The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:
<span><span>x1 </span>= 0.42801</span>
<span><span>x2 </span>= −1.51414</span>
<span><span>x3 </span>= 3.08613</span>
x1 and x2 are in the desired interval [-2, 2]
f'(x) = 3x^2 - 4x - 4
so we have:
3x^2 - 4x - 4 = 0
<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6
x_1 = -4/6 = -0.66
x_ 2 = 2
According to Rolle's theorem, we have one point in between:
x1 = 0.42801 and x2 = −1.51414
where f'(x) = 0, and that is <span>x_1 = -0.66</span>
so we see that Rolle's theorem holds in our function.
The solution of the given system of equation is x = -3 and y = 4 respectively.
<h3>What is a system of linear equations?</h3>
A system of linear equations can be defined as a number of equations needed to solve the equations. For n number of variables n number of equations are required.
The given system of equations is as,
y = 4x + 16 (1)
y = −2x − 2 (2)
In order to solve them, substitute equation (2) into (1) as follows,
4x + 16 = −2x − 2
=> 4x + 2x = -2 - 16
=> 6x = -18
=> x = -3
Then, y = -2 × -3 - 2 = 4
Hence, the solution of the given system of equation is x = -3 and y = 4.
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Answer:
f(x)= 10,000(2)^x
Step-by-step explanation:
Exponential equations can be modeled by a(r)^x where a is the initial amount, r is the difference, and x is how many units the equation should be squared by.
Answer:
There are 5 yellow balls
Step-by-step explanation:
40/4 = 10
10/2 = 5
