The position vector of a particle is r(t). Find the requested vector.The velocity at t = 0 for r(t) = ln(t3 - 5t2 + 5)i - 
j - 7cos(t)k
A. v(0) = 
i - 
j + 7k
B. v(0) = - 
j
C. v(0) = 
i - 
j
D. v(0) = 
j
Answer: B
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Solve the equation. Express radicals in simplest form.0.5x2 + 0.7x -0.9 = 0
A. -0.81, 2.22 B. 0.81, -2.21 C. 0.82, 2.21 D. -0.81, 2.21
Find the volume of the described solid.The solid lies between planes perpendicular to the x-axis at x = - 4 and x = 4. The cross sections perpendicular to the x-axis are semicircles whose diameters run from 
to 
A. 
?
B. 
?
C. 
?
D. 
?
Simplify the radical.-
A. -5 B. -25 C. 5 D. 25
Provide an appropriate response.The Cobb-Douglas production function for a company is given by 
where P is the monthly production value when k is the number of units of capital and l is the number of units of labor. Suppose that capital costs $150 per unit, labor costs $225 per unit, and the total cost of capital and labor is limited to $270,000. Use Lagrange multipliers to write the system of equations you would use to find the number of units of capital and labor that maximize production.
What will be an ideal response?