× Question 2 ▾ < > Score on last try: 0 of 1 pts. See Details for more. > Next question You can retry this question below Find two positive numbers x and y such that x + y = 14 and they minimize x² + y². x = У

Q: Question 1: Evaluate the following indefinite integrals. a) (5 points) sin(2x) 1 + cos² (x) dx b) (5…

A: (a) ∫1+cos2(x)sin(2x)​dx Step 1: Substituting u = 1 + cos2(x)Let: u=1+cos2(x). Now, differentiate…

Q: Use the information to find and compare Ay and dy. (Round your answers to four decimal places.)…

A: If you have any problem let me know in the comment section thankyou.

Q: For the following function f and real number a, find f' (a). f(x) = = √x+4; a = 0 f' (a)

A: Step 1: Step 2: Step 3: Step 4:

Q: please show all the work

A: Step 1: Step 2:Step 3: Step 4:

Q: 5. Euler's equation. Determine the values of a for which all solutions of the equation 5 x²y" + axy'…

A:

Q: X 4 324 6352 47 5. 7 0 = 11.6 = 6. 45 31 ngle. Round all measures to the nearest tenth.

A: From the given right triangles, We have, Angle = θOpposite = 4Hypotenuse = 7 Because opposite side…

Q: Calculate sin(10y(2)) where y is the solution of 4.149 12x²y" + 23xy' + 2y : - x such that y(1) = 1,…

A: To solve this problem, follow these steps:Step 1: Solve the Homogeneous EquationThe given…

Q: do number 7 pls

A: Given Information:∠A=50∘∠B=90∘ (Right Angle)∠C=40∘ (Since 180∘  −  90∘  − 50∘  = 40∘)BC = 14…

Q: 3. The general solution of the differential equation y′′ + 2y′ + y = 0 isA. c1e^−x + c2e^−x B.…

A: We are given the homogeneous second-order differential equation:y′′ + 2y′ + y = 0Form the…

Q: 3. f(7) 3. Find the domain of each of the following functions. 1 1. f(x)=2-6x+8 2. f(x)=√√7-x 4. A…

A: Problem 3: Calculate f(7) For the function f(x)=x2−6x+81​:  f(7)=72−6⋅7+81​=49−42+81​=151​For the…

Q: 1. Solve the initial value problem: y" -11y' + 30y = x³e6x y(0) 11, y'(0) = 36 =

A: Ans page 1:Ans page 2:Ans page 3:Ans page 4:

Q: "Use the Opposite Method to solve the following differential equation:" 4'"""" + 34" + 34 + 4 = x

A: Step 1:  Step 2: Also it can be solved by Method of undetermined coefficient. Step 3: Step 4:

Q: Solve by DrWz WI P L B dy Sind Ⓡ de max ⑦Ymax dx Solve by Dr ③Yat 0.75m from A w=6KN/M L=2 W2=9 kN/m…

A: Step 1:Step 2: Step 3: Step 4:

Q: 2) Find the maximum value of f(x, y) = x - y on the circle x² + y² - 4x - 2y - 4 = 0.

A:

Q: Each of the following statements is an attempt to show that a given series is convergent or…

A:

Q: The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given…

A: Key references:

Q: 9. a) Determie values of a and b so that the function is continuous. ax - 2b f(x) 2 x≤-2 -2x+a, x ≥2…

A: Step 1: Step 2: Step 3: Step 4:

Q: y"-9y+20y= 80t-156 y(0) = −6, y'(0) = 5 y(t) =

A: Step 1:Step 2:Step 3:Step 4:

Q: Solve please and thanks!

A:

Q: Question 1 (Implicit differentiation). Use implicit differentiation to find Əz/Əx and Əz/ǝy. (a)…

A: a) x² + 2y² + 3z² = 1 ∂z/∂x:Differentiate with respect to x, treating y as a constant and z as a…

Q: 2z = el+cos(x+y) 24 = olt etz dy = 1 dt dz e²² + cos (+²+1++). 2++ (1+++cos C+²+1++) (+) dz 2+. etz…

A: w=(yz)xx=e3+ty=3t2+3tz=sin⁡tYou are asked to find:2w/2t(probably means dw/dt using the chain rule)…

Q: Evaluate the integral using any appropriate algebraic method or trigonometric identity. S- dy 18 √2…

A: The given integral is:I=∫183y2​(1+y2/3)dy​ Step 1: Substitution  Let:y1/3=t Then,y=t3sody=3t2dt…

Q: Question 4 If log2(6x+3).= 4, then x = You may enter the exact value or round to 4 decimal places.

