Answer: The number pi is an irrational number
Step-by-step explanation:
Pi is irrational because it will never end and at the same time doesnt have a pattern in which the numbers repeat. Here are some of the numbers in pi 3.14159265359
291.87 is rational since the last (decimal) numbers aren't repeating.
If it was repeating (291.877777...) it would be irrational.
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:
Step-by-step explanation:
because both equations do not have matching numbers for the x or y variable, and both equations are positive you are going to have to multiply each equation by a number so that there will be at least one variable with the same number but with opposite signs.
it does not matter which variable you choose.
lets use y because 2 and 3 are smaller then 2 and 5.
so lets multiply the first equation by 2 in order to get y equal to 6.
2(2x)+2(3y)=(2)6
(do not forget to multiply what the equation is equal to also)
4x+6y=12
now for the second equation we need y to equal negative 6
-3(5x)+-3(2y)=-3(4)
-15x-6y=-12
now lets put the 2 new equations next to each other and see what we can cancel out
4x+6y=12
-15x-6y=-12
-11x=0
x=0
now plug 0 in for x and solve for y (it does not matter which of the 4 equations you choose to solve.
2(0)+3y=6
3y=6
y=2
so your answer is x=0, y=2