For each equation give X a value and solve for Y, do this at least two times for each equation.
Plot those dots on a graph to draw two lines.
The solution is where the two lines cross.
You will see the lines cross at (-1,-2)
Answer:
larger number = 35
smaller number = 26
Step-by-step explanation:
let larger number be x
and another ( x-9 )
so, x+x-9=61
2x = 70
x = 35
smaller number = 35 - 9
= 26
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Answer:
Using either method, we obtain: 
Step-by-step explanation:
a) By evaluating the integral:
![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as: ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: 
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and 
Since this this function 
is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
If you wanted to compute for your budget for natural gas
this month using the data you have recorded about your consumption of natural gas
for the past four months, the best estimate to be budgeted this month would be
the average consumption for the past 4 months. To get the average, you have to
add the four numbers and divide it by four.
$112
+ $108 + $99 + $89 = $408/4 = $102
