$\bf \cfrac{dx}{dt}=\cfrac{5}{t}\quad ,\quad x(0)=7\to 
\begin{cases}
f(t)=0\\
t=7
\end{cases}\\\\
-----------------------------\\\\
\displaystyle \int \cfrac{5}{t}\cdot dt\implies 5\int \cfrac{1}{t}\cdot dt\implies 5ln|t|+C= f(t)
\\\\\\
\textit{now, we know when f(t)=0, t=7}\implies 5ln|7|+C=0
\\\\\\
C=-5ln(7)
\\\\\\
thus\implies \boxed{5ln|t|-5ln(7)=f(t)=x}$

notice |7| 7 is positive, so we can simply remove the bars and use 7 by itself

6 0

2 years ago

The ratio of dogs to cats in a veterinarian’s office is 9:7. What is the ratio of the number of dogs to the total number of dogs

lara31 [8.8K]

The answer is 9:16 just add 9+7=16 and then we know out of the 16 nine were dogs so 9:16

3 0

2 years ago

The tank on a petrol lorry is a cylinder 2m in diameter and 7cm long

Nutka1998 [239]

Answer: 0.22 kilolitre

Step-by-step explanation:

First, let’s find the volume of the tank. We know the volume of a cylinder is represented by the equation V=πr^2h,

Radius = 1 m

Height = 7 cm = .07 m

The tank is 0.22 cubic meters

Now that we found the volume, we will try to find how many liters are in the tank.

1 cubic meter = 1 kilolitre

So, 0.22 cu. m = 0.22 kilolitre

5 0

3 years ago