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:
0.95, 2.15
Step-by-step explanation:
cookie-x
ice bar-y
7x+2y=10.95 (*3)
4x+3y=10.25 (*2)
21x+6y=32.85
8x+6y=20.5
21x-8x=32.85-20.5=12.35
13x=12.35
x=0.95
2y=10.95-7*0.95=4.3
y=2.15
Answer:
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
Step-by-step explanation:
Evaluate:
When a=-4, b=2, c=-3, and d =4
Solution:
Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
X: earn per hour during the week
y: earn per hour during the weekend
13x + 14y = 250.90
15x + 8y = 204.70
Multiply the first equation by 4 and the second equation by 7
52x + 56y = 1003.6
105x + 56y = 1432.90
Subtract the first equation from the second:
53x = 429.30
x = 429.30/ 53
x = 8.10
Solve any of the equation for y:
15x + 8y = 204.70
y = [204.70 - 15(8.10)]/8 = 10.40
y - x = 10.40 -8.10 = 2.30
Answer: she earns $2.30 per hour more during the weekend than during the week.