A: Step 1:Given that log2(6x+3) = 4 Take base exponent 2 to both sides, 2log2(6x+3) = 2⁴ 6x+3 = 16…

Q: 19. If the method of undetermined coefficients is used, the form of a particular solution ofy^(4) −…

A: Step 1: Identify the Right-Hand Side ComponentsThe non-homogeneous terms are:e−t (exponential…

Q: Use undetermined coefficients to find the particular solution to y"+2y-15y=2e3 Y(t) =

A: To find the particular solution to the differential equation:y′′+2y′−15y=2e3t,We can use the method…

Q: Find an equation of the line tangent to the graph of f(x) = (5x-9)(x+4) at (2,6).

A: Given, f(x)=(5x−9)(x+4) Multiply the terms, f(x)=5x2+11x−36 We need to find the equation of the…

Q: K x3 +216 complete the table and use the results to find lim k(x). If k(x) = X+6 X-6 X -6.1 -6.01 -…

A: We have given function, k(x)=x+6x3+216​  Step 1: Simplify the expression, k(x)=x+6(x+6)(x2−6x+36)​…

Q: 37. lim f (x) and lim f (x), where x+0+ x 0 Answer -> 38. lim f (x) and lim f (x), where +0x x―0M 2x…

A: If you have any questions let me know in the comment box immediately thankyou.

Q: Question 9 The plot below represents the function f(x) 8+ 7 6- ·6· -5 4-3-2-1 Evaluate f(4) f(4) = 4…

A: Evaluate f(4):Locate x = 4 on the graph.Identify the corresponding y-value.It shows that f(4) =…

Q: Determine whether the series is convergent or divergent. Justify your answer. If the series is…

A: Step 1: Step 2: Step 3: Step 4:

Q: For the system consisting of the lines: and 71 = (-8,5,6) + t(4, −5,3) 72 = (0, −24,9) + u(−1, 6,…

A: Step 1: a) Parallel Check The direction vectors of the lines are:Line 1: d1​=(4,−5,3)Line 2:…

Q: Use the information to find and compare Δy and dy. (Round your answers to four decimal places.) y =…

A: We are given the function:  y=x4+7 with   x=−3 and  Δx=dx=0.01. Step 1: Compute Δy  Δy=f(x+Δx)−f(x)…

Q: √5 Find Lª³ L² y-are y- arctan (+) dy dydx. Hint: Use integration by parts. SolidUnderSurface…

A: I hope you find this helpful.Please do Upvote, if the answer is helpful.Thank you.

Q: A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost…

A: Step 1: Define the given cost function The total cost function is:C(x,y)=x2+xy+4y2+400 where:x =…

Q: can you solve these questions with step by step with clear explaination please

A: Step 1: Getting acquainted with the network architectureThe network is a set of branches that…

Q: answer a, b, and c

A: ANSWER : Let's solve this problem step-by-step.Problem 4: Suppose a renewable population grows…

Q: Prove that if a and b are both positive, then y(x)⭢0 as x⭢∞ for all sloutions y of the question

A: We want to show that if a and b are both positive, then every solution  y(x) of the differential…

Q: 8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude,…

A:

Q: The twice differentiable functions fand g are defined for all real numbers of x. Values of f(x) and…

A: The value of the integral is -6.

Q: Chrome File Edit View History Bookmarks TC MyTCC: Studer × ALTI Launch ✓ Profiles Tab Window Help O…

A: It was stated that the electronic configuration of Helium is 1s2. We can interpret this as there are…

Q: Find and classify the critical points of z = (x² – 8x) (y² – 6y). Local maximums: Local minimums:…

A: STEP 1 ​​ STEP 2 ​​ STEP 3 ​​  STEP 4 ​​  STEP 5 ​​  Conclusion​​

Q: In the xy-plane, an angle 0, in standard position, has a measure of the following is true? T. Which…

A:

Q: Use Laplace transform to find L{f(t)}  f(t) = tsin(t)

A: Final AnswerL{tsin(t)}=(s2+1)22s​​ Thank you

Q: 6. Solve the system of differential equations using Laplace Transforms: x(t) = 3x₁ (t) + 4x2(t) x(t)…

A:

Q: Use the two methods "real number solution space basis" and "complex solution space basis"…

A: The given equation is a second order homogeneous linear differential equation with constant…

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(-3,4, -32) for the function…

A: We have given, The surface equation, f(x,y,z)=0 for the function  f(x,y,z)=ln(−5y−z−4x​)  Step 1 :…

Q: Find the point of diminishing returns (x,y) for the function R(X), where R(x) represents revenue (in…

A: To find the point of diminishing returns for the revenue function R(x)=10,000−x3+42x2+700x in the…

Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

A: Step 1:Step 2:Step 3: Step 4:

Q: Evaluate the following integral over the Region R. (Answer accurate to 2 decimal places). R - 1 ·…

A: Step 1:Step 2: Step 3: Step 4:

Q: Suppose that the graph below is the graph of f'(x), the derivative of f(x). Find the locations of…

A: Step 1: