Lời giải:

=2,4 giờ  x 6 + 2,4 giờ +2,4 giờ x 3

=2,4 giờ x (6+1+3)=2,4 giờ x 10=24 giờ

b: Sửa đề: \(B=1\cdot3+2\cdot4+3\cdot5+4\cdot6+\cdots+2018\cdot2020\)

\(=1\left(1+2\right)+2\left(2+2\right)+\cdots+2018\left(2018+2\right)\)

\(=\left(1^2+2^2+\cdots+2018^2\right)+2\left(1+2+\cdots+2018\right)\)

\(=\frac{2018\left(2018+1\right)\left(2\cdot2018+1\right)}{6}+2\cdot\frac{2018\cdot2019}{2}\)

\(=\frac{2018\cdot2019\cdot4037}{6}+2018\cdot2019=1009\cdot673\cdot4037+2018\cdot2019\)

\(=1009\cdot673\left(4037+2\cdot3\right)=1009\cdot673\cdot4043\)

=2745427451

c: Ta có: \(C=\left(1+2+3+\cdots+2020\right)\left(20192019\cdot2020-2019\cdot20202020\right)+\left(15-12\right)^2\)

\(=\frac{2020\left(2020+1\right)}{2}\cdot2019\cdot2020\cdot\left(10001-10001\right)+3^2\)

=0+9

=9

b: Sửa đề: \(B=1\cdot3+2\cdot4+3\cdot5+4\cdot6+\cdots+2018\cdot2020\)

\(=1\left(1+2\right)+2\left(2+2\right)+\cdots+2018\left(2018+2\right)\)

\(=\left(1^2+2^2+\cdots+2018^2\right)+2\left(1+2+\cdots+2018\right)\)

\(=\frac{2018\left(2018+1\right)\left(2\cdot2018+1\right)}{6}+2\cdot\frac{2018\cdot2019}{2}\)

\(=\frac{2018\cdot2019\cdot4037}{6}+2018\cdot2019=1009\cdot673\cdot4037+2018\cdot2019\)

\(=1009\cdot673\left(4037+2\cdot3\right)=1009\cdot673\cdot4043\)

=2745427451

c: Ta có: \(C=\left(1+2+3+\cdots+2020\right)\left(20192019\cdot2020-2019\cdot20202020\right)+\left(15-12\right)^2\)

\(=\frac{2020\left(2020+1\right)}{2}\cdot2019\cdot2020\cdot\left(10001-10001\right)+3^2\)

=0+9

=9

\(\frac{\left(3.4.4^4-2.4^5\right)}{4^5}=\frac{\left(3.4^5-2.4^5\right)}{4^5}=\frac{4^5.\left(3-2\right)}{4^5}=1.\)

( 12.4⁴- 2.4⁵ ) :4⁵
= ( 3. 4⁵- 2.4⁵):4⁵
=(4⁵.(3-2) ) :4⁵
=4⁵:4⁵
=1

\(\frac{4^2\cdot4^3}{2^{10}}\)

C1: \(=\frac{\left(2^2\right)^2\cdot\left(2^2\right)^3}{2^{10}}\)

\(=\frac{2^4\cdot2^6}{2^{10}}\)

\(=\frac{2^{10}}{2^{10}}=1\)

C2 : \(=\frac{4^{2+3}}{4^5}=\frac{4^5}{4^5}=1\)

gọi nhà bạn an là điểm a, nhà bạn b là điểm b, truờng học là điểm c, ta có

\(ab^2+bc^2=ac^2\)(định lý py-ta-go)

thay số vào ta có: \(2,4^2+3,2^2=4^2\)(km)

vậy nhà bạn an cách truờng \(4^2\)=16km