In the last census made in a farm, the number of chickens was determined as 8600 and the number of turkeys as 6400. In this farm, the number of chickens decreases by 120 every month, while the number of turkeys increases by 80. Accordingly, after how many months after the last census on this farm will the number of chickens equal the number of turkeys?
A) 7
B) 8
C) 9
D) 10
E) 11
3 answers
Let $m$ be the number of months that have passed since the last census. Then the number of chickens is $8600-120m$ and the number of turkeys is $6400+80m$. We want to find when $8600-120m=6400+80m$. Simplifying, we get $200m=2200$, so $m=11$. Therefore, the answer is $\boxed{\textbf{(E)}\ 11}$.
A hyperbola centred at (0,0) has verices (0,+-6) and one focus (0,-10) what is the standard form equation of the hyperbola.
The distance between the vertices is $2a=12$, where $a$ is the distance from the origin to either vertex. Since the center is the origin, $a = 6$. The distance from the center to a focus is $c=10$. The distance between a focus and vertex is $ae=10-6\implies e = 1.$ Thus we have the relation $b^2 = c^2-a^2 = 64.$ Therefore, the equation of the hyperbola is \[\dfrac{x^2}{36} - \dfrac{y^2}{64} = 1.\]
1 answer