I am a tutor by profession in the Bytedance Company.
Find the inverse of the matrix (if it exists). $$\left[\begin{array}{rrr}1 & 2 & -1 \\3 & 7 & -10 \\7 & 16 & -21\end{array}\right]$$
Find the inverse of the matrix (if it exists). $$\left[\begin{array}{rrr}10 & 5 & -7 \\-5 & 1 & 4 \\3 & 2 & -2\end{array}\right]$$
Find the inverse of the matrix (if it exists). $$\left[\begin{array}{rrr}1 & 1 & 2 \\3 & 1 & 0 \\-2 & 0 & 3\end{array}\right]$$
Find the inverse of the matrix (if it exists). $$\left[\begin{array}{rrr}3 & 2 & 5 \\2 & 2 & 4 \\-4 & 4 & 0\end{array}\right]$$
Find the inverse of the matrix (if it exists). $$\left[\begin{array}{lll}2 & 0 & 0 \\0 & 3 & 0 \\0 & 0 & 5\end{array}\right]$$
A particle moves along a line so that its position at any time t, in seconds, is s(t) = t^3 + 7t^2 + 11t - 2.5.a. Find the velocity and acceleration function at any time t.b. Find the times when the particle is at rest, and the times when it is speeding up and slowing down. Justify your answers.c. Find the values of t when the particle changes direction.
Find the gradient of ∅ when: b. ∅ = x^3 + y^3 + z^3 b. ∅ = sin(xyz) c. ∅ = e^(-xyz)
A rather flimsy spherical balloon is designed to pop at the instant its radius has reached 7 centimeters. Assuming the balloon is filled with helium at a rate of 16 cubic centimeters per second, calculate how fast the radius is growing at the instant it pops. (The volume of a sphere of radius r is V = (4/3)Ï€r^3. Round your answer to two decimal places.)
Show that the cylinder {(x, y, z) ∈ R3; x2 + y2 = 1} is a regular surface, and find parametrizations whose coordinate neighborhoods cover it.
If the daily cost per unit of producing a product by the AceCompany is 15 + 0.5x dollars, and ifthe price on the competitive market is $100, what is the maximumdaily profit the Ace Company can expect on this product?
The monthly profit from the sale of a product is given by P = 32x - 0.2x^2 - 200 dollars.(a) What level of production maximizes profit?units(b) What is the maximum possible profit? $
