Applications of Differential Equations A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there are 100milligrams of the material present and after two years it is observed that 5% of the original mass has decayed. Find an expression of the mass at any time (t). 100e-2.06t 1000e-0.026£ Option 1 Option 2 100e0.026t 1000e0.026t Option 3 Option 4

Q: Let's consider the marginal cost function C' (x) = 0.02x + 28, where x represents the level of produ...

A: Given c'(x)= -0.02x+28

Q: Evaluate the triple integral of (1 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 4, ...

A:

Q: Given the polor coordinate U, write it as a rectonguicr coordinate, anc write three other coordinate...

A:

Q: The shaded region shown below is bounded by the functions f (x) = -2x² + 0.75x + 4 and g(x) = 1.5x +...

A: The shaded region shown below is bounded by the functions fx=-2x2+0.75x+4, and gx=1.5x+2 and the lin...

Q: 5 and a is an angle in quadrant 1. 13 Suppose that a and B are angles given as follows: sin a cos B ...

A:

Q: Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the regi...

A:

Q: x+ 400р %3D2500

A: answer of given question is in step 2

Q: (iv) Consider the arrangements in a line of all the letters of the word ISOLATION (a) Calculate how ...

A: Here, the given word is ISOLATION which has 2 Is and 2 Os.

Q: 2n tan h 3x 3-) Arc sin tanh X

A:

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the ar...

A: Solve the following

Q: Consider the function 1 1- x4 Write a partial sum for the power series which represents this functio...

A: Consider the function

Q: Find the area of the surface generated by revolving the curve y=- 24 .Osxs/6. about the x-axis.

A: area = ∫06 ydx area = ∫06  x3dx/24 area = [x4/96]60 area = 6*6/96 - 0 area = 3/8

Q: Sondere ebch exprO sSn to G sngle logarithm 3. 2. 3. + log qfu + lay a to 3.

A:

Q: Determine the equation of the tangent line to the curve f(x) = sin4x – cos²x at x = Show all your st...

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 9. OShow My Work (Opti...

A:

Q: Use the method of variation of parameters to find a particular solution of the differential equation...

A: For given differential equation we have to find the particular solution                   4y"- 4y'+y...

Q: Determine the equation of the line that is tangent to y = elan"(2x) at x = 8

A:

Q: Determine whether the two functions are inverses. -5 -5-2x w (x) = and z (x) x+2 dz(x) = O The two f...

A: Given: w(x)=-5/(x+2) and z(x)=(-5-2x) /x. 

Q: If an open box is made from a tin sheet 9 in. square by cutting out identical squares from each corn...

A:

Q: 3 dx Vェ(エ+1) x(x +

A: The given integral is: I=∫0∞3x(x+1)dx...(1)

Q: 4. y = 5 cos 4x, 3rd derivative 5. y = 3 tan 3x, 2nd derivative %3D 5. y = 6 csc x, 2nd derivative

A:

Q: (v®) do 1 sec J2

A:

Q: Of all rectangles with a perimeter of 32, which one has the maximum area? (Give the dimensions.) The...

A: To find the length and width of the rectangle that has perimeter of 32 with maximum possible area. L...

Q: Sketch the region enclosed by the given curves. y = 3x, y = 3x

A:

Q: -3a 36)-216 3- 2 3p x²-e3x. 時le). ex² =e12

A:

Q: Write the standard form of the quadratic function whose graph is the parabola shown. (Let x be the i...

A: In this question we have to find the equation of parabola.

Q: The function f(x) = 2x + 1 is defined over the interval [2, 5]. If the interval is divided into n eq...

A:

Q: ine the limit of the sequence or show that the sequence diverges by using the appropriate Limit Laws...

A:

Q: Find the average value of f(x) = over the interval [1, 3]. %3D (2x² + 3)²

A: The objective of the question is evaluate the average value of the given function.

Q: (k) / te'dt (1) / e' sin(t) dt (i) e2t dt dt 1+ t2

A:

Q: Evaluate the integral. 2V3 dx 4 V 16 – x2

A:

Q: Determine if the relation defines y as a ône-to

A: The given graph is: To determine if it is one-to-one.

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

A: Use property of polynomial for evaluating the integral.

Q: Evaluate the integral: S (3x-3 + 3)dx Choose the most appropriate answer. ○ 응z + 3z + C O 2x5 + 3x +...

A: ∫xndx=xn+1n+1+C , C is a constant and for any real number n.

Q: Determine the limit of the sequence or show that the sequence diverges by using the appropriate Limi...

A: We can solve this as follows:

Q: S tam x &x 1.

A: Since we are given with the multiple number of question answered according to the guideline.

Q: 2. Find the equation of tangent and normal for the curve xsin2y = ycos2x at

A:

Q: Find the particular antiderivative that satisfies the following conditions: dy/dx=6x+8x√3;y(1)=5.dy...

A:

Q: Show that the sequence {xn}: cost -dt is a Cauchy sequence. t2

A:

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded b...

A:

Q: xydy – (y² – 3x²) dæ = 0

A:

Q: Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the curves...

A:

Q: Ted the of eae hee an t a

A:

Q: Suppose f(x) = [ 6t² /1+t° dt .

A:

Q: (* + 2)(r – 8) f(x)=- 6)(s + 4) x =-6, x= 4 h(x)3=

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: x2 + x + 1 xp Jo (x+1)2(x + 2) 2]

A:

Q: Find the general solution of'the following differential equation. + 13y+ 42y 0 NOTE: Use C, and cg a...

A:

Q: How many numbers are there between 500 and 1000 which have exactly one of their digits as 8? a.153 ...

A: Let's find. 

Q: 3. - +- 9 + - 8 10 7 9 +

A:

Q: Find the particular solution of the differential equation that satisfies the initial condition(s). f...

A: