If you want to use vector notation, then if the vector to A is a, and to B is b, etc. Then AB = b-a BC = c-b CA = a-c AB+BC+CA = b-a+c-b+a-c = 0 AB is b-a because if there is a vector u such that a+u=b, then u=b-a.
Looks to me like AB + BC + CA = 0 Similarly for the other one. Getting back to A, the sum is just 0 again. The vectors form a closed polygon, so the net result is zero.
54-24 = ?
30 <= 18+0.3(x-50) <= 45 12 <= .3(x-50) <= 27 40 <= x-50 <= 90 90 <= x <= 140
what's with the braces? Just use vertical bars: |8| = 8 |-9| = 9 and so on |x| = -x if x is negative otherwise, |x| = x
the scale Q'/Q = 2/3 2/3 * 15 = 10, the new length
consecutive angles are supplementary opposite angles are equal So, what do you have here?
my first guess is you are allergic to that fruit.
2 - 3 = -1 Oops. If by difference, you mean the larger minus the smaller, the conclusion is true. Technically, though, the difference is minuend - subtrahend ----------------- difference So it matters which is which.
MS Sue is trying to get you to figure out 8*(6ft+4in) = 8*6ft + 8*4in = 8*6*12in + 4in = ? in
7th grade math
(2/5 x) > 7 x > 7 * 5/2 x > 35/2 So, place a dot at 35/2 and shade to the right 2(x+7)-4 > 5(x-3) 2x+14-4 > 5x-15 2x+10 > 5x-15 25 > 3x 25/3 > x So, place an open circle at 25/3 and shade to the left
This is indeed the MVT. The secant line through (1,1/3) and (4,2/3) has slope 1/9. The MVT says that in the interval (1,4), there is some c where f'(c) = 1/9. f'(x) = 2/(x+2)^2 So, we want c such that 2/(c+2)^2 = 1/9 (c+2)^2 = 18 c+2 = ±3√2 c = -2±3...
use integration by parts u = x, du = dx dv = cos 15x dx, v = 1/15 sin 15x Now we have ∫x cos15x dx = 1/15 x sin15x - ∫1/15 sin15x dx And that's clear sailing. . . right?
no idea. However, what you have factors into (x-7)(x+4) = 0 Then the roots are clearly 7 and -4
IB Maths SL
The slope of the tangent to f(x) is f'(x) = (g'h-gh')/h^2 So, the normal has slope h^2/(gh'-g'h) At x=2, that is 6^2/(18*2-5*6) = 6 f(2) = g(2)/h(2) = 18/6 = 3 So, now you have a point and a slope, so the normal line at x=2 is y-3 = 6(x-2)
Cosine Law NEED HELP QUCIK
at 9:30 the hour hand has gone clockwise 9.5/12 * 360 = 285° from the top The minute hand is at 180° So, the angle between them is 105°. You want d where d^2 = 12^2 + 10^2 - 2*12*10*cos 105° d^2 = 306.1 d = 17.5 Just a straightforward application of the law of ...
Just looking at the figure, angles AHM and TMH are congruent, so 3x+5 = 7x-27 x = 8 So, m<AHM = 29 If you answered #15, #17 should have been obvious.
v = ∫[1,t] πr^2 dx where r=y=1/x. So, v = π∫[1,t] 1/x^2 dx = π(-1/x) [1,t] = π(1 - 1/t) as t→∞, v→π
Algebra 1--Please, help me! (Steve)
by now these should be getting easier. When multiplying/dividing powers, add/subtract the exponents. 3r^2t/6st^3 x 2r^2s^3t^2/8r^4s^2 = (3*2)/(6*8) r^(2+2-4) s^(-1+3-2) t^(-3+1+2) = 1/8 You gotta start using parentheses... x^2 + x/x^2 + 3x + 2 + 3/x + 2 = (x^2+x)/(x^2+3x+2) + ...
physics-force and pressure
well, geez - pressure is force/area, so that would be 300N/700cm^2 = 3/7 N/cm^2 Chances are you should convert that to N/m^2 so your answer could just be in Pa.
you are correct
You got (a) correct. So, for (b), just plug in x=5 and evaluate the fraction.
yes, #1 = 2a^2b/c^2 #2 = 1/(3x-15)
Hmmm. How about 2a^2b / c^2
when dividing by a fraction, just invert and multiply. So, #1 3a^4b/2a^2c^3 * 8c^4/12a^2c = 3*8/12 a^4/a^2 b c/c^3 ... #2 x^2+4x-5 = (x+5)(x-1) x^2-25 = (x+5)(x-5) So, you just have (x+5)(x-1) / 3(x-1) * 1 / (x+5)(x-5) = (x+5)(x-1) / 3(x+5)(x-1)(x-5) = ...
