Answer:
The vertex wold be (-3,4).
Step-by-step explanation:
This is because it is the highest point on the parabola. Since the parabola points down, (-3,4) is the highest point, so it is the vertex.
Answer:
![t=7.85 years](https://tex.z-dn.net/?f=t%3D7.85%20years)
Step-by-step explanation:
We can write this rate as an ordinary differential equation.
![\frac{dP}{dt}=aP](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%3DaP)
Where a is proportional constant, P the population variable, and t the time.
![\frac{dP}{P}=adt](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7BP%7D%3Dadt)
Integrating each side of the equation.
![\int \frac{dP}{P}=\int adt](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7BdP%7D%7BP%7D%3D%5Cint%20adt)
![ln(P)=at+c](https://tex.z-dn.net/?f=ln%28P%29%3Dat%2Bc)
![P=e^{c}e^{at}=Ce^{at}](https://tex.z-dn.net/?f=P%3De%5E%7Bc%7De%5E%7Bat%7D%3DCe%5E%7Bat%7D)
To find C we need to use the initial condiction, it means evaluae P at t=0.
![P_{0}=Ce^{0}=C](https://tex.z-dn.net/?f=P_%7B0%7D%3DCe%5E%7B0%7D%3DC)
![P=P_{0}e^{at}](https://tex.z-dn.net/?f=P%3DP_%7B0%7De%5E%7Bat%7D)
Now, we use the sentence the population has doubled in 5 years.
![2P_{0}=P_{0}e^{a5}](https://tex.z-dn.net/?f=2P_%7B0%7D%3DP_%7B0%7De%5E%7Ba5%7D)
We can find "a" in this condition.
![2=e^{a5}](https://tex.z-dn.net/?f=2%3De%5E%7Ba5%7D)
![ln(2)=a5](https://tex.z-dn.net/?f=ln%282%29%3Da5)
![a=\frac{ln(2)}{5}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bln%282%29%7D%7B5%7D)
![a=0.14](https://tex.z-dn.net/?f=a%3D0.14)
Finally, let's find how long will it take to triple.
![3P_{0}=P_{0}e^{0.14t}](https://tex.z-dn.net/?f=3P_%7B0%7D%3DP_%7B0%7De%5E%7B0.14t%7D)
![3=e^{0.14t}](https://tex.z-dn.net/?f=3%3De%5E%7B0.14t%7D)
![t=\frac{ln(3)}{0.14}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bln%283%29%7D%7B0.14%7D)
![t=7.85 years](https://tex.z-dn.net/?f=t%3D7.85%20years)
I hope it helps you!
Answer:
The answer is 13 1/8ft3
Explanation:
Substitute into the formula:
Volume = 3 1/2 x 2 1/2 x 1 1/2
= 7/2 x 5/2 x 3/2
= 105/8
= 13 1/8 ft3
The compound inequality to show the possible length of the third side is; 25 ≤ x +9+12≤ 30 and it's solution is; 4 ≤ x ≤ 9.
<h3>What is the compound inequality to represent the situation?</h3>
The required compound inequality as described in the task content in terms of the sum of all three sides is;
25 ≤ x +9+12≤ 30
25 -9 -12 ≤ x; 4 ≤ x.
x +9+12≤ 30
x ≤ 30 -9 -12
x ≤ 9
The compound solution is therefore; 4 ≤ x ≤ 9.
Read more on compound inequality;
brainly.com/question/1485854
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Answer:
you have to divide the shape into a semi-circle and 2 triangles
Step-by-step explanation: