1 Products Evaluate the product, and write the result in une 1orm a + bi. 31. (6 + 5i)(2 – 3i) 32. (-2 + i)(3 – 7i) 33. (2 + 5i)(2 – 5i) 34. (3 - 7i)(3 + 7i) 35. (2 + 5i) 36. (3 – 7i)

Q: Integration techniques Use the methods introduced evaluate the following integrals.

A: Given:∫dxx2-x-2

Q: In which form first-order linear differential equation can be written ?

A: A general first-order differential equation is given by the expression dydx+Pxy=Qx, where Px and Qx ...

Q: Solve the equation sin 2x = √3 sin x on the interval [0, 2π). Use exact values where possible or giv...

A: We have to solve the equation: sin 2x=3 sin x in the interval x∈[0, 2π) We know the identity, sin 2x...

Q: Curvature for y = ƒ(x) Find the curvature function of the following curve. ƒ(x) = ln cos x

A: We have to find curvature of the function: fx=lncos x We know the formula of curvature of function: ...

Q: Jacobians in three variables Evaluate the Jacobians J(u, ν, w) for the following transformation. x =...

A: We have x=v+w, y=u+w and z=u+v. Now, we will find partial derivative  with respect to each variable....

Q: A system of equations consists of a quadratic equation whose graph opens up and a quadratic equation...

A: Sketch the graphs as shown below. Figure 1: Figure 2: Figure 3:

Q: Given that u = sin-1 12 /13 , evaluate cos u, tan u, cot u, sec u, and csc u.

A: given that  u=sin-11213

Q: dy in term of x and y if Find dx (a) y +6x=x² (b) y-cos y=x+sinx (c) x² +4xy+3y² =3 %3D (d) 3y +2y+x...

A:

Q: Graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x...

A: Given information: fx=x2gx=x2+1

Q: Verify the identity: sin(α + β) sin(α - β) = cos2 β - cos2 α

A:

Q: Suppose a fellow student claims that the equation sin(a + b) = sin a + sin b is an identity. He's wo...

A: A right angle triangle having angles a and b is shown below.  

Q: Use the definition of the limit of a function of two variables to verify the limit.

A: We have to verify the limit: limx, y→1, 0x=1 According to limit value, x, y→1, 0 therefore, x=1y=0

Q: . Profit A small-appliance manufacturer finds that the profit P (in dollars) generated by producing ...

A: Given Profit function is P=110x300-x where, x is the number of ovens produce per week  0≤x≤200

Q: Solve the initial value problems d2y/dx2 = 2 - 6x; y'(0) = 4, y(0) = 1

A: We have to solve the initial value problem: d2ydx2=2-6x; y'0=4,  y0=1 Integrating both sides, ∫d2ydx...

Q: The figure shows the graph of f(x) = ex. Use transformations of this graph to graph the function h(x...

A: Graph of a function: At first we will draw f(x)=exThen we will draw f(x)=ex-1+2. The graph of the fu...

Q: Solve each equation for  x.   In (In x) =1

A: From the given data:

Q: Factor each trinomial, or state that trinomial is prime: x2 + 8x + 15?

A:

Q: Convert the polar equation 4r cos θ + r sin θ = 8 to a rectangular equation. Then use your knowledge...

A: Given polar equation is 4rcosθ+rsinθ=8. In rectangular coordinates, coordinates are given as: x=rcos...

Q: Factor completely, or state that the polynomial is prime. 2x2 - 2x - 112

A: the given polynomial is 2x2-2x-112 we have to factorise the given polynomial completely or state tha...

Q: Differentiate the function.

A: Given

Q: Use the Trapezoidal Rule and Simpson’s Rule to approximate the value of the definite integral for th...

A:

Q: In Exercises 47-60, solve the initial value problem.

A: we have to solve the initial value problem dzdt=t-32    , z(4)=-1

Q: Integrate by parts:

A:

Q: Write each number in decimal notation without the use of exponents. 9.2 x 102

A: Given number is 9.2×102. Given number can be written as: 9.2×102=9.2×100=9210×100=92×10=920=920.0

Q: Define what linear first-order equation forms?

A: Linear differential equation: a linear differential equation is a differential equation that is defi...

Q: Use the guidelines of the section to make a complete graph of ƒ. ƒ(x) = x3 - 147x + 286

A: Graph : ƒ(x) = x3 - 147x + 286 At first we will draw a graph of f(x)= x3   

Q: If v = 7i + 3j and w = 4i - 5j, find the vector v - w

A: If v = 7i + 3j and w = 4i - 5j, find the vector v - w

Q: 45. Consider the transformation T : P2 → R? defined by p(0) T(p(1)) = [P): For example, if p(t) = r²...

A:

Q: Use the Table of Integrals toevaluate the integral

A: Given information: ∫12x2-3x2dx  

Q: Find the area of the region between the curve y = 21-x and the interval -1≤ x ≤ 1 of the x-axis.

A: Given: y=21-x, -1,1

Q: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) = ...

A: Consider the provided information, fxx0,0=5,fyy0,0=3  and fxy0,0=-4 The Second Derivative Test to de...

Q: A marathoner ran the 26.2-mi New York City Marathon in 2.2 hours. Show that at least twice the marat...

A: Calculate the average speed as below. Average speed=26.2m2.2h=11.909 mph