Check that the point (−1, 1, 3) lies on the given surface. Then, viewing the surface as a level surface for a function f(x, y, z), find a vector normal to the surface and an equation for the tangent plane to the surface at (−1, 1, 3). 2x² − 3y² + 2z²: = 17

Q: The total cost function for a product is C(x)=700ln(x+100)−100, where x is the number of items…

A:

Q: Solve the given equation 3e*+2 = 75

A:

Q: classify and sketch the surface given by x2+2y2+z2-4x+4y-2z+3=0 (indicate the vertex coordinate)

A: Here we have given a surface equation as below:  x2+2y2+z2-4x+4y-2z+3=0 The surface given by the…

Q: Solve the given differential equation by separation of variables. 1 y In(x) dx = (v + ¹)² dy x³ln(x)…

A:

Q: Use the chain rule to find and, where First the pieces: дz ?х ?х дя ду Əs = дz Ət || = And putting…

A:

Q: The growth of a colony of bacteria can be described by exponential growth. If the colony initially…

A: Pt=P0ert⇒P0=initial population⇒r=Growth rate⇒Pt=Population at time t⇒t=time in hours

Q: 7. (1 point) An object starts from rest at the point P(1,2,0) and moves with an acceleration of a(t)…

A: Given an object starts from rest at the pont P(1,2,0) and moves with an acceleration of a(t)=j+2k.…

Q: List the points in the xy-plane, if any, at which the function z = 8 + √√(x − 6)² + (y + 7)² is not…

A:

Q: f ₁ f(x) dx = 15, 0 these values to evaluate the given definite integrals. [ f(a) da = -10, [² g(x)…

A: We have to find the value of given intregal part.

Q: If you want to earn 15% annual simple interest on an investment, how much should you pay for a note…

A: Simple interest Formula is given as  SI = P×R×t100 Where P is the principal amount  R is the rate of…

Q: If z = (x + y)e and x 2t and y = 1 — t², find the following derivative using the chain rule. Enter…

A: Function is  z=(x+y)ey, x=2t, y=1-t²

Q: Find the distance from the plane 6x+y+7z=54 to the plane 6x+y+7z=30 The distance is d= (Type an…

A: given planes are 6x+y+7z=54 and 6x+y+7z=30

Q: Please solve this 100% Correctly and ASAP. Thank you Find the slope of the tangent to y = 5-x at the…

A: Given function is y=5-x We have to find the slope of tangent at y=0.2

Q: etermine the moment of force F about point A. = 260 N swer: M₁ = (i 0.55 m 0.50 m i+i j+ i k) N-m

A:

Q: A plane has parametric equations x = 2-s + 3t = 4 + 3s-t y z = -5 + 2t where s, t E R a) Find the…

A: We need to find the scalar equation of the plane from given parametric form and find the value of k.

Q: Let Find e such that lim f(t) exists. t 2 The cis f(t) = 4 1 2t t + c for t 2

A:

Q: Let a = (0, 1) and b = (4, -4). Show that there are scalars s and t so that sa + tb = (16, −17) You…

A: We have, a = ⟨ 0, 1 ⟩  b = ⟨ 4 , -4 ⟩ sa + tb =⟨ 16 , -17 ⟩

Q: Calculate interval of convergence for series.

A: We use ratio test to find the interval of convergence.

Q: 2. For the vectors a = (1, 2, 3), b = (2, 1, 3), and c = (1, 1, 0), show that the following is true:…

A:

Q: If you want to earn 15% annual simple interest on an investment, how much should you pay for a note…

A: It is given that the annual simple interest on the investment is 15%.  also the amount after 3…

Q: A meteor follows a trajectory r(t) = (8,6,5) +t(7,6, -2) km with t in seconds, near the surface of…

A: A meteor follows a trajectory rt=8,6,5+t7,6,-2

Q: Solve ABC. Round the lengths of sides and measures of the angles to 1 decimal place if necessary. A…

A:

Q: 2. Given z(x, y) = x².3√/y+ex-y + 5 find oxoy²

A: Question 2)  Given function  z( x , y ) = x2.y3 + e4x-y + 5x2∂3z∂x∂y2 = ?

Q: volume is described as follows: 1 the base is the region bounded by y = 8-2² a and y = 0 .every…

A:

Q: [b] Take a limit of the standard slope formula, as shown below, to find the instantaneous rate of…

A: The given function is gx=x2+2x. To find the derivative at x=2 and the equation of tangent line at…

Q: A tank, shaped like a cone has height 4 meters and base radius 3 meters long. It is placed so that…

A: This is question of calculus. Here cone is given  And water in cone given  We have to find work for…

Q: 4. Check to see if the equation is exact. If so, Solve and check: {Exact} (2e²x + 2xy) dx + (x² −…

A:

Q: f(x) = 2; ; хо = -3

A:

Q: A plane has parametric equations x = 2-s + 3t y = 4 + 3s-t z = -5 + 2t where s, t E R a) Find the…

A: Given equation  x=2-s+3t y=4+3s-t z=-5+2t

Q: Find the equation of the tangent plane to z = e²+x+x³ + 10

A:

Q: Yes or No? If No, give a reason. Let f be a function. 8 and f(8) = 8? (a) Is it possible that f(7)…

A:

Q: pls solve within the time given. and make sure it is 100% correct thanks, Determine the concavity…

A:

Q: A curve in polar coordinates is given by: r = 7+2 cos 0. Point P is at 0 = 16 14 a.) Find polar…

A: We have,    r = 7 + 2 cos θ   Point P is at θ = 16π/14

Q: 3. A rectangular picnic area of 8000 m² is being constructed by the Parks Commission along the edge…

A: Let side opposite the river denoted by x Let other side is denoted by y As we know that area of…

Q: If the velocity of a moving object is t 2 1² v (t) = 20 2 in meters per second, then what is its…

A:

Q: (a) Verify that y=tan(x + c) is a one-parameter family of solutions of the differential equation y'…

A:

Q: Find the antiderivatives. Show any substitutions. [(7x+3) dx

A:

Q: Given: (x is number of items) Demand function: d(x) = 352.8 -0.2x² Supply function: s(x) = 0.6x²…

A:

Q: Suppose that R is the finite region bounded by y = x, y=x+2, x=0, and x = 4. Find the exact value of…

A:

Q: A certain electronics manufacturer found that the marginal cost C to produce x DVD/Blu- ray players…

A: marginal cost =c = 0.04xx =DVD/Blu- ray players DVD/Blu-ray players were produced 7x +800marginal…

Q: 3. Compute the area bounded by the three leaf rose curve given by r(0)=5sin30. Compute the area…

A:

Q: Show all steps to prove the statement is true. Neatly show each step of your work to earn full…

A: Given Trigonometric expression  ( 1 - sinx )( 1 + cscx ) = cscx - sinx

Q: Solving the equation C= Bat/D-K for t, using logarithms with base a, gives you t = 108a()+K A. Dloga…

A:

Q: 2 Rewrite cosx - sin³x cosx using only one trig function. Be sure to simplify.

A: To rewrite the expression cos x - sin2x × cos x ,using only one trigonometric function, we can…

Q: The Candy Factory sells candy by the pound, charging $1.60 per pound for quantities up to and…

A: Given, px = 1.60x for  x ≤ 301.30x+k  for  x > 30  We have to find the value of  k such that…

Q: Use the chain rule to find dw dt dw dt W = In (√x² + y² + z²), x = 9 sin(t), y = 8 cos(t), z = 5…

A: W=lnx2+y2+z2 x=9 sin(t) y=8 cos(t) z=5 tan(t)

Q: .1/3 Let ƒ(x) = x¹/³, and let T₁(x) be the nth Taylor polynomial of f centered at a =

A:

Q: The equation of the line that goes through the point (5,9) and is perpendicular to the line 4x + 2y…

A: given line goes through the point (5,9) and perpendicular to line 4x+2y=2

Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Sub a drinking cup…

A: Let’s solve this problem using calculus. Let’s say the radius of the cup is r and the height is h.…

Q: 3. Which of the following statements are TRUE about how y=-4 arcsin 3 I. Vertical stretch of 4 II.…

A: Given a transformed trigonometric function, we need to write down the transformations.