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Answers by Tarik Z.

Find the absolute extrema? (answer)

Hi Sun, That's a great start and you have almost solved the problem.   You found the critical point at (0,1), but you need to find the discriminant in order to determine if this is the max or min of the function.  The discriminant is found as fxxfyy -fxy2 = 6*4 = 24.  Since...

can anyone help me?? (answer)

The rational zeros theorem is a method to determine the possible roots of a function.  The rational zeros are p/q, where p are all of the factors of the constant term, and q are all of the factors of the leading coefficient.  For this function, p = +/- 28, +/- 14, +/- 7,...

college algebra (answer)

When the boat is traveling upstream, it's speed is v - 3, and similarly for downstream its v + 3, where v is the speed of the boat relative to the water.  The time to go upstream is 3/(v-3) and to go downstream its 3/(v+3). With total time = 8, we have  3/(v-3) + 3/(v+3)...

Consider the function f(x, y)=y^2-x^2-yx^3. (answer)

For a function f(x,y,z) = 0, the directional derivative is given by the gradient of the function, <fx,fy,fz>.  Since a function defined as z = f(x,y), this is essentially equivalent to 0 = f(x,y) - z, then the gradient is <fx,fy,-1>.   b) The gradient will be normal...

How do I find the exponential key/growth of something? (answer)

The general form for an exponential growth equation is P(t) = Ae^(rt), where P(t) is the number of bacteria after time t, A is the initial number, and r is the growth rate. If they quadruple every hour, then P/A = 4 when t = 1. So 4 = e^(r*1).  Taking LN of both sides gives r =...

Factor the following binomial. (answer)

Hi Jamal, Any time you have want to factor an expression in the form (a - b), you can always break it into (sqrt(a) + sqrt(b)) (sqrt(a) - sqrt(b)) In this case, "a" would be 100x^2 and "b" would be 1.   So it can be factored to (10x + 1) (10x - 1...

Factor the following sum of two cubes. (answer)

Hi Jamal, To factor this completely, you start by determining the first, most apparent factor, which you get by setting the expression equal to zero and solving for z.   You get z^3 = -125   ------>>   z = -5 Therefore, one of your factors is (z+5).   To...

Find the equation for the parabola with focus (3,4) and vertex (3,3)? (answer)

First of all, you need to determine if this parabola is opening vertically or horizontally.  Since the vertex and the focus share the same x-value, the line of symmetry is at x = 3, which is vertical.  The standard form of a vertical parabola is. 4p*(y-k) = (x - h)^2, where (h,k) are...

(1249/x)/6.849=39.08 (answer)

Hi Camila, Don't be intimidated by numbers with decimals, they are still just constants and treated like any other. So to solve, you want to isolate the variable x.   (1249/x)/6.849 = 39.08  > Multiply both sides by 6.849 1249/x = 39.08*6.849   > Flip both sides...

explanation (answer)

Hi Amad, The reason you subtract 23 from both sides is to isolate the variable, x. By having x by itself, you have answered the question, "what value of x will make this equation true?" Beyond that, the only reason for doing it is to learn and understand the underlying logic of...

1/2q^(2)-5/4q-3=0 (answer)

Hi Jamie, It's generally going to be easiest to complete the square if the coefficient in front of the x^2 (or in this case, q^2) term is 1, so start by multiplying through by 2.  This gives: q^2 - 5/2q -6 = 0. Then, take the coefficient of the linear term (-5/2), divide it by 2,...

Use Stokes' Theorem to compute the surface integral? (answer)

Start by finding the parametric form of the curves that bound the surface.  The 3 corners of the tetrahedron occur with the intersection of each coordinate axis, so simply set 2 of the variables equal to zero to get the intercept. P1 = (2,0,0)     P2 = (0,2,0)      P3...

find (f+g) and (f*g) (5) (answer)

Assuming you meant f(x) = x^2 + 1.   f + g = x^2 + 1 + (3x - 4) = x^2 + 3x - 3. f*g(5) = ( 5^2+1)*(3*5-4) = 26*11 = 286.  

solve each problem (answer)

When adding numbers with a decimal, be sure to line up the decimal point when you write it out vertically and proceed as usual.  1.43 0.50 +  1.93 =