Question

Question 4:

QA: once is the depth of each diver for three minutes from now
QB: in how many minutes will the assistant be 33.3 m below the surface
QC: according to the algebraic model, in how many minutes will the divers be at the same depth

Answer 1

a. Jacques will be 46.4m below the surface and his assistant will be 78.1m below the surface.

b. 10 minutes

c. 6 minutes

Explanation:

Let the equation for Justin's motion be J(x)=-13.9-7.5x (where J(x) is his distance from the surface in metres and x is time in minutes), because he starts off 13.9m below the surface and descends 7.5m every minutes.

Let the equation for the assistant be a(x)=-97.3=+6.4x (where a(x) is his distance from the surface in metres and x is time in minutes), because he starts off 97.3m below the surface and ascends 6.4m every minutes.

a.

J(x)=-13.9-7.5x

J(3)=-13.9-7.5(3)=-13.9-22.5=-36.4

a(x)=-97.3=+6.4x

a(3)=-97.3+6.4(3)=-97.3+19.2=-78.1

b.

a(x)=-97.3=+6.4x

-33.3=-97.3=+6.4x

64=6.4x

x=10

c.

when divers are at the same depth, J(x)=a(x)

J(x)=a(x)

-13.9-7.5x=-97.3=+6.4x

83.4=13.9x

x=6