Count Iblis

Hi Jen, I've seen the drawing. My site is down at the moment. Draw a line from Venus (either of the two positions) to the line Earth-Sun at right angles. Let's call the distance Earth Venus d. Then you have a right angle triangle with a hypotenuse d, the...

18 years ago

RP^2=RQ^2 + QP^2 -2(RQ)*(QP)cosQ (1) QP = 24 (km/min) t (2) Diffentiate both sides w.r.t. the time t: 2 RP* d Rp/dt = 2 t [24 (km/min)]^2 -2(RQ)* 24 (km/min) cosQ (3) Using (1) and (2) you find out what RP is at t = 4 minutes. You plug that into (3) and s...

18 years ago

i^6 = (i^2)^3 = (-1)^3 = -1 The square, not the square root of -1 is 1. :) B.t.w., can you prove that -1 times -1 is 1? Hint, try to prove first that for any number X: -1 times X equals -X How do you find the square root of -1? The square of any real numb...

18 years ago

Ideal Gas Law: PV = N k T ---> N = PV/(k T) N = 1.387*10^(29) mass of one helium atom is approximately 4*u = 6.642*10^27 kg 4u*N = 921 kg A Goodyear blimp typically contains 4770 m3 of helium (He) at an absolute pressure of 1.10 x 105 Pa. The temperature...

18 years ago

|2x + 4| is always larger than or equal to zero. This means that the left hand side of the equation is always 6 or less, so there are no solutions. 6 - 3|2x + 4| = 12 So I just put NO Soution? No solutions, or if you have to write down the solution in the...

18 years ago

correction: 9/25(u+7)u^11 du = 9/25(u^12 + 7 u^11) du and you can easily integrate this indefinate integral of 9x(5x-7)^11 dx using the u substitution method: i know u= (5x-7) but when i use this the x in the 9x doesn't cancel thus x= (u+7)/5. however whe...

18 years ago

This reply to some student got deleted, so I'm reposting it. Cos(pi/4 + h) = Cos(pi/4)Cos(h) - Sin(pi/4)Sin(h) = 1/sqrt(2)[1 - h - h^2/2 + h^3/6 + h^4/24 - h^5/120 - h^6/720 + ...] Note that the way students like you are asked to solve this and similar pr...

18 years ago

This is a reply to the question posted here http://www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we den...

18 years ago

momentum What is a kilogram meter per second? vesc=(2GM/R)1/2

18 years ago

Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x...

18 years ago

Original qustion posted here: http://www.jiskha.com/display.cgi?id=1239379999 If you do computations Modulo some number, say Modulo 11, then you identify numbers from the ordinary number system that differ by a mulitple of 11. A rigorous mathematical defi...

16 years ago

Correct. Next problem: expand the product (1 + 2x^3 + x^6)(4 + x + 2x^2)(1+x^5)

17 years ago

"Would I do first times the derivative of the second + second times the derivative of the first?" That's right. But whenever you are not sure about such a rule you should derive it yourself from first principles. Otherwise you are just going to use a rule...

18 years ago

You just write below the summation sign which variable(s) you are summing over, indicting the starting value(s) and on top you write the upper limits to the summation variable(s).

18 years ago

I think you mean the identity: a dot ( b cross c) = c dot (a cross b) This can most easily be proved byintroducing the anti-symmetric pseudo tensor e_{i,j,k}: e_{i,j,k} = 1 if (i,j,k) is a cyclic permutation of (1,2,3) e_{i,j,k} = -1 if (i,j,k) is a cycli...

17 years ago

999999999999999999 = 10^18 - 1 9999 = 10^4 - 1 999999999999999999 * 9999 = (10^18 - 1)* (10^4 - 1) = 10^22 - 10^18 - 10^4 + 1

18 years ago

Use arithmetic Modulo 100. The Mod operator is defined as follows: x Mod y is, by definition, the remainder you get when you divide x by y. This is the same as subtracting from x that multiple of y that makes the resulting number smaller than y. Example 1...

18 years ago

x(y + z) = xy + xz (1) If you substitute x = p + q, you get: (p + q)(y+z) = (p+q)y + (p+q)z Applying the rule (1) again: (p+q)y = py + qy (p+q)z = pz + qz Therefore: (p + q)(y+z) = py + pz + qy + qz In general: (a_1 + a_2 + a_3 + ... )* (b_1 + b_2 + b_3 +...

18 years ago

Yes, let's look at the difference: (a+b)^3 - (a^3 + b^3) = 3a^2b + 3 ab^2 = 3ab(a+b) This is zero if a or b equals zero or if a = -b

18 years ago

(number + 5)^2 = number^2 + 10 number + 25

18 years ago

If A = B, then that implies that: A + a = B + a for any number a. So, if X + (-9) = -5 then choosing a = 9 we get: X + (-9) + 9 = -5 + 9 Since (-9) + 9 = 0 we have X = -5 + 9

18 years ago

3(x-2)+4=4(x-2)+1 ---> (x-2) = 3 ---> x = 5

18 years ago

Divide the sum of squares by N and work with the averages. Let's use the notation: <X> for the average of X. E.g.: <X> = ∑(X)/N = Mean And: <(X-<X>)^2> = <X^2 - 2X<X> + <X>^2> = <X^2> - <X>^2 Note that <a X> = a <X> for a constant factor a. In an average...

18 years ago

Sorry, that was a typo. I meant to write: <<X>^2> = <X>^2

18 years ago

E = f/2 N k_b T N is the number of gas molecules, k_b is Boltzmann's constant: k_b = 1.38065*10^(-23) J/K T is the absolute temperature and f is the number of degrees of freedom per molecule. For a mono-atomic gas like e.g. helium f = 3. This is because a...

18 years ago

2B means 20 + B here. 299 = 13*23, so B = 3

18 years ago

The general equation for a circle is: (x-a)^2 + (y-b)^2 = R^2 R is the radius of the circle and the point (a,b) is the center. To solve the problem you just insert the coordinates of the three points that are known to be on the circle in the equation and...

18 years ago

The circle is tangent to the y-axis at y = 3. From this it follows that the center of the circle must be located somewhere on the line y = 3. Therefore b = 3. The point (0,3) is on the circle, so: a^2 = r^2 The point (1,0) is on the circle: (1-a)^2 + 9 =...

18 years ago

From the original question (not posted here) it was clear that 2B means 20 + B here, because B was referred to aa a digit. Also, as drwls pointed out, the question doesn't make sense if 2B is interpreted as 2*B As I replied below, from the fact that 23 is...

18 years ago

I'm sure you know about energy levels for electrons in atoms. If you confine a particle in a box then, just like in case of electrons in atoms, there will be energy levels that that particle can occupy. The smaller the box is, the higher the lowest possib...

18 years ago

If the physical quantity you want to measure is discrete (i.e. an integer multiple of some number, then you can measure it exactly. An example is electric charge. The electric charge is always a multiple of the elementary charge (minus the charge of the e...

18 years ago

You can also solve this problem purely algebraically without using geometry or drawing diagrams. If we denote the resultant force by R, the force of magnitude 8 N at an angle of 30° to the resultant by y and the unknown force by x, we have: x + y = R ----...

17 years ago

The limit is of the form: Lim x--> 0 f(x)/g(x) where f(0) = g(0) = 0. So we can't take the limits for f and g separately and divide them. Rewrite the limit as: Lim x--> 0 [f(x) - 0]/[g(x) - 0] = Lim x--> 0 [f(x)-f(0)]/[g(x)-g(0)] Lim x-->0{[f(x)-f(0)]/x}/...

18 years ago

Total energy is conserved. This is a consequence of the fact that the laws of physics don't change over time. The relation with entropy depends on the system. Entropy can be defined as the amount of information you would need to describe the exact state o...

18 years ago

z^6-z^2 = z^2 (z^4 - 1) = z^2 (z^2 + 1) (z^2 - 1) = z^2 (z^2 + 1)(z + 1)(z - 1)

18 years ago

(1 + x)dy/dx - xy = x + x^2 ---> y' - x/(1+x) y = x First solve the homogeneous part of the equation: y_h' - x/(1+x) y_h =0 ---> y_h = A exp(x)/(1+x) Then you promote A from a constant to a function of x and put: y = A(x) Exp(x)/(1+x) If you subsitute thi...

18 years ago

f '(c) = f(b) - f(a) / b-a = 13 - 4 / 3 = 9 / 3 = 3. There exists a point c in the interval [1,4] such that f'(c) = 3

18 years ago

"I have worked on this equation for two days." Well, you could have spend the two days better by learning some more maths :) The answer is b) and c). Two lines: y1 = m1 x + c1 and y2 = m2 x + c2 are perpendicular if m1*m2 = -1 The reason why you have diff...

18 years ago

Lim x-->0 of (3 sin 4x) / sin 3x Both the numerator and denominator are zero in this limit, so you can use L'Hopital's rule. Lim x-->0 of (3 sin 4x) / sin 3x = Lim x-->0 (12 cos 4x) / (3 cos 3x ) = 4

18 years ago

If x^2 = a, then: x = ± sqrt[a] If x^2 + p x + q = 0, then you want to get rid of the linear p x term. You can do that by substituting: x = y - p/2 The linear term in y then cancels and you can solve for y by taking the square root. Third and fourth degre...

18 years ago

You just start from any 3 by 3 magic square, e.g.: 2 9 4 7 5 3 6 1 8 If you subtract 2 from each number you get a magic square that contains the numbers ranging from -1 to 7

18 years ago

Well, I actually believe that nothing "really" exists. What we call reality could just be a mathematical world alongside all possible other mathematicaly definable worlds. See also here: http://arxiv.org/abs/0704.0646

18 years ago

Do you mean least common multiple?

18 years ago

I don't believe in a separate physical world apart from the mathematics that describes it. If a physical world really exists (in the sense that it is more than just maths), then we'll never be able to pin down what it is. There will always be something un...

18 years ago

Long division is equivalent to writing down an equation and solving it as follows: 18x^2-25x-10 = (9x+1)(ax + b) + c ---> 18x^2-25x-10 = 9ax^2 + (9b+a)x + b + c 9 a = 18 ---> a = 2 9b+a = -25 ----> b = 3 b + c = -10 ---> c = -13

18 years ago

If the plane is orthogonal to (5,-6,-1) + t(3,10,-3), then it is also orthogonal to the parallel line t(3,10,-3) which moves through the origin. Consider first the plane orthogonal to this line which contains the origin. If the point (x,y,z) is on that pl...

18 years ago

Well, it would be more of an accident if you assume a physical universe, or even a God (why did God choose to crreate you?). In a mathematical universe, in the sense that all posible mathematical models exists, your existence is guaranteed. Anyway, astrop...

18 years ago

Try to find another source for the solubility. When I get confused about notations/conventions in some source I always try to find alternate sources. Also, you can look up a well known solubility (like NaCl )in the source you are using and compare with th...

18 years ago

Yes. If an object is not moving relative to you and I am moving relative to you, then relative to me, the object will be moving. The laws of physics are the same for all non-accelerating observers. When defining what we mean by "equilibrium", you will wan...

18 years ago

The limit for x --> a is 2 a A function is continuous if Lim x-->y f(x) = f(y) for all y.

18 years ago

A function f is odd iff f(-x) = - f(x) Put h(x) = f(x) + g(x) and calculate h(-x): h(-x) = f(-x) + g(-x) = -f(x) - g(x) = -[f(x) + g(x)] = -h(x) So, we see that h is odd because h(-x) = -h(x) Now put h(x) = g[f(x)] h(-x) = g[f(-x)] = g[-f(x)] = -g[f(x)] =...

18 years ago

Suppose that statement Z says that a piece of paper will burn, Y says that a piece of paper will burn when put in a fire, and that X says that the piece of paper is in the fire. Then Y can be written as: X ----> Z Modus ponens then says that if X is true...

18 years ago

Q= (pi)R^n(P2-P1)/ 8nL Just substitute the dimentsions for all the symbols: Q = L^3 T^(-1) R = L P2 - P1 = M L^(-1)T^(-2) n = M L^(-1)T^(-1) L^3 T^(-1) = L^n M L^(-1)T^(-2)M^(-1) L T = L^n T^(-1) ----> n = 3

18 years ago

4.9*10^(-2) is known to two significant figures, so the answer should be given in to significant figures. Note that this is only a rule of thumb. In general you need to work as follows. You have some function like: f(x1,x2,x3,x4) E.g., in this case f(x1,x...

18 years ago

4/(X-3) - 4X/(X-3)^2

18 years ago

You can take for g(x) an arbitrary function with an inverse g_inv(x). Then you take f(x) to be f(x) = 2 (g_inv(x))^2 + 11 g_inv(x) - 6 f(g(x)) = 2 (g_inv(g(x)))^2 + 11 g_inv(g(x)) - 6 = 2x^2+11x-6 E.g. If you take g(x) = Log(x), then g_inv(x) = Exp(x) and...

18 years ago

I recommend that you study this general solution as long as it takes for you to understand it. Students are given problems in order to master maths. Trying to find a solution to a problem without understanding the issues involved is pointless.

18 years ago

There are 7 days in a week, so it's the same day of the week 7, 14, 21, 28,.. days from now. E.g., to find out what day of the week it is 30 days from now, you can use that 28 days from now it's the same day, so it will be two days later in the week (e.g....

18 years ago

(sin 2x)^3dx = (sin 2x)^2 (sin 2x)dx = -1/2(1-(cos 2x)^2)dcos(2x)

18 years ago

The only thing that can be improved is to substitute the numbers including the units for the quantities. Then you never have to think about the units, the maths itself will take care of that.

18 years ago

You have to study maths yourself from books.

18 years ago

The acceleration is assumed to be constant until the car has a velocity of zero w.r.t. the ground or when it collides with the van. You could write down coordinates of the car and the van as a function of time and see if at some time the become equal. A s...

18 years ago

Suppose you have two sets, P and S. Suppose that all the elements that are in P are also members of S. Then we say that P is a subset of S. Now, the set S is itself a subset of S, because all elements of S are in S (a trivial statement). We say that P is...

18 years ago

Simplify the problem by adding a number to the number you are subtracting. After you obtain the answer, correct for that by adding that number, which you have subtrcted extra, back. Subtracting decimals using the standard method taught in primary school i...

18 years ago

You just move the persons to the next room. Person in room 1 goes to room 2 person in room 2 goes to room 3 etc. Then room 1 will be free.

18 years ago

one minus this probability is the probability that everyone has a different birthday. The first selected person has a certian birthday, the second person has a probability of 364/365 of havng a different birthday, the third person has a probability of 363...

18 years ago

You can do these problems in slightly different ways. I prefer to do it using the "passive method", e.g.: 3.7m = 3.7* 100 cm = 370 cm Here I just substituted m = 100 cm.

18 years ago

5/6 is the probability that you won't get a six. The probability of not getting a six, six times in a row is therefore (5/6)^6

18 years ago

11/18

18 years ago

8/(1/4) = 8*4 = 32

18 years ago

x^3 + 4xy^2 - y^4 = 7 ---> d[x^3 + 4xy^2 - y^4 ] = 0 -----> 3x^2 dx + 4y^2 dx + 8yx dy -4 y^3 dy = 0 3x^2 dx + 4y^2 dx =(4y^3 - 8yx) dy --> 3x^2+ 4y^2=(4y^3 - 8yx) dy/dx ----> dy/dx = (3x^2+ 4y^2)/(4y^3 - 8yx)

18 years ago

y^3 + y = 2cosx ----> (3 y^2 + 1 )dy = -2sin(x) dx ----> dy/dx = -2 sin(x)/(3 y^2 + 1)

18 years ago

The solar system was formed when a gas cloud collapsed under its gravity. The initial angular momentum caused the cloud to collaps into a disk.

18 years ago

It's undefined. Just use the definition of division. By a/b we mean the value of x that satisfies the equation: b x = a If you take b and a equal to zero, you have: 0 * x = 0 Any value for x will satisfy this equation (zero times any number is zero). So,...

18 years ago

When the car is over the top of the bump it is accelerating downward. The acceleration is a = v^2/r = (13 m/s)^2/(33.2 m) = 5.09 m/s^2 72.7 kg person is thus accelerated downward at this acceleration. Newton's second law says that: F = m a Let'S apply thi...

