Question

1. What were the factors that made it difficult for the explorers to venture into the continent of Africa?
2. Where does R. Nile originate?
3. How the rivers of Africa can be harnessed for hydroelectricity?

Please answer those questions as fast as you can...
Please answer it fast... ​

Answer 1

Answer:

Let us learn about cross multiplication formula first:

We consider two linear equations

$\quad\quad \mathsf{a_{1}x+b_{1}y+c_{1}=0}$

$\quad\quad \mathsf{a_{2}x+b_{2}y+c_{2}=0}$

Using the formula for cross multiplication, we get

$\quad\mathsf{\dfrac{x}{b_{1}c_{2}-b_{2}c_{1}}=\dfrac{y}{c_{1}a_{2}-c_{2}a_{1}}=\dfrac{1}{a_{1}b_{2}-a_{2}b_{1}}}$

Now we proceed to solve the given problem:

The given equations are

$\quad\quad \mathsf{\dfrac{15}{x}+\dfrac{2}{y}=17}$

$\quad\quad \mathsf{\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{36}{5}}$

Then the given equations become

$\quad\quad \mathsf{15p+2q=17}$15p+2q=17

$\quad\quad \mathsf{p+q=\frac{36}{5}}$

$\quad\quad \mathsf{15p+2q-17=0}15p+2q−17=0$

$\quad\quad \mathsf{5p+5q-36=0}5p+5q−36=0$

Now comparing these equations with the general equations, we have

$\quad\quad \mathsf{a_{1}=15,\:b_{1}=2,\:c_{1}=-17}$

$\quad\quad \mathsf{a_{2}=5,\:b_{2}=5,\:c_{2}=-36}$

Using the formula for cross multiplication, we get

$\quad\mathsf{\dfrac{p}{b_{1}c_{2}-b_{2}c_{1}}=\dfrac{q}{c_{1}a_{2}-c_{2}a_{1}}=\dfrac{1}{a_{1}b_{2}-a_{2}b_{1}}}$

$\to \mathsf{\dfrac{p}{2\times (-36)-5\times (-17)}=\dfrac{q}{(-17)\times 5-(-36)\times 15}=\dfrac{1}{15\times 5-5\times 2}}$

$\to \mathsf{\dfrac{p}{-72+85}=\dfrac{q}{-85+540}=\dfrac{1}{75-10}}$

$\to \mathsf{\dfrac{p}{13}=\dfrac{q}{455}=\dfrac{1}{65}}$

$\quad\quad \mathsf{\dfrac{p}{13}=\dfrac{1}{65}}$

$\implies \mathsf{p=\dfrac{13}{65}}$⟹

$\implies \mathsf{p=\dfrac{1}{5}}$⟹p

$\implies \mathsf{\dfrac{1}{x}=\dfrac{1}{5}\quad [\because p=\dfrac{1}{x}]}$

$\implies \mathsf{\dfrac{1}{y}=7\quad [\because q=\dfrac{1}{y}]}$

Therefore the required solution is

$\quad\quad \underline{\boxed{\bold{x=5,\:y=\dfrac{1}{7}}}}$