The substance's amount at time t may be modeled by an exponential function. Substance X has an initial mass of 300 mg. After 10 days, only 285.5 mg remained. Write the formula for the half-life (h) of a substance. Note: The initial mass of the substance is N and the mass remaining at time t is M.

Q: x +1 Evaluate the integral | dr. x2+2x +3 1 1 (a) 4Vr2 + 2x + 3 + C 2Vx2 + 2x + 3 + C Vx2 + 2x + 3…

A:

Q: Solve Nonhomogeneous Equations - Undetermined Coefficients (D^2 + 1)y = sinx

A:

Q: dr 4.

A:

Q: Find the equivalent DE for the given family of curves All vertical parabolas

A: Find the equivalent DE for the given family of curves All vertical parabolas

Q: Find f. f '''(x) = cos(x), f(0) = 2, f '(0) = 6, f ''(0) = 3

A: Given, f'''(x)=cos(x) Taking integration on both side f''(x)=sin(x)+A…

Q: 12 x*y dx dy 12 I*y dx dy i

A: topic - double integration

Q: x+4x+3 dx 5. 24—5х2+4

A:

Q: Find the area of the shaded region. NOTE: Enter the exact answer. y = z +3 A 3.

A: Note: As per our guidelines, we are not restricted to handwritten or typewritten. We are free to…

Q: Given the differential equation y" - 6 x y' = 10 x %3D Using Reduction of Order and the letter "R"…

A:

Q: SECTION I: MATRIX OPERATIONS 2 -1 4 -0.5] -1 1.5 0.25 1.5 A = 4 C = -7 B = -3 2.75 0.1 3 |-0.5 1 0.2…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: ex - (1+ x) Use series to evaluate lim 6x2 ex-(1+x) lim %3D 6x2 (Type a simplified fraction.)

A:

Q: Activities in Logarithm dy Find the dx 1. y = In(x? – 7x) -

A:

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

A:

Q: Find the total area enclosed between y = r and y = x over the interval [-1,5]. NOTE: Enter the ezact…

A:

Q: 1- sin (t) Simplify to an expression involving a single trig function with no fractions. sin (t) If…

A: Given:       1-sin2tsin2t   We know that            cos2t+sin2t=1  then  1-sin2t=cos2t

Q: Solve for the volume of the solid generated by rotating the plane bounded by the equations below…

A:

Q: ニ1 近。 Question 2 D. O E OA 3. (A) 3. 3. (). 32 3. (C) 16. (B) zg (7) The area of the region enclosed…

A: To determine the area of the region enclosed by the graph of  y=x2+1, and the line y=5.

Q: Problem 1. Which gives the Laplace transforms of the given time-domain function? Let a = %3D 2 O…

A:

Q: Assume that the recursively defined sequence converges and find its limit. 15 a, = 1, an + 1-2+ an…

A:

Q: A car rental agency rents 190 cars per day at a rate of 31 dollars per day. For each 1 dollar…

A:

Q: The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants…

A:

Q: 5. S dx

A:

Q: e cos(2)d.z 4. Evaluate as a power series. Write out the first three nonzero terms

A:

Q: Find f. (x + 1) f'(x) = (1) = 3 %3D f(x) =

A:

Q: Q3/ Find the area of zone bounded by curves: y= x , y= 3x+8

A: To find the area of the region bounded by the given curve

Q: Find the values of a, b, c, and d in the matrix equation below. 3 4 +2 56 10 11 c d 11 12 a = b = C…

A: A detailed solution is given in step 2.

Q: Consider the curve segments: $1: yx from xto x= 3 and $2: y = Vi trom x to x= 9. Set up integrals…

A:

Q: Find the area enclosed by the curves y = y = 2 1- 9x2 2n 9. 5n 6. D

A: We need to find area.

Q: r(1) = 2 Ans: In + = de II

A:

Q: 3- f xvx2 +1 dx

A:

Q: Given the differential equation 8 x y" = Using Reduction of Order and the letter "R" to this…

A: Given query is to find the value of R.

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. p5-y y dx dy 3y

A: the solution is as follow

Q: Write the following first-order differential equations in simplified standard form. dy (5х + 3)у +…

A: We have to write the given first order differential equation in standard form .

Q: Solve the given differential equation. Ans: + cos x = c 1. y' +y2 sin x = 0 %3D y

A: The objective of the question is solving the differential equations.

Q: curves

A:

Q: For what values of a, if any, does the series shown below converge? 00 a 2 Σ n+6 n+9 n= 1 Select the…

A:

Q: Find the area bounded by the lines and curves y = x? - 2 and y = 2

A: Graph:

Q: n equation for the function that is described by the given characteristics. (Use x as the depend A…

A: Follow the procedure given below.

Q: ah4.

A: answer is in next step

Q: 8. The base of a solid is a region in the first quadrant bounded by the r-axis, the y-axis, and the…

A: The given is a half cone which has radius =4 Height =8

Q: Perform the elementary row operation R→R, on the given matrix. 3 2 1. 4 -2 -6 Resulting matrix: 1/2

A: We have to perform elementary row operation on the resulting matrix.

Q: Approximately the greatest error in calculating the hypotenuse of a right triangle from the lengths…

A:

Q: 9. Given that u = (1,5) and v = (-2,3), determine the following %3D -3u – 4v =

A:

Q: Find the following Laplace and Inverse Laplace Transform of the function. 5. f(t) = e-4t (t-cos(t))

A:

Q: Suppose that f(x) = 3iV4x?² + 2 (A) Find all critical values of f. If there are no critical values,…

A:

Q: 5. Determine the following limits. If infinite, specify ∞ or -o. If an answer does not exist,…

A:

Q: S 3+4x+3 dx x4-5x2+4 5.

A: Here, x3+4x+3x4-5x2+4=x3+4x+3(x2-1)(x2-4)⇒x3+4x+3x4-5x2+4=x3+4x+3(x-1)(x+1)(x-2)(x+2)

Q: S x2+x+1 2x2+2+x3+x

A:

Q: pyramid hip roofs (see la). As an eco-conscious person, Sharon would like to install solar panels on…

A: answer is in first step

Q: Example 11 Determine the points at which the limacon defined by the polar equation r = 3+2 sin 0 has…

A: