The Clyde Tunnel, which passes beneath the River Clyde in Glasgow, is 762 m long. 93 fire engines can fit end to end along its length.

Q. Find the length of one fire engine, in metres, giving your answer to one decimal place?

Here is a student’s attempt at a solution, with the correct numerical result:

762 = 762/93 = 8.2 = length

(a)With reference to good mathematical communication (GMC), describe three aspects of the student’s solution that could be improved. [6] (b) Write out your own solution to this question.

In: Advanced Math

A
rectangular piece of cardboard, whose area is 170 square
centimeters, is made into an open box by cutting a 2- centimeter
square from each corner and turning up the sides. If the box is to
have a volume of 156 cubic centimeters, what size cardboard should
you start with?

In: Advanced Math

- Consider a relation from daily life that can be represented in
a directed acyclic graph (DAG).
- Describe the relation in words and draw the directed acyclic graph.

- Give a topological sort of the directed acyclic graph.

In: Advanced Math

A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. Find the equation of motion (solve the IVP) if the mass is driven by an external force equal to f(t) = 5 cos(2t).

Graph the solution. What part of the graph shows the transient behavior? What is the steady-state behavior?

In: Advanced Math

Use a graphing utility to graph V(x) = x(12- 2x)^{2},
which expresses the volume of a box, V, as a function of the
length of the side of the square cut from each corner, x, of a
sheet of square cardboard with a side length of 12 inches. Then use
the trace button or maximum function feature to find the length of
the side of the square that should be cut from each corner of the
cardboard to create a box with the greatest possible volume. What
is the maximum volume of the open box?

a. What is the length of the side of the square that should be cut from each corner of the cardboard to create a box with the greatest possible volume?

(Round to the nearest inch as needed.)

b. What is the maximum volume of the open box?

_ in^{3} (round to nearest inch)

In: Advanced Math

Consider the following differential equation to be solved by the method of undetermined coefficients.

* y''* + 6

Find the complementary function for the differential equation.

*y*_{c}(* x*)
=

Find the particular solution for the differential equation.

*y*_{p}(* x*)
=

Find the general solution for the differential equation.

* y*(

In: Advanced Math

Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. If it is assumed that the rate at which the virus spreads is proportional not only to the number x of infected students but also to the number of students not infected, and assume that no one leaves the campus throughout the duration of the disease, determine the number of infected students after 6 days if it is further observed that after 4 days x(4) = 50.

In: Advanced Math

How do you show that the function "f(x) = {[x-1;x<2], [2x-3;x>=2]}" is not differentiable at "x=2”?

In: Advanced Math

Find a root of an equation f(x)=5x3-3x2+8 initial solution x0=-0.81, using Newton Raphson method

In: Advanced Math

How do I determine if a big number (6+ digits) is a perfect square or not?

In: Advanced Math

Suppose G has precisely one subgroup of order 5, and one subgroup of order 7. What is G?

In: Advanced Math

How is f(x) =|x-1| differentiable at x=2?

Give details Explaination.

In: Advanced Math

Where is the function f(z) =|z|^2+I (x-iy) +1 differentiable at?

In: Advanced Math

What is the residue of f(z) =1/(z-1) ^3 at its pole? give details Explaination

In: Advanced Math

A complex valued function f(z) =z3−1−I, what is the solution of f (z) =0? Note: exp(z) = e^z

In: Advanced Math