18 years ago

Chain rule: d/dx [1/(sin(x-sinx))] = -1/[sin^2(x-sin(x)] * d/dx [sin(x-sin(x))] = -cos(x-sin(x))/[sin^2(x-sin(x)]* d/dx [x-sin(x)] = [cos(x)-1]cos(x-sin(x))/[sin^2(x-sin(x)]

18 years ago

x^2+5x-14 = (x-2)(x+7)

18 years ago

Differentiate both sides of: f(2x) = 4f(x)+6 -----> f'(2x) = 2f'(x) -------> f'(x) = a x --------> f(x) = b x^2 + c Insert this in the functional equation to find that c = -2 The first equaton f(1) = 1 then gives: f(x) = 3 x^2 - 2

18 years ago

Put x = exp(i t) Then: x + 1/x = 2 cos(t) x + 1/x = sqrt(3) ----> cos(t) = sqrt(3)/2 ----> t = ±pi/6 (adding a multiple of 2 pi leaves x invariant) x^(13) + x^(-13) = 2 cos(13 t) = 2 cos(13/6 pi) = 2 cos(pi/6) = sqrt(3)

18 years ago

Put x = exp(i t) Then: x + 1/x = 2 cos(t) x + 1/x = sqrt(3) ----> cos(t) = sqrt(3)/2 ----> t = ±pi/6 (adding a multiple of 2 pi leaves x invariant) x^(13) + x^(-13) = 2 cos(13 t) = 2 cos(13/6 pi) = 2 cos(pi/6) = sqrt(3)

18 years ago

120 = 12*10 12 = 2*2*3 10 = 2*5 120 = 2*2*2*3*5

17 years ago

You can use the equation: 760mm Hg=101,325 Pa You simply write it as: Pa = 760mm Hg/(101,325) You then substitute this in the expression for pressure in the container: 435kPa = 435k*760mm Hg/(101,325) = 435*1000*760mm Hg/101,325 = 3362.8mm Hg

17 years ago

Substitute x = y^1/3 to express it in terms of the Beta function. The integral can then be expressed as: 1/3 Gamma(4/3)Gamma(1/3)/Gamma(5/3) = 0.883319375... Gamma(x) = (x-1)! and most calculators will evaluate it correctly for fractional values of x.

17 years ago

f(x+h)-f(x-h) = f(x+h) - f(x) + f(x) - f(x-h) lim as h -> 0 [f(x+h)-f(x-h)]/ h = lim as h -> 0 [f(x+h)-f(x)]/ h + lim as h -> 0 [f(x)-f(x-h)]/ h lim as h -> 0 [f(x)-f(x-h)]/ h also equals the derivative of f if the functon is differentiable.

17 years ago

The electromagnetic force keeps electrons in orbit around the nucleus. The adjective "greatest" is not really appropriate here. One can talk about the range of the force or the interaction strength between particles. Gravity is the weakest of the four for...

17 years ago

The strong force is the strongest. The Weak force is not really weak, it is as strong as the electromagnetic force. However, the weak force decays exponentially as a function of distance.

17 years ago

Electrons have an intrinsic angular momentum, which is called spin. It is as if a electron is a rotating ball of electric charge. The directon of the spin is what the rotation axis would be. In a permanent magnet some fraction of the electron spins are al...

17 years ago

Yes, you can do integration by parts. Another way is to integrate e^(xy) and then differentiate the answer w.r.t. x. Integral of e^(x y)dy = 1/x e^(xy) + c Differentiate both sides w.r.t. x: Integral of ye^(x y)dy = (y/x - 1/x^2) e^(xy) + c' If you use th...

17 years ago

tan^n(x) = sin^2(x)/cos^2(x)tan^(n-2)(x) sin^2(x)/cos^2(x) = [1-cos^2(x)]/cos^2(x) = 1/cos^2(x) - 1 So: tan^n(x) = tan^(n-2)(x)/cos^2(x) - tan^(n-2)(x) Integral of tan^(n-2)(x)/cos^2(x)dx = tan^(n-1)(x)/(n-1)

17 years ago

All electrons have the same charge. Protons have the opposite charge. Atoms have as many protons as electrons, so they are electrically neutral. If protons don't have the opposte charge of electron, then atoms are not exactly neutral. This will lead to ce...

17 years ago

It is important to note here that the reason why there is no field inside the conductor is simply due the fact that charges repel. However, the reason why the charges go to the surface is due to the inverse square Coulomb law. Also, the fact that the elec...

17 years ago

"At the atomic level, what is meant by saying something is electrically charged? - When something is electrically charged it means that it has a positive charge" Electrically charged atoms are called ions. Ions can be positively or negatively charged. "Wh...