Algebra 1--Please, help me!
#1 also t=0, since t^2-t = t(t-1) The original expression must be examined for excluded values. (t-1)/(t^2-t) = 1/t, so t≠0. But dividing top and bottom by t-1 to get there means that t≠1, because you cannot divide by zero. #2 huh? There is no x-2 in the denominato...
x(x-2) + y(x-2) (x+y)(x-2)
trig - incomplete
as usual, draw a diagram and recall your basic trig definitions. If the ledge is at height a, and at distance x from the tree (with height h), then we have (h-a)/x = tan25° a/x = tan10° Now eliminate a to get h-x tan25° = x tan10° h = x(tan25°+tan10°) N...
take a look at http://www.wolframalpha.com/input/?i=solve+z^5+%3D+i Note that the angles given are pi/2 + k*2pi/5
if y = u^v, where u and v are functions of x, y' = v u^(v-1) u' + ln(u) u^v v' If you look carefully, you will see that y=u^n and y=a^v are just special cases, where u' or v' = 0. Anyway, just plug in u = x^2 v = sinx and you get (2x sinx)*(x^2)(sinx-1) + l...
maths - still bogus
1983 is not a leap year. After you fix that, just divide the number of years involved by 4, but watch for remainders. Then post your work, so we can see how you solved it...
If you're planning to attend a school where English is the language of choice, I suggest you improve your language and writing skills first.
First, there was no 29th of Feb in 1983; that was not a leap year Second, you give no date to end the calculation.
98-14 (also, the verb is "lose," not "loose." Unless she deliberately threw them away.)
I assume you know how to find the volumes of such solids. Just subtract the volume of the sphere from that of the cylinder. The leftover space holds the water: π(2x)^2*(2x) - 4/3 πx^3
algebra 2 and Trigeonomerty
(a) You have to multiply for the three draws, and allow for the changing population of blues and the total: 12/30 * 11/29 * 10/28 (b) That would be 18/30 * 17/29
math - incomplete
no table provided
just multiply each event by its probability. The sum is the expected value of income. Then subtract the costs involved: (395000)(1/40)+(125000)(1/20)-25000 Technically, we need all the probabilities to add to 1, so we should include the term for a dry well: (0)(37/40) but that...
Algebra 1--How Am I Supposed to Solve This?!
just divide the two, as you would do with any ratio: (πrl + πr^2) / (2πrh + 2πr^2) πr(l+r) / 2πr(h+r) = (l+r) / 2(h+r)
Algebra 1--how am I suppose to graph this?!
plot it the way you plot any function! Pick some values of x and calculate y. Then plot the point at (x,y). The curve will be smooth, but the only poi9nts that make sense in the real world are where x is a divisor of 75. Your graph should look like this: http://www.wolframalph...
mixed numbers are useless for calculation. Convert them to fractions and things get easy. 21/10 * 15/7 = ?
Precal, please help asap!
You need to clarify the diagram. Label the airplane A, the tower T and the post P. The plane is at altitude h, with AP=t and AT=p. Point Q is directly below the plane. The distance PQ=q and thus TQ = 2-q. If the plane is between the tower and the post, then h/q = tanα h/(...
Algebra, Need help with last part.Thank you
you are correct on the first two. The last should also be no sweat. There is only 1 2-hearts in the deck of 52 There are 4 twos in the deck. So, how many hearts are there? Also, just as advice, usually you will need to reduce your fractions for your final answers. 4/52 = 1/13 ...
since xy = k is constant, k = (1/2)(-10)
If you mean x = √(y+3) then x^2 = y+3 y = x^2-3 If you mean x = √y + 3 then x-3 = √y y = (x-3)^2 If you mean √x = y+3 then y = √x - 3 It sure helps if you proofread your posts to make it quite clear what's going on. Use parentheses if there is...
you know the volume is x*y*z = 12x So, y*z = 12 y cannot be less than 1, so z cannot be more than 12
You know that if the remainder is zero, x is a multiple of 3. But, there is a remainder of z, so add that in. Only one of the choices is a multiple of 3, with an extra z
algebra/Did I do this right
(x^5+x^2-3)(x^3-1) = x^8-3x^3-x^2+3 Now subtract -3x^3+x^2-4x and you get x^8-2x^2+4x+3 Now subtract 2x^2-4x and you get x^8+3 So, the whole thing is just (x^5+x^2-3)(x^3-1)-(-3x^3+x^2-4x)-(2x^2-4x)
x is the total amount added. Since you get x=10, that means that 5m was added on each side. I'm interested in how you made this calculation: (10+x)(20+x)=600 200+10x+20x+4x^2=600 Where did the 4x^2 come from? looks like answer analysis to me. In addition, you did not solve...
what is h when d=0? As you know the vertex of a parabola is where d = -b/2a = -4.4/-.88 So, figure h for that value of d. What is h when d=14? Or, how far away is the ball when h=0 (it hits the floor)?
(a) x(t) = 0 (since it went straight up) y(t) = 75 + 76t - 16t^2 (b) Just plug in t=2
(a) If you got the equations, answering the last 4 questions should be no sweat. (b) the ball is in the air while y(t)>0.That is, solve for t when y=0. (c) Knowing how long it took to hit, plug that into x(t). (d) y(t) is just a parabola. As usual, the vertex (where the bal...
boarding at t=0, the height y at time t minutes is y = -60cos(pi/6 t) + 6 Now just start plugging in your numbers.
since the horizontal speed does not change, we have the usual x(t) = 150 cos 30° t y(t) = 150 sin 30° t - 16 t^2 The rest is downhill from here
Math, grade 10
except, don't make my typo. Better say x+y = 17
Math, grade 10
follow the same logic I used in your previous post: x+y = 18 x^2+y^2 = 185 go for it
Math, grade 10
x+y = 18 x^2 + 6y = 163 now substitute for y: x^2 + 6(18-x) = 163 x^2 - 6x + 108 = 163 x^2 - 6x - 55 = 0 (x-11)(x+5) = 0 x=11 and y=7
slope = rise/run, so 1.9 = 4/run run = 4/1.9
slope = rise/run = 5/15
No, x=5 is not correct. The solution set to an inequality is an interval, not just a single point. Your logic should have been: -5(x-7) < 15 -5x+35 < 15 -5x < -20 x > 4 You could have checked your answer to see that x=5 works, but it is not the only number which do...
Not sure what a 2x3 matrix has to do with coordinates. Can you splain a bit, please?
7s/1320ft * 1313ft = 6.96 s assuming instant change in velocity. Assuming a constant acceleration, 1/2 a*49 = 1320, so a = 53.877 ft/s^2 Now, to get 1313 ft using the same acceleration, we have 53.877/2 t^2 = 1313 t = 6.98 s
3 21 (3,21) -3 0 (-3,0) I think. Hard to say just what you are after.
h/100 = tan 24
Algebra 1--Please, help me!
#1 we have n calculators that cost c each. Since nc = k is constant, 24*60 = 80n #2 Actually, the cost must be a positive integer divisor of 75, since the number of packages must be an integer. #3 well, you have the formulas, and you want the ratio scone/scyl = (πrl + ...
geometry math help
(a) two layers means 24 cans per layer. The cans are 10 cm across, so the 46x60 dimensions of the box allow for that many cans. The height of the box will accommodate the two layers. (b) You know the way to compute the volume of the box. Now, just subtract 48 times the volume ...
no idea. what does the pattern represent? How many more terms are to be considered? Ans why the ?? marks around the 20?
the angle is x, where sin x = 50/120
just askin', but did you complete the table?
just solve 2.903 t - 1.98 = 18 when you get t, add that to 2000 such bogus wordage. 4 <= t <= 9 is the condition.
At 12:00 the hands are together After h hours, the hour hand has gone h/12 * 360 degrees After m minutes, minute hand has gone m/60 * 360 degrees 9:30 = 9.5 hours :30 = 30 minutes So, the hour hand has gone 9.5/12*360 = 285° and the minute hand is at 180° So, the angle...
sinB/b = sinC/c that will get you B Then A+B+C=180 gets you A a^2 = b^2+c^2 - 2bc cosA gets you A. Then, b/sinB = c/sinC = a/sinA gets you A and B
3D Shapes & Scale
a 2m cube occupies 8 times the volume of a 1m cube. I assume the trailer is enclosed, so the volume makes a difference. So, what's 128/8?
h/65 = sin 32
Earth Science Regents!!!
