16: Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the Hyperbola y^2-16x^2=1.

Foci

Vertices:

Eccentricity, e=

Length of latus rectum=

Step-by-step explanation:

We are given that

The equation of hyperbola is along y-axis because y is positive

Compare the equation with

(Along y-axis)

We get

a=1, b=1/4

Therefore,

The coordinates of foci=

The coordinated of vertices=

Eccentricity, e=c/a

Length of latus rectum=

Length of latus rectum=

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

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

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

The answer is in the image 

The answer is in the image 

The solution is given in the image below

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.