17 years ago

Answer is correct.

17 years ago

Correct.

17 years ago

Use the definition of sin and cos using a right triangle and then use Pythagoras's formula.

17 years ago

I(n) = Integral of dx/cos^n(x) 1/cos^n(x) = cos^2(x)/cos^(n+2)(x) = [1-sin^2(x)]/cos^(n+2)(x). So, I(n) = I(n+2) - Integral of sin^(2)(x)/cos^(n+2)(x) dx Integral of sin^(2)(x)/cos^(n+2)(x) dx = -Integral of sin(x)/cos^(n+2)(x)dcos(x) = (Partial integrati...

17 years ago

It think that the question is flawed, as it confuses the idea of matter waves with the Bohr model of the atom. Bohr postulated that angular momentum is quantized in order to explain the discrete energy levels of atoms, see here: http://en.wikipedia.org/wi...

17 years ago

Depends on the duration of the acceleration, see e.g. here: http://en.wikipedia.org/wiki/John_Stapp

17 years ago

Minimize S=x+2y with xy=2 and both x and y > 0 Put F(x,y) = xy Then we have: dS/dx = lambda dF/dx (1) dS/dy = lambda dF/dy (2) Eq. (1) gives: lambda y = 1 (3) Eq. (2) gives: lambda x = 2 (4) If you divide (4) by (3 you get: x/y = 2 (5) We also know that x...

17 years ago

(x+3)(x+1)/[x(x^2+x+1)] = A/x + (B + C x)/(x^2 + x + 1) To find A multiply both sides by x and take the limit x --> 0: A = 3 To find B and C you can just move the A/x term to the other side and simplify: (B + C x)/(x^2 + x + 1) = (x+3)(x+1)/[x(x^2+x+1)] -...

17 years ago

Drop in potential energy from horizontal to vertical orientation is 2 meters *m* g This must equal 1/2 m v^2, because velocity is zero when the rope is horizontal. This means that: v^2 = 4 meters*g ---> v^2/(2meters) = 2 g is the centripetal acceleration....

17 years ago

P(X<Y) + P(X=Y) + P(X>Y) = 1 P(X>Y) = P(X<Y) by symmetry and P(X=Y)=1/6, therefore: P(X<Y) = 5/12

17 years ago

g/day µg/kg kg day/mg 1/kg = µg*g/mg *(1/kg) = 10^(-6)

17 years ago

By symmetry this is 1/3! P(X,Y,Z are all different) P(X,Y,Z are all different) = 1- P(X,Y,Z are not all different) X,Y,Z are not all different if and only if one or more of the three conditions are satisfied: c1: X = Y c2: X = Z c3: Y = Z Terefore: P(X,Y,...

17 years ago

Another way to compute this is by counting the number of ways you can make the three numbers diffrent. If you choose X first, then you have 6 choices for X. If Y is next then there are 5 choices for Y lft and 4 for Z. So, there are 6*5*4 possibilities. Th...

17 years ago

cos^2(x) + 2 cos(x) + 1 = [cos(x) + 1]^2 So, cos(x) = -1 ------> x = (2n+1)pi

17 years ago

Part a: (all expressions are Mod q) Consider the q-1 numbers p, 2p, 3p, 4p, 5p,...,(q-1)p. All these numbers are different and nonzero. If ap = bp and p and q don't have divisors in common then a = b. So, a - b must be zero or a multiple of q, which means...

17 years ago

The matrix method is the most efficcient way. -23 is the same as 27 mod 50. 13x= 20 (everything = mod 50)----> x = 13^(-1)*20 = 27*20 = (25 + 2)*20 = 40

17 years ago

125/72

17 years ago

u = <a, 1,1> v = <1,2,1> u dot v = 1/2 sqrt(2) |u| |v| ----> (u dot v)^2 = 1/2 |u|^2 |v|^2 ----> (a+3)^2 = 1/2 (a^2 + 2)*6 ----> 2 a^2 -6 a -3 = 0 Let u = 3i + j; v = 5i - 2j; and w = i - j. Find scalars, a and b such that u = av +bw. av+bw = (5a +b)i + (...

17 years ago

f(x) = x^3

17 years ago