A capacitor has two parallel metal plates measuring 0.45 m² each. The distance between the plates is 1 cm in free air. If a dielectric material whose permittivity is 4 and 5 mm thick is placed in the uppe plate, leaving the air gap between the bottom plate and the dielectric, what is the capacitance of th capacitor?

Q: Find the radius of convergence for the series 3 n³ xn 3n OR=3 O O OR= 8 n=1 R = R= - الله R = 1 8

A:

Q: Find the exact values of inverse trigonometric expressions for Parts a to c in radians. Sketch the…

A:

Q: Find the second derivative of f(t) = [(1 + 3)¯¹ + 1]¯¹

A:

Q: dy Assuming - 2x³ + 8y² + 6xy = 0 defines y as a differentiable function of x, use the theorem dx dy…

A:

Q: x= t2 - 4t y= 2t3 - 6t what is the minimum and the maximum point?

A:

Q: 2. a) Write sin(3-1) in the form of a + bi. b) Find all the values of (3)-in

A: Concept: Simplifying expressions: Expressions are mathematical statements with at least two terms…

Q: Consider the series. 2 3 4 10 (¹) + ( )² + ( )² + ( )* +-- ∞ This series can be written as a…

A:

Q: x² dx -1 (2x²+2x+1)² sº₁

A: We have to evaluate the integral. ∫dxa2+x2=1atan-1(xa)+c

Q: Physical Applications of First-Order Differential Equations A body of unknown temperature is placed…

A:

Q: lim X→+∞ 5 In³ x 2 X²

A: Let's evaluate limit.

Q: X f(x) =< Q 14/15 7 x + 1 3 ;0≤x≤2 ;2≤ x ≤3 5 Tov Then what is the result of 3 (fx) dx 1

A:

Q: 2. Find the eigenvalues and eigenvectors of A = 2 1 0 1 2 1 1 2,

A: Given

Q: 4) Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find angle C

A:

Q: Find the center of mass of a thin plate of constant density & covering the given region. The region…

A: Let's find center of mass.

Q: how did you get the final answer??

A: Let's find value of rate of change of slope with respect to x.

Q: What is the volume of the solid generated by revolving about the x-axis, the region bounded by y =…

A: The given problem is solved below in detail.

Q: (2x²² +ex) dx + (x² + 1) = "² dy (x²-y) dx x dy

A:

Q: Find L(sin 2t cos 2t) inned with CamScanner

A:

Q: e²x-2x-1 x² f(x) = a) lim f(x) x⇒0+

A: Use limit concept

Q: A bolt is being loosened by a 40 cm wrench. The torque in this situation has a magnitude of 12 J and…

A:

Q: Find the equation of the tangent line to the function f(x) = 5* at x = 4. (Use symbolic notation and…

A:

Q: 1. Consider the differential equation y" - ry - y = 0 a) Determine two linearly independent power…

A: answer is in next step

Q: [x³√₁-x² x2

A:

Q: 4. Determine whether the following statements are True or False? y = f(x)

A:

Q: Find the total area of the shaded regions. C 5 y= ex 4 3- 2- 1- 0- -1- -2- -3 ✪ Q G The total area…

A:

Q: Find the equation for the line tangent to the curve 2exy = x + y

A:

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

A:

Q: The area of the region bounded by the curve y = x² and the line y = 16 64/3 256/3 128/3 32/3

A: Given :   y=x2 y=16

Q: f) y = sin-¹ (x² - 1)

A:

Q: 1. Evaluate the given integral Q. Q • S S (² (x - y) dx dy -

A: Evaluating the given integral

Q: Find the equation of the tangent line to the graph of the function f(x) = sin (3/7) at the point…

A:

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of dy /…

A: Question- Assuming that the equation below defines y as a differentiable function of x, find the…

Q: The displacement (in meters) of a particle moving in a straight line is given by s= t2 - 5t + 16,…

A: We want to find average velocity.

Q: 27777 Memo No. Date 1 Mo Tu We Th Fr Sa Su Solve the following 1)√(x² + 2x²) dx if (cosx - sinx) dx

A:

Q: дz дz Suppose z is a function of r and y and tan(√x + y) = e²². Determine and 3x ду

A: given function tanx+y=ez2

Q: a. lim+ 2x 3x²

A:

Q: Let f be continuous on [a,b] and differentiable on (a,b). Prove that if f'(x)>0 for all x=(a,b) then…

A:

Q: Find the interval of convergence of the series xn Σ n8" n=1

A:

Q: Use the series to evaluate the limit tan-¹ y - siny lim y→0 y³ cosy

A: Expand series and solve

Q: 3. A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing when…

A: We know that volume of the balloon is V=43πr3                          (1) Given that Spherical…

Q: 17. What is the amplitude of the graph y = -4sin (x - 2)? The amplitude is. units. 04 02 O 2T O K|N…

A: For the equation  y=A sinBx+C+D   A-  Amplitude   B- Frequency   C- Horizontal shift   D-  Vertical…

Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e5xy = sin…

A: Given query is to find the derivative of the expression.

Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let the length of a diagonal is = d1=x m So the length of the other diagonal = d2=(x+2) m. Given…

Q: Evaluate the definite integral. 8 (2n-²-n-³) dn 8 (2n-²-n-³) dn=[ 4 (Type an integer or a simplified…

A:

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Evaluate the following integrals: (show solution) a x² +2 b.) 1 x+1 x+√x c) f(sec x d.) e 4x 4x+1 x…

A:

Q: TYPEWRITTEN ONLY PLEASE. ILL UPVOTE ONLY IF TYPEWRITTEN, COMPLETE, AND CORRECT. DONT ANSWER IF YOU…

A: To differentiate the functions.

Q: Q/Use Lagrangian polynomial to find f'(2.1) from the following table x 1 2 3 17 22 f(x) 10

A:

Q: The half life of a decaying substance is the amount of time it takes for the substance to reduced to…

A: Let us assume it takes n half-lifes to reach 10mg

Q: dx 1. S √3x²–2x+1 2 2. √₁² √√x² - 4x + 8

A: