Prove that 1/sin^2A -1/tan^2A= 1

Step-by-step explanation:

Hint: 1 - Cos² A = Sin² A

To prove that:

LHS =

Using basic trigonometric identity,

Using trigonometric identity:

      = 1

      = RHS

LHS = RHS

Hence proved.

To prove that:

LHS =

Using basic trigonometric identity,

Using trigonometric identity:

      = 1

      = RHS

LHS = RHS

Hence proved.

1.

The annual net cost savings promised by the automated welding machine

Annual Costs savings in replacing 6 welders $108,000

Reduced Material costs $6,500

Total annual Costs savings = $114,500

Note there is a $3,000 annual maintenance cost that will then be taken off this savings amount to make up the Annual Net cash inflow of $111,500

2

A. The Net Present value is $72,227. Kindly refer to the attached document for the clear presentation

B. The project should be accepted because it delivers a positive NPV. Meaning the net benefit outweighs the cost of owning the new Assets.

3.

The Discounted net Cash flow for the 6 years (aside the initial outlay) is $402,227.

Annually this comes to $67,038.

The benefit the business gets in the switch to the automatic welders is approximately $67,038 annually.

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The answer is in the image 

The total nom of  code that can be used is equal to 5+3 = 8

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg