We have the sum of cubes identity
and observing that 1 + 4 = 2 + 3, we have
and
Then
Alternatively, we have the well-known sum of cubes formula
The sum under the square root is this sum with . Then
and so the square root again reduces to 15.
Answer:
Step-by-step explanation:
For this case we need to define some notation:
represent the remaining length of the candle in inches
represent the time in hours that have elapsed since the candle was lit.
For this case we assume that L and f are related so then we can write this like that: L is a function of t.
And for this case we have a constant rate given of:
And we know a initial condition
So then since we have a constant rate of change we can use a linear model given by:
Where m is given and we need to find b. If we use the initial condition we have this:
And solving for b we got:
So then our lineal model would be given by:
Given equation: y =2x^2+12x+13.
We need to find the axis of symmetry and the coordinates of the vertex of the graph of the function.
The formula of axis of symmetry is : .
a= 2 and b=12.
Therefore, .
<h3>Therefore, axis of symmetry is x=-3.</h3>
Let us find y-coordinate of the vertex.
Plugging x=-3 in given quadratic y =2x^2+12x+13.
y= 2(-3)^2+12(-3)+13 = 2(9) -36 +13 = 18-36 +13 = -5.
We got x-coordinate of the vertex -3 and y-coordinate of the vertex -5.
<h3>Therefore, vertex of the graph is (-3,-5).</h3>
<span>First of all, a solution to a system can be thought of in two ways: Graphically, the solution is where the lines produced by the two equations intersect. If you graphed y = -x +3 and also graphed y = 2x + 1, the solution is where the graphs 'cross' or intersect. Numerically, the solution to the system is where a particular x-value produces the same y-value in each equation. The solution would be found numerically when we plugged in a particular value for x into both equations and the y-value is the same for both equations.
For part 5a.) We know the solution is between the highlighted rows of x = 0.5 and x = 1 because the line y = -x +3 decreases while the line y = 2x+1 increases. It is easiest to think of it graphically. We know that y = -x +3 and y = 2x+1 are both lines, so we can easily sketch the graphs of each using the table. The line y = -x+3 would go through the point (0.5, 2.5) and then continue downward to the point (1,2). Meanwhile the line y = 2x + 1 would go through the point (0.5,2) and continue upward to the point (1,3). Thus in-between the x-values 0.5 and 1, one of the lines is going downward from 2.5 to 2, while the other is going upward from 2 to 3. Somewhere in this range the two lines must have an intersection point, which we know is the solution to the system.
For part 5b.) we can complete the table by plugging in the given x-value into each of the equations. The table should look as follows:
x y = -x+3 y=2x+1
0.5 2.5 2
0.6 2.4 2.2
0.7 2.3 2.4
0.8 2.2 2.6
0.9 2.1 2.8
1 2 3</span>