Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x+y'-3x-3y = e−3t x'y' +6x+3y = e3t
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- Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 9x - 10y + sint and y' = 5x - y - cost. Write the system in operator form.f(z)=1-3z2; z=-2, z=0 determine the net change between the given values of the variable.
- An insect is in a toxic environment. The level of toxicity is given by T(x,y)=2x* -4y If the insect is at (-3,4), in which direction should it move so that the toxicity decreases as quickly as possible and thus avoid being affected by it?From Variation of parameters for the Linear system. Find the general solution to the system X'Find the linearization of the function f(x) = 1/(9x+8) at x = -1.
- The dosage for a certain type of chemotherapy drug depends on several parameters of the particular drug as well as the age, weight, and sex of the patient. For female patients, the formulas giving the dosage for such drugs are D = 0.85A(c + 25) and c = (140 - y)= W 72x' where A and x depend on which drug is used, D is the dosage in milligrams (mg), c is called the creatinine clearance, y is the patient's age in years, and w is the patient's weight in kilograms. Complete parts (a) through (e) below. a) Suppose that a patient is a 46-year-old woman and the drug has parameters A=4 and x = 0.5. Use this information to write formulas for D and c that give D as a function of c, and c as a function of w.Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x %3D 1.find the derivative of (z+j)? j2:+2z z4+ j4z³+6z² – j4z+1 j2:2-2z 24+j4z–6z2 – j4z+1 j2:+2z 24+j4:-6z2+j4z+1 j2:2 -2z z4 - j4z+6z² – j4z+1
- linearise R = AT + BT2The procedure to find the stationary points of a particular function f(x, y) leads to the eq 3x² +18x3y² +27= 0, -6xy +by = 0. The second of these equations has solutions y = 0 or x = 1. Select the option that gives a complete list of the stationary points of the function. Select one: O (-3,0), (1, –4), (1, 4) O (0, -3), (-4, 1), (4, 1) O(1, -3), (-4, 0), (4,0) O(-3, 1), (0, -4), (0, 4)Find the equation of the family of orthogonal trajectories of the system of parabolas y? = 2x + C. y = Cex y = Ce2x y = Cex y = Ce 2x