Step-by-step explanation:
1.Get the equation in the form y = ax2 + bx + c.
2.Calculate -b / 2a. This is the x-coordinate of the vertex.
3.To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
Answer:
*reward
Step-by-step explanation:
i has helped your welcome
To determine the measure of the angle with the cosine value equal to 0.208, we have to use the inverse trigonometric functions. In this number, we have the arccosine which is also written below.
cos⁻¹(0.208) = 77.9948⁰
Therefore, the measure of the angle with cosine equal to 0.208 rounded to the nearest thousandth is <em>77.995⁰</em>.
<h3>There are 189 bacteria in 5 hours</h3><h3>There are 13382588 bacteria in 1 day</h3><h3>There are
![10(1.8)^{168}](https://tex.z-dn.net/?f=10%281.8%29%5E%7B168%7D)
bacteria in 1 week</h3>
<em><u>Solution:</u></em>
Given that,
A type of bacteria has a very high exponential growth rate of 80% every hour
There are 10 bacteria
<em><u>The increasing function is given as:</u></em>
![y = a(1+r)^t](https://tex.z-dn.net/?f=y%20%3D%20a%281%2Br%29%5Et)
Where,
y is future value
a is initial value
r is growth rate
t is time period
From given,
a = 10
![r = 80 \5 = \frac{80}{100} = 0.8](https://tex.z-dn.net/?f=r%20%3D%2080%20%5C5%20%3D%20%5Cfrac%7B80%7D%7B100%7D%20%3D%200.8)
<em><u>Determine how many will be in 5 hours</u></em>
Substitute t = 5
![y = 10(1 + 0.8)^5\\\\y = 10(1.8)^5\\\\y = 10 \times 18.89568\\\\y \approx 188.96](https://tex.z-dn.net/?f=y%20%3D%2010%281%20%2B%200.8%29%5E5%5C%5C%5C%5Cy%20%3D%2010%281.8%29%5E5%5C%5C%5C%5Cy%20%3D%2010%20%5Ctimes%2018.89568%5C%5C%5C%5Cy%20%5Capprox%20188.96)
y = 189
Thus, there are 189 bacteria in 5 hours
<em><u>Determine how many will be in 1 day ?</u></em>
1 day = 24 hours
Substitute t = 24
![y = 10(1 + 0.8)^{24}\\\\y = 10(1.8)^{24}\\\\y = 10 \times 1338258.84\\\\y = 13382588.45\\\\y \approx 13382588](https://tex.z-dn.net/?f=y%20%3D%2010%281%20%2B%200.8%29%5E%7B24%7D%5C%5C%5C%5Cy%20%3D%2010%281.8%29%5E%7B24%7D%5C%5C%5C%5Cy%20%3D%2010%20%5Ctimes%201338258.84%5C%5C%5C%5Cy%20%3D%2013382588.45%5C%5C%5C%5Cy%20%5Capprox%2013382588)
Thus, there are 13382588 bacteria in 1 day
<em><u>Determine how many will be in 1 week</u></em>
1 week = 168
Substitute t = 168
![y = 10(1 + 0.8)^{168}\\\\y = 10(1.8)^{168}](https://tex.z-dn.net/?f=y%20%3D%2010%281%20%2B%200.8%29%5E%7B168%7D%5C%5C%5C%5Cy%20%3D%2010%281.8%29%5E%7B168%7D)
Thus there are
bacteria in 1 week