Answer:
- the value of the function changes sign in the interval
- the function is monotonic in the interval
Step-by-step explanation:
All polynomial functions are continuous, so we know from the intermediate value theorem that if the expression on the left changes sign in the interval [-2, 1] then there will be a zero in that interval. If the function is monotonic in the interval, there can only be one zero.
a) For f(x) = x^3 +x +3 = (x^2 +1)x +3, the values at the ends of the interval are ...
f(-2) = (4+1)(-2) +3 = -7
f(-1) = (1 +1)(-1) +3 = 1
The function value goes from -7 to +1 in the interval, so there exists at least one root in that interval.
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b) The derivative of the function is ...
f'(x) = 3x^2 +1
This is positive for any x, so is positive in the interval [-2, -1]. That is, the function is continuously increasing in that interval, so cannot have more than one crossing of the x-axis. There is exactly one root in the interval [-2, -1].
Answer:
0.57
Step-by-step explanation:
57 / 100 = 0.57
You need to divide the percent by 100
Answer:
triangle B
Step-by-step explanation:
It is the only triangle with an angle wider than 90
Answer:
5/126
Step-by-step explanation:
Let's go through this scenario step-by-step. At the beginning, we have a 5/9 possibility of picking a boy - 5 boys out of 9 students. If we pick 1 boy, we now have 4 boys out of 8 students we could potentially pick, giving us a 4/8 or 1/2 chance of picking a second boy after the 1st. For the third boy, we have 3 out of 7 remaining students, giving us a 3/7 chance of picking a third after the first two, and for the fourth boy, we 2 possibilities out of 6, giving us a 2/6 or 1/3 chance of picking the 4 boys.
To find the total probability, we can multiply all of these individual ones together:
There are many ways of solving a system of equation, a very used one is by elimination of variables, which consists in eliminating one of the variables by combining the equations.
Let's do the following combination: (eq 1) + (eq 2)
This means that we add each term vertically:
⇒
When I said "add vertically" means that you add the first term of the first equation with the first term of the second equation. The second term of the first equation with the second term of the second equations, and so on.
This allowed us to remove the "y" temporarily so we can get a linear one-variable equation we can easily solve:
Now that we know the value of "x", we can plug it in any of the starting equations and get "y":
Therefore, our answer looks like this: