Algebra Answers

It took nick two-thirds of an hour to complete his mathematics homework on Monday, one fourth of an hour on Tuesday.how many hours did it take him to complete his homework altogether?

What is asked?

What are the given facts?

What operation to be use?

What is the number of sentence?

Solution

Answer

 A boy is swinging on playground exercise gym. He swings through an arc of 1 m on his first swing. On each successive swing, he swings through an arc 70% of the previous length.

a) Show that the total distance the boy swings in his first n swings is 10

given by S  3 1 0.7 where n 1,2,3,.... nn

Hence, find the total distance travelled by the boy after six swings.

The volume of Alicia's swimming pool is 2,500

2,500 cubic feet. It has a pump that filters the water at a rate of 40

40 gallons per minute.

How can Alicia determine how long it will take the pump to filter all the water in the pool?

1. A lifeguard has been given 500m of rope to enclose a rectangular swim area designated for toddlers and children. The swimming area will be accessed from the beach; therefore only three sides must be roped in. Determine the dimensions of the rectangle that would maximize the swimming area.

Represents this rational equation through table and graph. Identify whether the graph forms a straight line or a curve.

P(x) =x²+1/x+1

Let z, w ∈ C. Show |z + w| =

p

|z|

2 + 2Re(zw) + |w|

2 =

p

|z|

2 + 2|z||w| cos(θz − θw) + |w|

2 and

|z + w| = (|z| + |w|)

s

1 −



√

2 sin([θz−θw]/2)

|z|/|w|+

√

|w|/|z|

2

, if z 6= 0 and w 6= 0.

f(x)=4x+2 and g(x)=3x-1, find (f-g)(4)

Two water tanks at PPV Aman and PPV Damai consists of x and 3000 litres of water, respectively, on the first day.

a) Subsequently, y litres of water is used from the tank in PPV Aman everyday. Volume of water left at the end of 18th day is 2520 litres and the tank will be expected empty by the day 81. Find the value of x and y. [8 marks]

b) The usage of water in PPV Damai constantly 30 litres per day. Find the day for both, tank at PPV Aman and PPV Damai, has the same amount of water. [4 marks]

Suppose C and D represent two different school populations where C > D and C and D must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary.

A: (C + D)²

B: 2(C + D)

C: C² + D²

D: C² − D²

(10 points)

All outbound packages from a distribution center are routed to a person for packing. 60% of packages are easy and can be packed at a rate of 45 packages per hour. The remaining packages are more difficult and can only be packed at a rate of 12 packages per hour. There is no specialization, packages are randomly assigned to any available packer. What is the average packing rate for each packer?