Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter: (−2, 4, −5), (−4, 0, 3)

Q: In this exercise, the group will define three piecewise functions. Each function should have three p...

A: Given:  Define three piecewise functions. Each function should have three pieces and two values of x...

Q: The graph of an equation is symmetric with respect to the ...................if substituting -y for ...

A: Explanation: If we substitute -y for y in the equation that leads to an equivalent equation. That me...

Q: Use the binomial expansion formula to expand (x + 1 )9 .

A: x+19 Binomial theorem is, a+bn=C0nan+C1nan-1b+C2nan-2b2+C3nan-3b3+----+Cnnbn

Q: integration of e^x^2

A: Here, we have to find the integration of ex2, So, the given term becomes, ∫ex2dx, Now, in this case ...

Q: What is the standard linear approximation?

A: A linear approximation is an approximation of a general function using a linear function. They are w...

Q: Determine whether the equation 2x + y2 = 6 defines y as a function of x.

A: We have to determine whether the equation 2x+y2=6 defines y as a function of x . We know that for y ...

Q: 4 The determinant value of the matrix A =5 -7 -4 is %3D 4 9. O -65 O -71 O -73 O-63 O -68 2] 4 5

A: Given: Matrix A=4045-7-4429

Q: Find the derivatives of the following function f(x) from the first principles  (i)x3

A:  

Q: When an object is removed from a furnace and placed in an environment with a constant temperature of...

A: Given: constant temperature =80°F core temperature =1500°F

Q: Find the inverse ƒ-11x2 of each function (on the given interval, if specified). ƒ1x2= log10 4x

A: fx=log104x

Q: At what points (x, y) in the plane are the functions in Exercises 31–34 continuous?

A: Since you have asked multiple question, we will solve the first two question for you. If you want an...

Q: maximum and minimum

A: To find: The absolute extremum of the given function

Q: Describe all solutions of Ax= 0 in parametric vector form, where A is row equivalent to the given ma...

A: Given information: The matrix is 130-4260-8. Calculation: Reduce the matrix into row echelon form. A...

Q: I need to integrate  the following equation:

A: Given,          ∫039-x2dx

Q: The graph of an exponential function is given. Select the function for the graph from the following ...

A: Given graph,

Q: find the solution of the given initial value problem 10. y′+2y=te−2t,y(1)=0

A: Given: The initial value problem y'+2y=te-2t and y1=0, To find: The solution of given initial value ...

Q: verify that each given function is a solution of the given partial differential equation. 19.uxx+uyy...

A: Given, u1(x,y)=cosxcoshyu2(x,y)=ln(x2+y2)

Q: find the average rate of change of the function overthe given interval or intervals. g(t) = 2 + cos ...

A: gt=2+cost,  0, π

Q: Approximating real numbers Use an appropriate Taylor series to find the first four nonzero terms of ...

A: By using appropriate series To find The first four nonzero terms of an infinite series that is equal...

Q: Find the equation(s) of the tangent line(s) to the graph of the curve                  y = x3 − 9x t...

A: Consider the curves, y=x3-9x To check the points (1,-9) is on the graph, Substitute x=1 and y=-9 the...

Q: x2 (4) Calculate the result of the equation Having x= 0 , 1 , 2 /5+ x

A:

Q: Explore the Alternating Series Remainder. (a) Use a graphing utility to find the indicated partial s...

A: (Note: We are entitled to solve only one question at a time and upto 3 subparts only) Given: ∑n=1∞-1...

Q: Point P (0,2) is the point of intersection of y axis and perpendicular bisector of line segment join...

A:

Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0), x(...

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get ⇒∫dx2x+2=∫dtt2+2t⇒∫dx2x+1=∫dtt2+...

Q: For each of the piecewise-defined functions in determine whether or not the function is one-to-one, ...

A: Let x < 0 Then we get, f(x) = x^2 Let us consider two numbers x < 0 and y < 0. Also let us ...

Q: Write the complex number 8(cos 60° + i sin 60°) in rectangular form. If necessary, round to the near...

A: Given, 8cos 60°+isin 60°

Q: Solve the triangle A = 42°, a = 63, b = 57. Round lengths to the nearest tenth and angle measures to...

A: Only one obtuse scalene triangle exists for the given dimensions. Use the sine formula to determine ...

Q: Fill in the blank/s: The function f(x) = logb x is the __________ function with base  _____________

A: The function fx=logbx is the __________ function with base  _____________.

Q: Write the partial fraction decomposition of the rational expression.

A: x2x-12x+1 It can be written as, x2x-12x+1=Ax-1+Bx-12+Cx+1  →1 On simplification, we get ⇒x2x-12x+1=A...

Q: Evaluate or indicate that the root is not a real number √36 ?

A: 36

Q: Prove that the graph of the equation Ax2 + Cy2 + Dx + Ey + F = 0 is one of the following (except in ...

A: Given, The graph of the equation is, Ax2+Cy2+Dx+Ey+F=0 Let A=1, C=0 so that, x2+Dx+Ey+F=0 By complet...