, not including the base one of them: base = 11 hypotenuse = 15 height^2 + 5.5^2 = 15^2 height^2 = 194.75 height = √194.75 area of one of them = (1/2)(11)√194.75 = ap...
I am sure you meant: (4-7i)/(2+5i) = (4-7i)/(2+5i)*(2-5i)/(2-5i) = (8 -20i - 14i + 35i^2 )/(4 - 5) = 8 - 34i - 35)/-1 = 27 + 34i
5 - 12i r = 13 , but we want it in the form r(cosØ + isinØ) cosØ = 5/13 , so Ø could be in I or IV sinØ = -12/13, so Ø could be in III or IV so Ø must be in IV taking Damon's angle of 292.6° 5 - 12i = 13(cos292.6 + i sin...
x^2 + 7x - 30 = (x+10)(x-3) so the sides could be (x+10) and (x-3) , were x > 3 or x^2 + 7x - 30 = (x-2)(x+9 - 12/(x-2) ) so the sides could be x-2 and x+9 - 12/(x-2) or x^2 + 7x - 30 = (x+5)((x+2 - 40/(x+5) ) so the sides could be x+5 and x+2 - 40/(x+5) or ... as you can s...
you should know the formula for the area of a circle just plug in 3x+2 for r and look at your choices (which you did not give us)
did that one for you, look for your previous post
tough one! are you sure you did not mean 4^x = 8^x ? that would be easy. What you typed requires some sort of sophisticated method such as "Newton's Method" but an intuitively obvious answer would be x = 2 however there is another one between 0 and 1 let me know ...
looks like a lot of nonsense and mathematical gibberish.
make a sketch, join the centre to A, and complete the right-angled triangle. let the distance from the centre to the chord be x x^2 + 5^2 = 13^2 x^2 = 169-25 = 144 x = √144 = 12 Where does CD enter the picture? Where is D ? Your opening sentence of "center C has a r...
all lines of the type y = (-3/2)x + b , where b is any real number would be perpendicular to your given line Where there any choices? so just make sure the answer starts with y = (-3/2)x ...
area of lot = (6x)(9x) = 54x^2 area of circle = π(4x)^2 = 16πx^2 amount left over = 54x^2 - 16πx^2 = (54-16π)x^2
let the original cost of one shirt be x so three shirts cost 3x reduced by 30% leaves you with .7(3x) .7(3x) = 63 2.1x = 63 x = 63/2.1 = 30 Just noticed this same question was asked last year. http://www.jiskha.com/display.cgi?id=1361331485 Now you have 3 different solutions, ...
What is 8/9 - 3/5 ?
As I understand the question, you simply want the circumference of a sector of central angle 7(15°) or 105° with a radius of 24 cm circumference of a circle with radius 24 is 48π cm so using a simple ratio ... 105/360 = x/48π gives an arc length of 105(48`...
You have conflicting information. At the beginning of his "retirement period" he will need: 35000( 1 - 1.08^-15)/.08 = 299,581.75 so he would not need $400,000 at that time. To assure that he will have that $299,581.75 available 20 years from now , he needs a present...
using sin(A+B) = sinAcosB + cosAsinB 4sin(π/2+x) = 4(sin(π/2)cosx + cos(π/2)sinx) = 4( (1)cosx + (0)sinx) = 4 cosx
I too made a Venn diagram and after filling in the given information , found two missing sections 1. Those that only walked 2. Those that took the bus or the car, but did not walk confirm this please #2, dA/dr means the rate of change of the surface area with respect to the ra...
I = PRT 960 =4000(R)(3) solve for R (I got 8%)
Steve is right, I made a silly adding vs subtracting error in the 3rd last line 3y + 27/5 = 2x - 48/5 3y - 2x = -21/5 should be 3y + 27/5 = 2x - 48/5 3y - 2x = -75/5 to give 10x - 15y = 75 , reducing to 2x - 3y = 15
the the point of contact be P(x,y) Make a sketch to see that there would be two points P 2x + 8y dy/dx = 0 dy/dx = -2x/(8y) = -x/(4y) slope of tangent = (y-3)/(x-12) then (y-3)/(x-12) = -x/(4y) 4y^2 - 12y = -x^2 + 12x x^2 + 4y^2 = 12x + 12y but x^2 + 4y^2 = 36 12x + 12y = 36 x...