Q and A for the topic: General

I have a complex function I would like to integrate over. I can use two approaches and they should give the same solution. If I want to find the contour integral ∫𝛾𝑧¯𝑑𝑧 for where 𝛾 is the circle |𝑧−𝑖|=3 oriented counterclockwise I get the following: ∫2𝜋0𝑖+3𝑒𝑖𝑡⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯𝑑(𝑖+3𝑒𝑖𝑡)=∫2𝜋03𝑖(−𝑖+3𝑒−𝑖𝑡)𝑒𝑖𝑡𝑑𝑡=18𝜋𝑖 If I directly apply the Residue Theorem, I would get ∫𝛾𝑧¯𝑑𝑧=2𝜋𝑖Res(𝑓,𝑧=0)=2𝜋𝑖

Paul invites 12 friends to his birthday. He wants to give 15 candies to everyone two. The candies are sold in packs of 25. How many should he buy? packages?

13/25+7/16

The company produces a product with a variable cost of $90 per unit. With fixed costs of $150,000 and a selling price of $1,200 per item, how many units must be sold to achieve a profit of $400,000?

The supply of a good registers periodic increases. With each increase in the offer, the total receipts of the bidders increase. Indicate the correct statement: a) demand is elastic b) demand is inelastic c) supply is inelastic d) supply has unit elasticity.

f(x)= 9-x^2 find (f(x+h)-f(x) )/h

f(r) = 1/r+9 find f(x^2) + 1

Let f(x)=-1/2x+5 evaluate f(-6)

15=5(x+3)

x(squared) -8x=0

t+72/t=-17

Dano forgot his computer password. The password was four characters long. Dano remembered only three characters: 3, g, N. The last character was one of the numbers 3, 5, 7, 9. How many possible expansions are there for Dano's password?

The length of a rectangle is five more than its width. if the perimeter is 120, find both the length and the width.

Slope (7,3) and (9,5)

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 55.0 min at 100.0 km/h, 14.0 min at 65.0 km/h, and 45.0 min at 60.0 km/h and spends 20.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.

If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.

A grain silo has a height of 8.8m with a 11.4m diameter. If it is filled 0.5% of it's volume, how much grain (m^3) is stored in the silo? (0 decimal places)

An export company grants a bonus of $100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?

Mark is gluing a ribbon around the sides of a picture frame. The frame is 11 inches long and 7 includes wide. How much ribbon does Mark need?

A small box measures 10 in. by 4 in. by 6 in. high. Find the volume of the box.