<u>In Bar Graphs;</u>
- Bars have equal space
- One the y-axis, we have numbers & on the x-axis, we have data which can be anything.
<u> In Histograms;</u>
- Bars are fixed
- On the y-axis, we have numbers & and on the x-axis, we have data which in continuous & will always be number.
<u>An easy way you can remember the difference is looking at the spaces of the bars. </u>
<em>A bar graph has gaps</em>
<em>A histogram has no gaps.</em>
Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.
Step-by-step explanation:
Salt in the tank is modelled by the Principle of Mass Conservation, which states:
(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)
Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:
By expanding the previous equation:
The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:
Since there is no accumulation within the tank, expression is simplified to this:
By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:
, where
.
The solution of this equation is:
The salt concentration after 8 minutes is:
The instantaneous amount of salt in the tank is:
Answer:
One of the sides is 6 cm and the other is 8 cm
Step-by-step explanation:
Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:
a + b + hypotenuse = 24
a + b + 10 = 24
a + b = 14
b = 14 - a
So now we can right the Pythagorean theorem as follows:
and from this expression in factor form to be zero a must be 6 or a must be 8.
Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)
or a = 8 (and therefore b = 14 - 8 = 6)