It is clearly #2. Since both observations were made at the same time, the orbit traveled by the planet can have nothing to do with it. Only separate observations at different times could indicate how the earth has moved. If the earth were flat, the star is so distant that all ...
well, that's 2(1/2) + 2/5 = 1 + 2/5 = 7/5
more logarithms help!
just plug in your values: 24000(1-0.15)^n = 2500 Now solve for n. First step is .85^n = 2500/24000
logarithm math help
log(x^n) = n*log(x) log(u/v0 = log(u) - log(v) Now go for it.
Math binomial formula and sequence
Almost: C(8,4)(2x)^4(-3)^4 90720x^4 ar^3 = 16 ar^6 = -128 r^3 = -8 r = -2 so, a = -2 a_n = -2*(-2)^(n-1) = -(-2)^n S15 = 15/2 (2*8+14*4) = 540
Math - Ratio
(a) 2.5km/10^4 = 2.5*10^5cm/10^4 = 25 cm .5cm:2.5km = .5:2.5*10^5 = 1:5*10^5 = 1:500,000 Just as a check, the 1:10,000 scale used 25cm, and .5cm is 1/50 of that, so the scale should be 1:500,000
If you are assuming a parabola, then a little work will show that the equation is y = ax^2+bx+c 2500a-50b+c = 50 2500a+50b+c = 70 a(-b/2a)^2 + b(-b/2a) + c = 47 y = 1/200 x^2 - 1/5 x + 47 and the vertex is at (20,47) Now, the length of cable is thus s = ∫[-50,50] √...
Math - Logarithms
(a) x^5 = 100, so x = 100^(1/5) (b) I assume you mean 3^(x+5) = 81 we know that 3^4 = 81, so x+5 = 4 (c) log (4x+2)/2 = log 6x the logs are equal, so we just have (4x+2)/2 = 6 I guess you can probably handle that one, eh?
review the description of a circle with center at (h,k) and radius r: (x-h)^2 + (y-k)^2 = r^2
4x^2-y^2-24x-10y+11=0 4(x^2-6x) - (y^2+10y) = -11 4(x^2-6x+9) - (y^2+10y+25) = -11 + 4(9) + 25 4(x-3)^2 - (y+5)^2 = 50 Better check to see what you lost while completing those squares.
a = -2 r = -2 so, T20 = -2*(-2)^19
I also get 1/2 * 1/2 = 1/4 since the two events are independent.
If the box originally had side s, then the new box has side s-6, since 3" was cut off each corner. The height of the box is just the 3" that was cut off. So, s(s-6)^2 = 675 Now, just by inspection, 675 = 3*225 = 3*15^2 So, the box now has sides of 15, and height=3 Th...
Math - eh?
since T3 = T1 * r^2, r = 3 No idea what "124 of the fifth" means
Math - Linear Equations
T = k√L so, T/√L is constant. (a) .63/√9 = T/√25 (b) .63/√9 = 1.5/√L
since time = distance/speed, d/(12-5) + d/(12+5) = 3 now just solve for d. Assuming the round trip takes 3 hours.
Assuming they both work the same time, Alma works 4/3 as fast as Kevin, so she does 4/7 of the work, or 57% Or, you can find how long it takes to do the whole job together: 1/x = 1/4 + 1/3 x = 12/7 So, in 12/7 hours, Alma does 1/3 * 12/7 = 4/7 of the work.
they have 1/4 the distance to go. They have walked 3/4, or 3 times that far.
Nice homework dump. Can you show any effort on any of the problems?
The nth term has 2^-n, so the ratio is 2^-1 = 1/2 Did you try listing the first few terms? That would have made it clear that 2 was not the ratio.
Math - Linear Equations
total trucks: x+y = 8 total loads: 10x + 5y = 70 I expect you can solve that with little difficulty.
Algebra 1--Please, help me!
The question still is poorly worded. What is the "side" of a roof? I expect we are looking at the end of the building, at the cross-section area. The triangle has area a1=b2*h/2 The trapezoid has area a2=(b1+b2)*h/2 The ratio of areas is thus a1/a2 = (b2*h/2) / (b1+b...
Math - Variation
T = kd^4n^2 if we replace n by 2n and d by d/2, we have T' = k(d/2)^4(2n)^2 = kd^4n^2/4 = T/4