The graphs of f(x) = x and g(x) = ax2 intersect at the points (0, 0) and (1/a, 1/a). Find a (a > 0) such that the area of the region bounded by the graphs of these two functions is 27/2. a = Submit Answer

Q: Use the triangle method to evaluate

A: Step 1: two approch are there either convert into angle individual or try to get a common turm under…

Q: • Surface Area of a parametric curve revolved around the x-axis: 2 dx S=2T (+) dt a 2 dy dt dt

A: The derivation of the formula for the surface area of a parametric curve revolved around the x-axis…

Q: d) -1 2(1 + 1)d

A: Ans:

Q: Use Stokes' Theorem to find the line integral of F = 6yi +3zj + 3xk around the boundary of the…

A: Step 1:Given that, F=6yi^+4zj^​+3xk^  around the  boundary of the surface S given by: z=9−(x2+y2)…

Q: 2. Assume that f is continuous on [1,5] and that f(1) = 20, f(5) = 100. Determine whether each of…

A: 2. 3.

Q: Solution to question 4 please

A:

Q: The demand for a particular item is given by the function D (x) = 1,450 - 3x². Find the consumer's…

A: If you have any questions let me know in comment box thankyou for your question.

Q: sech¹ x = cosh X Prove mathematically that the right-hand side is equal to the left-hand side for…

A: Step 1: Step 2: Step 3: Step 4:

Q: 2 x = (y-1)² x = 3 y 1 X = 2√y 2 x

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

Q: 1 Find the 3rd degree Taylor polynomial for f(x) = √1+2x around a = 4. Use this to approximate…

A: Step 1:Finding the Taylor Polynomial:We are given the function: f(x) = 1 / √(1 + 2x) around a = 4…

Q: What is the most preferred flavor of coffee at Starbuck? A survey was done with 40 customers of…

A: The objective of the question is to understand the statistical terms in the context of a survey…

Q: Q3 please

A: Part (a):     To show that the point (0, 2) lies on the polar curve (r=2+2cos(θ)), we need to…

Q: Question 5

A:

Q: K The population density of a city is given by P(x,y) = -20x² - 20y² + 200x +480y+ 190, where x and…

A: To find the maximum population density, we need to find the critical points of the function and then…

Q: Solve this problem and provide a detailed explanation with full mathematical steps and reasoning…

A: Distance to the sidewalk from the car d1=17 kmDistance to the entrance from the sidewalk d2=19…

Q: Find the points of intersection of the graphs of the equations. (Enter (0, 0) for the pole.) r = e r…

A: Step 1:To find the points of intersection between the two polar curves, we need to set the equations…

Q: question 2 please

A: However, based on your description and the fact that it's related to a predator-prey model, I can…

Q: In Exercises 43 and 44, graph the functions. Notice in each case that the numerator and denominator…

A:

Q: Please do the following questions with full handwritten working out.

A:

Q: The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The…

A:

Q: 4. Find the sum Σ-4 2-4-- n n+1

A:

Q: I Find the following indefinite integrals. dx = cos(t) (5 sin(t) +12)² dt = +C +C

A:

Q: Can you please solve this integral with a step by step explanation?

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the value of the constant C for which the integral 3x 3C dx 4x + 1 (11) + converges. C =…

A: You can simplify it more by putting value of ln( 2 ). Depends on your need .ln(2)= 0.6931471806

Q: Use the properties of exponents to simplify the expression. Assume that all variables are nonzero.…

A:

Q: Assume the acceleration of the object is a(t) = -32 feet per second per second. (neglect air…

A: Step 1:Step 2:

Q: Please don't provide handwritten solution ...

A:

Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

A: Steps

Q: the answer i have for this question 81496800 need to make sure i am right please help

A: any doubt, please ask

Q: Question 7 Find the equilibrium point for a product D (x) = 25 - 0.009x² and S (x) = 0.007x². Round…

A: We know that The equilibrium point occurs when the demand function (D(x)) equals the supply function…

Q: Find the derivative

A: Step 1: Step 2: Step 3: Step 4:

Q: • Evaluate the surface integral s F dS where F= (3x, z,-y) and S is the part of the sphere x² +…

A: Surface Integral over a Parametrized SurfaceWe can evaluate a surface integral over a surface S…

Q: 4. 2

A:

Q: Consider the elipse with equation x^2+4y^2 = 4  a) Find a paramentrization of the ellipse that…

A: Step 1: Step 2: Step 3: Step 4:

Q: The sum of the areas of the rectangles approximates the area under the curve, though not very well.…

A: Notice that there are four rectangles in the figure. Let us name them A1, A2, A3, and A4, starting…

Q: I am needing assitance with the question in the attached image, 6.7.

A: Step 1: Step 2: Step 3: Step 4:

Q: 7) Two residential buildings are to be constructed with a grassy recreational area between them. The…

A: The solution has been attached below:

Q: Please can you confirm if the answers are correct?

A:

Q: Step by step help please

A: Step 1: Step 2: Step 3: Step 4:

Q: 4. Let F(x) = f(t)dt, where ƒ is the function whose graph is shown. 0 -5 LO 5 0 5 -5- Does have an…

A: Hence the required answer is mentioned above.Hope you got it. If any query then raise it. Please…

Q: K If $5000 is invested for t years at 9% interest compounded continuously, the future value is given…

A: If $5000 is invested for t years at 9% interest compounded continuously, the future value is given…

Q: The temperature of the earth is rising, as a result of the "greenhouse effect," in which carbon…

A:

Q: (a) Evaluate the integral 2 32 -dx. x² +4 Your answer should be in the form kл, where k is an…

A:

Q: Please do 3

A: To find the work done by the force field F(x,y,z)=(z,x,y) in moving the particle from point  to…

Q: 24. Write a vector (-3, 22, -3) as a linear combination of the vectors (-1, 2, 3) and (0, 4, -3).…

A: 24)  (−3,22,−3)=a(−1,2,3)+b(0,4,−3)(−3,22,−3)=(−a,2a,3a)+(0,4b,−3b)(−3,22,−3)=(−a,2a+4b,3a−3b) To…

Q: 2 Given f(x) = x²-3x-4, find the difference quotient h2+2xh+x2-2h-3x-4 Oh-2x+3 O h h²+2xh+x² -…

A: Step 1: Step 2: Step 3: Step 4:

Q: I need help finding theta.

A: Step 1: Step 2: Step 3: Step 4:

Q: Suppose a thin plate is bounded by y=0 , x=0, x=1, and y=e^-x and has areal density of p(x,y)= xy.…

A: To find the center of mass of the thin plate, we need to calculate the moments with respect to the…

Q: Find a polynomial that will approximate f(x) throughout the given interval with an error of…

A: Step 1: It is given that f(x)=∫0x​tan−1(t)dt for all t∈[0,0.45] To find the approximate polynomial…

Q: • Surface Area of a parametric curve revolved around the y-axis: S=2T b 2 2 dz dy x(t). dt dt dt

A: The formula you provided represents the surface area of a parametric curve revolved around the…