The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
What is the intermediate value theorem?
Intermediate value theorem is theorem about all possible y-value in between two known y-value.
x-intercepts
-x^2 + x + 2 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, x = 2
y intercepts
f(0) = -x^2 + x + 2
f(0) = -0^2 + 0 + 2
f(0) = 2
(Graph attached)
From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3
For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.
<em>Your question is not complete, but most probably your full questions was</em>
<em>Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?</em>
Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
Learn more about intermediate value theorem here:
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No bc parallel means they don’t touch, so they wouldn’t meet to form and acute angle
The machine will sort 11050 packages when it is operating at 85% capacity.
To solve this question, we have to find the rate at which the machine is operating at 85% capacity.
Data;
<h3>Rate</h3>
This is used to compare two values with respect to one another mostly under similar conditions.
cross multiply both sides and solve for x
The machine will sort 11050 packages when it is operating at 85%
Learn more on rates here;
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Well for solving arithmetic sequences you have to add the numbers like for example if you had 2,4,6,8 The Common ratio would be 2 because you're constantly adding 2. Now for a geometric sequence it's a little different instead of adding the numbers you use multiplication to solve those ones so if the numbers were 4,16,64,256 the common ratio would be 4.
Now here comes the answers. For the matching :)
1. B Arithmetic, common difference is 2.
2. C Arithmetic, common difference is -4.
3. D Geometric, common ratio is 2.
4. A Geometric, common ratio is 0.5.
Hope This Helps You! Have A Wonderful Day. :)
Answer:
0.4
Step-by-step explanation:
Hope that helps!
