Let z1 = rie01 and z2 = rzei02. || Show that |21 + z2| = Vrỉ + r + 2r1r2 cos(01 – 62). (d)

Q: Assume a quantity decreases by 5.1% in 7.5 hours.What is the half-life of the substance?

A: Given that a quantity decreases by 5.1% in 7.5 hours.

Q: A company charting its profits notices that the relationship between the number of units sold, x, an...

A: Suppose that the number of units sold is x and the profit is p. Given that the relation is linear so

Q: Show that the diagonals of a rhombus (parallelogram with sides of equal length) are perpendicular.

A: Show that the diagonals of a rhombus (parallelogram with sides of equal length) are perpendicular

Q: please solve and show your work

A: Two end points of the line segment are: (0,4) and (-5,-3)

Q: How do you find equations for spheres in space? Give examples.

A: How to find equation of spheres in space? Give example

Q: Find the point on the curve y = ex where the curvature is greatest.

A: Given: Find the point on the curve y = ex where the curvature is greatest.

Q: A projectile is fired at a speed of 840 m/ sec at an angle of 60°. How long will it take to get 21 k...

A: Given:

Q: x3 :/ V? +3 dt then If f(x) = 3

A: According to the given information it is required to calculate the definite integral of the followin...

Q: Find two solutions of each equation. Give your answers in degrees  (0° ≤ θ < 360°)  and in radian...

A: Part (a) The expression is sin(θ) = (√3)/2. 

Q: 2x and the interval - 1<x<1 of the x-axis. Find the area, A, of the region between the curve y = 1+x...

A: Find the area of the region bounded by the curves

Q: Please solve and show your work

A: Given:

Q: Suppose r(t) = (et cos t)i + (et sin t)j. Show that the angle between r and a never changes. What is...

A: Given information:

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the coordinate planes. Describ...

A: The given lines are,

Q: Let y(x) = ax2 + bx + c. The function y(x) is not invertible, however, like the function f(x) = x2 w...

A: Given:

Q: 2.4.6 Use the graph of the function to determine the indicated limit, if it exists. Ay lim f(x) 4- S...

A: To find: -

Q: 1.15. Show the following vector identities by writing each vector in terms of Cartesian unit vectors...

A: (f)Let

Q: #30

A: Given the function:

Q: Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets ...

A: We first have to find  the line through the origin perpendicular to the plane 2x - y - z = 4Directio...

Q: is the line x = 1 - 2t, y = 2 + 5t, z =-3t parallel to the plane 2x + y - z = 8? Give reasons for yo...

A: Given,

Q: a. Cauchy-Schwartz inequality Since u .v = |u || v| cos u, show that the inequality | u . v|&lt;= |u...

A:

Q: Show that if u is a unit vector, then the arc length parameter along the line r(t) = P0 + t u from t...

A: It is known that,

Q: What are the vector and parametric equations for ideal projectile motion? How do you find a projecti...

A: The vector equation and the Parametric Equation for ideal projectile motion :

Q: Which of the following are equations for the plane through the points P(1, 1, -1), Q(3, 0, 2), and R...

A: First find PQ and PR , two lines on the plane

Q: Find the one-sided limit ( if it exsit)

A: The given limit is,

Q: 27. Points A, B, and P are collinear points along a hillside. A blimp located at point Q is directly...

A: Given that Points A, B, and P are collinear points along a hillside. A blimp located at point Q is d...

Q: Is the attached question true or false? Please explain.

A: To show the below property is true or false:

Q: I don't get it

A: Given

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8 interse...

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become: 

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=3f(x)+1x. If the...

A:  Derivative of a function using the formula f′(x)=3f(x)+1x and f(3)=6. We know that approximate valu...

Q: Evaluate the surface integral. (4x + 4y + 4z)dS Where S is the parallelogram with parametric equatio...

A: To evaluate this integral, first change the variables to the parameters given in the surface as.

Q: In Exercises 1–4, let u = &lt;-3, 4&gt; and v = &lt;2, -5&gt;. Find (a) the component form of the ve...

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: Show that squares are the only rect-angles with perpendicular diagonals.

A: Consider u and v as the sides of the rectangle.The diagonals are perpendicular.Consider the diagonal...

Q: Find the limit "L" The prove how the limit is "L"

A: Given function is

Q: Can someone show me how to get the top interval of this problem. I think the integral is u^3, but I ...

A: Express x in terms of u

Q: If u * v = u * w and u ≠ 0, then does v = w? Give reasons for your answer.

A: GivenIf u * v = u * w and u ≠ 0, then does v = w? Give reasons for your answer.

Q: 52. If F(x) = ƒ(t) dt, where f is the function whose granhis given, which of the following values is...

A: Given

Q: In Exercises 33–34, find the distance from the point to the line. 33. (2, 1, 3); x = 2 + 2t, y = 1 +...

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question...

Q: In Exercises 1 and 2, graph the curves and sketch their velocity and acceleration vectors at the giv...

A:

Q: #17

A: Given:

Q: Find h'(t) if h(t) = %3D t1/2 1617 h'(t)=

A: Given:

Q: Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

A: WE know that equation of line through (x1,y1,z1) and parallel to vector ai+bj+ck is 

Q: The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $470 per person p...

A: Given:Let x be the number of passengers above 20.

Q: A rectangular box is to have a square base and a volume of 40 ft3. The material for the base costs 3...

A: Given that length = x, width = x, height = ySo volume= length * width * height = x*x*y = x^2*yGiven ...

Q: How do you define N and k for curves in space? How are these quantities related? Give examples.

A: Calculation:

Q: Find the limit, if it exists. sin(8x) lim х

A: The given limit to calculate is

Q: The graph of (x/a) + (y/b) + (z/c) = 1 is a plane for any non-zero numbers a, b, and c. Which planes...

A: The graph of given plane is,

Q: A manufacturer has a monthly fixed cost of $36,000 and a production cost of $7 for each unit produce...

A: Part a)Formula for profit function:

Q: How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200-N ...

A: given How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a ...

Q: please solve and show your work

A: The given points are

Q: 2.3.54-Setup & Solve Find the following limit or state that it does not exist. Assume k is a fixed n...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...