2. Find an equation of the sphere satisfying the given conditions. a. It is concentric with the sphere x2 + y2 + z2 – 2y + 8z – 9 = 0.

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: Solution :let, side of square=xArea of square=Adxdt= 8 cm/secA= 36 sq. cmA=x2    Area of square=side…

Q: Given the function below find the value of f(-4). * if x -5 2x² + 1 f(x) = O -67/16 None of these O…

A:

Q: S sin 2x sin 4x dx 7.

A:

Q: What is the edge of a cube whose volume is equal to that of a rectangular bar measuring 100 cmlong,…

A: Let the edge length of the cube be 'a' units

Q: Write the equation of the tangent line to the graph exy + cos v = + COS at He %3D point (-0.3, 2.12)

A:

Q: Find the value of x for which the value of the function f(x) = x +3x2 - 2 is minimum? %3D Answer:…

A:

Q: a2f_ If f(x, y) = xe?y + 6xy, then is given by: dydx O 2xe?y + 6 None of these e2y + 6 2 xe?y + 6 2…

A: We have to find the derivative

Q: Differentiate implicitly to find dy Then find the slope of the curve at the given point dx 8x-9y…

A: topic - implicit differentiation

Q: After a rest of 20 minutes the hikers ascend into a steep climb, still following the trajectory of…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: Use the position function s(t) --4.9+ 650, which gives the height (in meters) of an object that has…

A:

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 3y2 + 2, (3, 5) Vf(3, 5) =

A: Given: fx,y=2x+3y2+2 ; Px,y=3,5   As we know that; The expression for the gradient vector.…

Q: Find Ay and f'(x)Ax for y = f(x) = 6x°, x = 4, and Ax = 0.06. Ay = (Round to four decimal places as…

A:

Q: 1 a. f(x)3D 4 b. g(x) = - X c. h(x) = 3 -

A:

Q: S4tan3 (пх + 1)dx

A: ∫ 4tan3πx+1dx=4·∫tan3πx+1dxLet u=πx+1.=4·∫tan3u1πdu=4·1π·∫tan3udu=4·1π·∫-1+sec2utanuduLet…

Q: Graph the equation below. Choose the correct graph. y = 5.5* OA. O B. OC. OD.

A:

Q: Assume that C(x) is in dollars and x is the number of units produced and sold. For the total-cost…

A:

Q: Let the region R be the area enclosed by the function f (x) = e® + 2 and g(x) = 6x + 3. Write an…

A: Given: f(x) = ex +2,    g(x)=6x+3

Q: u = (-2, 0, -6), v = (-3, 7, 8) %3D

A: answer is in step 2

Q: Several statements about a differentiable, invertible function f(r) and its inverse f-(z) are…

A: Note: As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: dx Example: Evaluate 3 + sin x + cos x

A:

Q: dx 11 J V64x2 - 121 8 11 18 – In-x+ 8 3 A +C 64x2 – 121 B In 1 V64x2 - 121 +C 11 In V64x2 - 121 +C…

A:

Q: Which of the following is not equivalent to cos(0 + 0)? cos 8 cos 0- sin 60 sin 0 1- 2 sin? 0 O…

A:

Q: 13n Illustrate and find the smallest positive coterminal angle of 3.

A: We have to find smallest positive coterminal angle of -13π/3. And we have to illustrate that angle…

Q: e^x(y'-y)=2xy^2 bernoulli differential equation

A:

Q: Give the augmented matrix for the following system of linear equations. -3x1+10x2-6x3-4x4+8x5 = -4…

A:

Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

A: There is more than 1 question, as per the Q&A guidelines, We are answering the 1st question. If…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A:

Q: Write an equivalent exponential equation. 2 log 8 4= 3 The equivalent exponential equation is (Type…

A:

Q: A solid in the formof a cube of edge 12 cm. is melted and formed into three smaller cubes of…

A:

Q: (w°t wz? -z) dw +(z² tw² -w) dz= 0

A: Let's find.

Q: 2) y TC cos 30 1 b: Period: a: d: Phase Shift: C:

A: We have to find a,b,c,d, period and phase shift.

Q: Which of the following is TRUE if sin 3A = cos 6B, where 3A and 6B are complementary angles? * A + B…

A:

Q: Which of the following is not equivalent to sin 0?

A: We are asked to find which is not equivalent to sinθ

Q: 1. The Fibonacci sequence is given by the recurrence relation a, = a,-1 + a,-2; a, = 0, a, =1. Write…

A:

Q: Pharmaceutical theft has been rising rapidly in recent years. Experts believe that pharmaceuticals…

A:

Q: xdx Evaluate (x²-2)5

A: We have to use rules of integration to solve the question

Q: Consider the function y = 5cos(x). What are the exact values of C in the interval [0, 2pi] such that…

A:

Q: dx Assume that x= x(t) and y= y(t). Let y =x +4 and -5 when x= 1. dt dy Find when x= 1. dt

A:

Q: hFind the gradient of the function at the given point. W = x tan(y + z), (19, 4, –1) Vw(19, 4, –1) =

A:

Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 5, -1) Vw(9, 5, -1) =

A: Explained below

Q: Shasta was working at differentiating a function p(x) and they found that p'(0) = In Unfortunately,…

A: We will determine the value of the constant a as following.

Q: The shaded region shown below is bounded by the functions f(x) = -4x? + 10 and g(x) = x + 6 and the…

A: area

Q: What is the magnitude of the vector cos 0 i + sin 0j+ 1? 01 O2

A:

Q: r(3x² x + 8x – 12)d: .3 x' +7x +12x

A: Given:          ∫3x2+8x-12x3+7x2+12xdx Factor the denominator:       =∫3x2+8x-12xx+3x+4dx The form…

Q: Find the general form of f if f'(x)= 9f(x). f(x) = ]

A:

Q: a) Find the degree 4 Taylor polynomial T(x) for the function f (x) = 2e" centered at the point a 3.

A: Given that fx=2ex  centered at the point a=3we defined the nth taylor polynomial centered at x=a Tn…

Q: A reservoir is shaped like a square prism. If the area of the base is 225 sq. em., how many liters…

A: Given: Area of the base = 225 cm2

Q: Calculate L4 for f(x) = 24 cos () %3D L4

A:

Q: A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting…

A: maximum volume