Answer:
E
Step-by-step explanation:
We are given that a particle's position along the x-axis at time <em>t </em>is modeled by:
And we want to determine at which time(s) <em>t</em> is the particle at rest.
If the particle is at rest, this suggests that its velocity at that time is 0.
Since are we given the position function, we can differentiate it to find the velocity function.
So, by differentiating both sides with respect to <em>t</em>, we acquire:
![\displaystyle x^\prime(t)=v(t)=\frac{d}{dt}\big[2t^3-21t^2+72t-53\big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E%5Cprime%28t%29%3Dv%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cbig%5B2t%5E3-21t%5E2%2B72t-53%5Cbig%5D)
Differentiate. So, our velocity function is:
So, we will set the velocity to 0 and solve for <em>t</em>. Hence:
We can divide both sides by 6:
Factoring yields:
By the Zero Product Property:
Hence:
Therefore, at the 3rd and 4th seconds, the velocity of the particle is 0, impling that the particle is at rest.
Our answer is E.
Answer:
The required expression that represents the number of pound of coffees B is 
Step-by-step explanation:
Consider the provided information.
You want to mix two coffees in order to obtain 100 pounds of a blend.
Let x represents the number of pounds of coffee A and y represents the number of pounds of coffee B.
The obtained weight is 100 pounds.
Hence, the required expression that represents the number of pound of coffees B is
Answer:
<u>Test the conjecture for 10 even numbers</u>
10 = 3 + 7
12 = 5 + 7
14 = 7 + 7
16 = 5 + 11
18 = 5 + 13
20 = 7 + 13
22 = 11 + 11
24 = 11 + 13
26 = 13 + 13
28 = 11 + 17
<u>Do you think the conjecture is true? Why or why not?</u>
I believe the conjecture is true because the sum of two odd numbers is an even number and you can find two prime odd numbers for every even number whose sum is that even number.
Answer:
Step-by-step explanation:
the 2nd one
