How do you graph 2 3/7 on the number line ?
1 answer:
You might be interested in
Answer:
The Line integral is π/2.
Step-by-step explanation:
We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:
we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence
(Remember that c is treated like a constant just for the x-variable).
This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.
Where, again, the constant of integration depends on Z.
As a result,
if we derivate f over z, we obtain
That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)
The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.
Answer:
Part 1) "a" value is
Part 2) The vertex is the point
Part 3) The equation of the axis of symmetry is
Part 4) The vertex is a minimum
Part 5) The quadratic equation in standard form is
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
if a > 0 then the parabola open upward (vertex is a minimum)
if a < 0 then the parabola open downward (vertex is a maximum)
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
so
In this problem we have
-----> this is the equation in vertex form of a vertical parabola
The value of
so
a>0 then the parabola open upward (vertex is a minimum)
The vertex is the point
so
The equation of the axis of symmetry is
The equation of a vertical parabola in standard form is equal to
Convert vertex form in standard form
see the attached figure to better understand the problem
