Tom drives 200 miles in 4 hours, he drives the first 32 miles at an average speed of 64mph, work out his average speed for the rest of the journey.

Tom's average speed for the rest of the journey = 48mph

Step-by-step explanation:

Total distance driven = 200 miles

total time taken = 4hours

first 32 miles , he drove at an average speed of 64mph, To find the amount of time taken for the first 32 miles,

We Use the formulae

Speed = distance / time

Time = Distance / speed

=32/64 = 1/2 =0.5 hours

The remaining distance = Total distance covered - first 32 miles covered

= 200 -32= 168 miles

The remaining time for rest of journey = Total time taken - time covered in the first 32miles

4hours - 0.5 hours

=3.5 hours

Therefore Average speed for the rest of the journey = Distance for the remaining journey/  remaining time

168miles/ 3.5hours = 48mph

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.