4. Write the following in the form, a + bi, where a, b € R: 1

Q: y= (2+6 times x)^x Use Logarithmic Differentiation to find dy/dx

A: Conclusion :  dxdy​=(2+6x)x [(2+6x)6x​+log(2+6x)]Explanation:Step 1: Approach 1 ) Take both side…

Q: 2 Determine a quadratic function f(x) f(x) = ax² + bx+ C in standard form, if its graph passes…

A: The objective of this question is to find the coefficients a, b, and c of the quadratic function…

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A: The lengths of the legs of the right triangle areThe rate at which the short edge is changing, The…

Q: Find an equation of the tangent plane to the given surface at the specified point. zy In(x), (1, 8,…

A: Therefore, the equation of the tangent plane isz=8x−8.Explanation:Q. Find an equation of the tangent…

Q: Suppose for a particular commodity, & = 1.4 and that currently 30,000 units are selling for $18…

A:

Q: The area of a circle is increasing at a constant rate of 88 square meters per second. At the instant…

A: The area of a circle is increasing at a constant rate of 88 square meters per second.dAdt=88 square…

Q: g(x)=x³ sin (√√x) sin(√)

A:

Q: Prove that 3 is prime.

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile…

A: Please refer below for answersExplanation:To find how fast the height (h) of the pile is increasing…

Q: Determine a value for k such that the two planes are coincident. -3y+z=-27 -x- 3x+k²y+kz = k* a. k=3…

A: Final answers: (1)   d (2)  cExplanation:###(1)For two planes to be coincident, their normal vectors…

Q: Match the magnitudes to their Cartesian vectors. S y↑ 4 U Y 2 R T -4 -2 2 2 4 x * PQ A. 5 B. √10 C.…

A: Given the data about the vectors.

Q: +a2+C √ √√a² + u²du = ½ (u√u² + a² + a²]n]u + √u² + a² 1) + T 114

A:

Q: No hand written responses.

A: (A) N is discontinuous at t2, t4, t5, t7 and t8 . (B)Option A. limt→t6​​N(t)=4 Option A. N(t6) = 4…

Q: Let (f : [0, infinity) -> R be an arbitrary continuous function, which is differentiable on…

A: The objective of this question is to prove that a function f(x), which is continuous and…

Q: The velocity of blood through a vessel is given by v = K(R² - 2), where K is a constant, R is the…

A: The required volume is:V=0.05 cm3Explanation:The given expression for the volume is: V=∫0R​v(2πr) dr…

Q: Question 3 Let f(x) = 0 - {rm (4) cos x0 x = 0 " Show that f is continuous at x = 0.

A: we need to show that the function is continuous at x=0.

Q: (a) Find the extreme values of f(x) = 2x3 + 3x2 - 12x + 1 on the interval (0, 2). (b) If f' (x) =…

A:

Q: The 3 × 3 matrix B satisfies the equation B^3 = −B. Show that B cannot have an inverse

A: We proved that, the matrix B cannot have an inverse if it satisfies the equation…

Q: A company estimates that it can sell 4,000 units each month of its product if it prices each unit at…

A:

Q: A medical laboratory raises its own rabbits. The number of rabbits N(t) available at any time t…

A: (A) The function is discontinuous at t=t2​,t4​,t5​,t7​,t8​(B)limt→t6​​N(t)=5N(t6​)=5(C) Limit…

Q: 5. 3. The graph of f is given below. If g(x) = f(t) dt, find the following value. Use the provide…

A: I'm uploading images for all questions.Explanation:Ques 5-1Ques 5-b Ques 3 Last ques

Q: a. Using the Law of Sines, determine the value of m/C. You should notice that there are actually two…

A:

Q: Find the minimum distance from the point (-2, -2, 0) to the surface z = √√9-2x-2y. (Hint: To…

A: To find the minimum distance from the point .

Q: An executive recently traveled to London, Paris, and Rome. While in London, he paid $180 per night…

A: Solution is attached Explanation:Step 1: Step 2: Step 3: Step 4:

Q: (Text' . | Find a ⋅ b if |a| = 5, |b| = 4, and the angle between a and b is radians. 8 • a b =

A: The formula for the dot product is : a⋅b = ∣a∣ ∣b∣ cos(θ)a⋅b  = 5* 4 *cos(π/8)a⋅b   = 18.4776…

Q: e problem below. In (10x4) 4x y' = y(1) = 0 arithmic functions in parentheses.

A: To solve the following initial value problem.

Q: 20. Given a = [3, −5, 1], b = [−2, 4, −1] and ♂ = [7,3, −2], find a) b.z b) ax c c) 0, the angle…

A:

Q: imit: 6-xy lim (x,y)-(2,2) x²+2y²

A:

Q: No hand written responses. I need help with a step-by-step breakdown in laymen terms for each part…

A: Answer AOption A , t2​, t4​, t5​, t7​, t8​Answer Blimt→t6​​N(t)=7N(t6​)=7Answer CThe Limit does not…

Q: 20. Given a = [3,-5, 1], b = [−2, 4, −1] and ♂ = [7,3, −2], find a) b.z b) ax c c) 0, the angle…

A:

Q: 6. Consider the curve y = 4x². Determine the equation of the line(s) (in standard form), such that…

A: We need to find an equation of a tangent line that passes through the point given.

Q: Use implicit differentiation to find Əz/ǝx and Əz/ǝy. x8+ y + z³ = 8xyz дх 88 || მ მყ ||

A: The required answer is given below.Explanation:

Q: = 17. A triangle is to be inscribed in the ellipse x² + y² with one vertex of the triangle at (-2,…

A: Solution is following in explanation step.

Q: let F(x) = f^5 and G(x)=(f(x))^5 you also know that a^4 = 11, f(a)=2, f prime of a =11, f prime of…

A: F'(a) = 880 G'(a) = 880Explanation:Detailed explanation:Understanding the FunctionsF(x) = f^5: This…

Q: Consider the function graphed below. 7+ 6 5 4 3 AN -6-5-4-3-2-1 2 1 2 3 4 5 Determine the following…

A: 1.)a.) Amplitude: 3b.) Period: 5c.) Equation of Midline: y = 3 2.)A = 5D = 0B = π/7s =…

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^5, y=1…

A: Given that the region is bounded by the curve  ,line  and the y-axis in the first quadrant.

Q: Determine the point of intersection between the following pair of lines (0, 1,3) + s(5,-1,2), SER…

A: The intersection point is (−5,2,1).Explanation:Steps and explanations are as follows:In case of any…

Q: Let -3x3 + 3y³ - 4z³ – 3xyz - - Use partial derivatives to calculate the point (-6, 1, −2). 647 = 0.…

A:

Q: pls help on all asked questions pls

A:

Q: Consider the functional S[31, 32] = [ dx [7y² + 24y,y2+21y2² +4y² + 12y1y2+9y3] · - Y₁ = azı 322, y2…

A: Functional separability lets you break down a complex functional (think fancy function) into simpler…

Q: b. How would you rewrite each expression if it was an integrand for a trig. integral? Just the first…

A: We have to rewrite each integrand1.    Sin3xcos4x2.     Sin2x3.      Cosec3xcot3x

Q: 3. Find f'(x) if f(x) differentiation) === 023 * xsin(x)

A:

Q: Find the limit, if it exists, or type 'DNE' if it does not exist.

A:

Q: Find f'(x) if f(x)=7e6x f'(x)= 0

A:

Q: iv. Σ n=1 40n (2n-1)2 (2n+1)2

A: The given series

Q: a. · b = . ) Find a ⋅ b if |a| = 2, |b| = 2, and the angle between a and b is - radians.

A: a⋅b≈3.76Explanation:The dot product of A and B is,a⋅b=∣a∣∣b∣cosθ Given the…

Q: Find the indicated partial derivative. f(x, t) = x5e-ct fttt 0 ftxx = 0 × ×

A: Answers:  fttt​=−c3x5e−ctftxx​=−20cx3e−ctExplanation:Step 1:

Q: Q3/ Find the general solution of the differential equation dy 3x2 tan y)+ x³sec2y- = COS X dx 17.10.…

A:

Q: The world’s total consumption of natural gas was 1824 million tons oil equivalent (mtoe) in 1994.…

A: ### ConclusionHence, the natural gas reserves would have lasted for approximately 44 years under the…

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^5, y=1…

A: The objective of this problem is to find the volume of a solid with a given base and cross-sections.…