In the given question, all the necessary information's are already provided. Using these information's it is easy to find the average speed of the car in miles per hour. It is given that the car covers 10 laps in 18 minutes and each lap is 3.6 miles in length.
Total distance covered by the car = (10 * 3.6) miles
   = 36 miles
Now we have to convert the time from minutes to hours. So
18 minutes = 18/60 hours
   = 3/10 hours
Now we can easily calculate the average speed of the favorite car of Mathew.
Average Speed = 36 * (10/3) miles/hour
   = 120 miles/ hour

8 0

3 years ago

Find the zeros of polynomial function and solve polynomials equations.<br> f(x)=24x^3-64x^2-21x+56

8090 [49]

Since this polynomial has 4 terms, factoring by grouping should be the first thing we try here.

So, we have:

$8x^2(3x-8)-7(3x-8)=0 \implies\\ (8x^2-7)(3x-8)=0$

So, we can use ZPP to find out roots:

$3x-8 =0 \implies\\ x=\frac{8}{3}\\ 8x^2-7=0 \implies \\ 8x^2=7 \implies \\ x^2=\frac{7}{8} \implies \\ x=\pm\frac{\sqrt{7}}{\sqrt{{8}}}\\ \text{Rationalizing denominator:}\\ x=\pm\frac{\sqrt{56}}{8}$

So our three roots are:

$x \in \{\frac{8}{3},\frac{\sqrt{56}}{8},-\frac{\sqrt{56}}{8}\}$

8 0

3 years ago