The cost function is a quadratic. The basic form of a quadratic equation is ax^2 + bx + c = 0. You must find the values of the coefficients a, b and c.

Use the given data to construct 3 simultaneous linear equations in x:

5 = a(2)^2 + b(2) + c
143 = a(4)^2 + b(4) + c
869 = a(10)^2 + b(10) + c

You must solve for a, b and c and then write the quadratic equation
y = ax^2 + bx + c that governs the production costs. Then let x=7 and calculate y, which is the figure you want.

Using matrices, I found that a=6.5, b=30 and c=-81.

Can you now write the quadratic equation and evaluate it at x = 7?

4 0

3 years ago

Use the divergence theorem to evaluate the integral i = z z ∂w f · ds when f(x, y, z) = y i − 4yz j + 3z 2 k and ∂w is the bound

andre [41]

$\vec f(x,y,z)=y\,\vec\imath-4yz\,\vec\jmath+3z^2\,\vec k$

$\implies\nabla\cdot\vec f(x,y,z)=0-4z+6z=2z$

By the divergence theorem,

$\displaystyle\iint_{\partial W}\vec f\cdot\mathrm d\vec S=\iiint_W2z\,\mathrm dV$

I'll assume a sphere of radius $r$ centered at the origin, and that $W$ is bounded below by the plane $z=0$ . Convert to spherical coordinates, taking

$x=\rho\cos\theta\sin\varphi$

$y=\rho\sin\theta\sin\varphi$

$z=\rho\cos\varphi$

Then

$\displaystyle\iiint_W2z\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^r2\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\pi r^4$

6 0

3 years ago

I need help with 3-4 quick

jeka94

If you subtract three minus four then it would be one

8 0

3 years ago