Correct answer is B (2,2)
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.
Answer:
2. trust me.. i did it before.
Answer:
The mixture C is the correct option
Step-by-step explanation:
According to the given scenario, the calculation is as follows:
For Mixture A
Blue Paint - 5 cups
White Paint - 12 cups
The ratio between them is 5:12
For Mixture B
Blue Paint - 6 cups
White Paint - 6 cups
The ratio between them is 6:6 = 12:12
It came by multiply the numerator and denominator by 12
For Mixture C
Blue Paint - 4 cups
White Paint - 12 cups
The ratio between them is 4:12
For Mixture D
Blue Paint - 5 cups
White Paint - 6 cups
The ratio between them is 5:6 = 10:12
It came by multiply the numerator and denominator by 12
As it can be seen that in all four mixtures the denominator is the same so for calculating the lowest ratio we have to see the small value in the numerator
As it can be seen that there is a small value of 4
hence, the mixture C is the correct option
