20. The points P₁ (1, 1, 1), P₂ (1, 2, 3) and P3 (2, 2, 4) are on a plane. (a) Give the explicit equation of this plane. (b) If I start from an arbitrary point on this plane and move 2 units in the direction of the x-axis and 3 units in the direction of the y-axis, how many units do I have to move in the direction of the z-axis to stay on the plane?

Q: Find g[f(-2)]. f(x)=x² +4; g(x)=4x-1 g[f(-2)] = (Simplify your answer.)

A: Given: f(x)=x2+4; g(x)=4x-1

Q: The number of Drosophila fruit flies in a controlled experiment assumes the following growth pattern…

A: Given: N(t)=7501+14e−0.4t

Q: Acceleration of a Car The distance s (in feet) covered by a car t seconds after starting is given by…

A:

Q: Exact differential Equation    M(x,y)dx + N(x,y)dy =0 ∂M/∂y = ∂N/∂x   solve the following…

A:

Q: 85,000 is deposited in a saving account with 6.35% annual interest. When will be the initial sum…

A: To solve this problem, we can use the formula for compound interest:

Q: Find the derivative of the function. g'(t) = g(t) = (5t + 2)² (2t² - 8)-³

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 7xeox dx 6x [7xe 7…

A:

Q: Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -5 x…

A:

Q: 1. Solve the ODE by integration. a. y' + 2 sin 27x = 0 c. y' = -1.5y C. b. y' = y

A: To solve the following ODE by integration. (a) y'+2 sin2πx=0 (b) y'=y (c) y'=-1.5y

Q: Find the direction of BC in standard form. Note: There are TWO (2) correct answers! -18.435° 116.565…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Consider the following function. g(v) = v³ - 75v + 5 Find the derivative of the function. g'(v) =…

A:

Q: [cos* xdx

A:

Q: 2. When given the fact that a b=0, prove that a 1 b.

A:

Q: 8 1. Σ n=1 (80) 92n

A:

Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

A:

Q: Find the area of the region bounded by the parabola y 3x², the tangent line to this parabola at…

A:

Q: be In the first answer field, write out the derivative using the quotient rule without simplifying.…

A:

Q: W Convert 50(1.16) – 200 to logarithmic form and use the change of base formula to solve for w.…

A:

Q: a) y ' — 2xy = x b) y' + sin(x)y=sin(x)

A:

Q: What is the smallest counting number that has factors of 2,3,4,10,12, and 18 ? Explain/show how you…

A: Given Factors  2,3,4,10,12, and 18      L.C.M of these numbers gives the required number

Q: N(t) = 750 1+14e-0.4t where t measured in days. A. How many fruit files were there in the beginning?…

A:

Q: Find the absolute maximum and absolute minimum values of f on each interval. (If an answer does not…

A: Absolute maximum of a function f is the highest value of f. Absolute minimum of a function f is the…

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = 5x4 - 20x³ +6

A:

Q: n=1 ncosan ૦૬, Itn³ 3

A: Solution: ∑n=1∞πcos2(n)1+n3Apply the constant multiplication rule:=π·∑n=1∞cos2(n)1+n3

Q: The cost, in thousands of dollars, of airing x 30-second television commercials during a major…

A:

Q: 2 Find the volume of the solid under z = 6 + x² + y² over the first quadrant of x² + y² ≤ 36 Give…

A:

Q: Find the inverse of the following atrix by using (Adjoint matrix method). 1410-18 A = [²²₂ =²5] [**]…

A:

Q: y' = = x/n(x)

A: We can find the derivative of the given function by using logarithmic differentiation.

Q: Find the following limit. lim "

A:

Q: For the function y = f(x) = x² - 2x - 3, x ≥ 1, find (f¹)'(-3)= df 1 dy ly 3

A: We can solve this as follows:

Q: 1 A 3 2 1 To find the blue shaded area above, we would calculate: [ f(x) dx Where: a = f(x) = area =…

A:

Q: = Find the length of the entire perimeter of the region inside r = = 3. outside r = Answer: 11 sin…

A:

Q: q(x) = 1 x² + 3 on [-4,2]

A:

Q: The position function of a particle is given below. s(t) = t³ + 1.5t²- 58t, tz 0 When does the…

A: Derivative

Q: 3. y = cos x - sinx, [0, 2л]

A:

Q: SSYDA Dis bounded by y = x-12 2 x = y ²

A: Given that:- D is the region bounded by y=x-12 and x=y2

Q: 9. Use the first 4 non-zero terms of the power series for f(x) = ln (x + 1) to approximate In ()

A:

Q: Evaluate the following indefinite integrals. cos(tan-¹) 1+x² (a) [ (b) / tan³ z dr. dx.

A:

Q: Suppose that f(x, y) = 2x + 2y on the domain D = {(x, y) | 1 ≤ x ≤ 2, x² ≤ y ≤ 4}. Then the double…

A: Suppose that fx, y=2x+2y on the domain D=x, y 1≤x≤2, x2≤y≤4 Then to evaluate the double integral…

Q: Minimizing Packaging Costs What are the dimensions of a closed rectangular box that has a square…

A:

Q: Hey I cant read what you sent can you please type the answer or write it better

A: We have to find the derivative of v.

Q: Find the absolute maximum and absolute minimum values of f on each interval. (If an answer does not…

A:

Q: Find two numbers, and y, whose difference is 42 and whose product is a minimum. (Answer as a common…

A:

Q: ermine the intervals on which the graph of y f(x) = 9x² + x4 concave up or concave down, and find…

A:

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: The revenue function is R(x)=40x-0.5x2 Cost of producing x units is C(x)=6x+10 Profit function is…

Q: Find the absolute minimum and absolute maximum values of f on the give f(x) = x - In(2x), [1/1, 2]…

A:

Q: The linear approximation at z = 0 to sin(92) is A + B where A is: and where B is: Question Help:…

A: Topic =Derivative

Q: Evaluate the following integral. sin(2x) In (sin x) dx

A:

Q: 3. City A (1, 4) and City B (4, 10) are located on a graph at the coordinates listed (all distances…

A: As we know the formula for the distance when it passes through the two points Ax1,y1 and Bx2,y2:…

Q: The temperature at a point (x,y,z) of a solid E bounded by the coordinate planes and the plane…

A: Given, x + y + z  =1Tx,y,z=-9xy + 8z + 20