Answer:
Step-by-step explanation:
Given function is
(a)F(x)=
=
(b)F(x)=
=![\frac{\left [ 2\left ( x-3\right )\right \left ( x-5\right )+\left ( x-3\right )^2]\left [ \left ( x-4\right )^2\left ( x^2+3\right )^5\right ]-\left [ 2\left ( x-4\right )^{3}\left ( x^2+3\right )^5+5\left ( x^2+3\right )^4\left ( 2x\right )\left ( x-4\right )^2\right ]\left [ \left ( x-3\right )^2\left ( x-5\right )\right ]}{\left [\left ( x-4\right )^2\left ( x^2+3\right )^5\right ]^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%20%5B%202%5Cleft%20%28%20x-3%5Cright%20%29%5Cright%20%5Cleft%20%28%20x-5%5Cright%20%29%2B%5Cleft%20%28%20x-3%5Cright%20%29%5E2%5D%5Cleft%20%5B%20%5Cleft%20%28%20x-4%5Cright%20%29%5E2%5Cleft%20%28%20x%5E2%2B3%5Cright%20%29%5E5%5Cright%20%5D-%5Cleft%20%5B%202%5Cleft%20%28%20x-4%5Cright%20%29%5E%7B3%7D%5Cleft%20%28%20x%5E2%2B3%5Cright%20%29%5E5%2B5%5Cleft%20%28%20x%5E2%2B3%5Cright%20%29%5E4%5Cleft%20%28%202x%5Cright%20%29%5Cleft%20%28%20x-4%5Cright%20%29%5E2%5Cright%20%5D%5Cleft%20%5B%20%5Cleft%20%28%20x-3%5Cright%20%29%5E2%5Cleft%20%28%20x-5%5Cright%20%29%5Cright%20%5D%7D%7B%5Cleft%20%5B%5Cleft%20%28%20x-4%5Cright%20%29%5E2%5Cleft%20%28%20x%5E2%2B3%5Cright%20%29%5E5%5Cright%20%5D%5E2%7D)
The correct model of the height of rocket above water is;
h(t) = -16t² + 96t + 112
Answer:
time to reach max height = 3 seconds
h_max = 256 ft
Time to hit the water = 7 seconds
Step-by-step explanation:
We are given height of water above rocket;
h(t) = -16t² + 96t + 112
From labeling quadratic equations, we know that from the equation given, we have;
a = -16 and b = 96 and c = 112
To find the time to reach maximum height, we will use the vertex formula which is; -b/2a
t_max = -96/(2 × -16)
t_max = 3 seconds
Thus, maximum height will be at t = 3 secs
Thus;
h_max = h(3) = -16(3)² + 96(3) + 112
h_max = -144 + 288 + 112
h_max = 256 ft
Time for it to hit the water means that height is zero.
Thus;
-16t² + 96t + 112 = 0
From online quadratic formula, we have;
t = 7 seconds
Answer: a. 34
Step-by-step explanation:
34,600.
7 is higher than 4, so it rounds up.
The exponential equation for the growth is f(x)=57
where x is the number of days and the population on 21st march is 2069983.5 of microbes.
Given:
Days population
0 57
1 95
5 700
10 8525
We have to form exponential equation which shows the growth of microbes.
We know that exponential equation which shows the sum is as under:
f(x)=P
where r is the rate of growth and x is the number of days, months or years depending on how things grows.
In the question when x=0 population is 57.
f(0)=57
P
=57
P=57
When x=1, population is 95.
f(1)=95
P
=95
57 =95
57=95/----1
when x=5,population is 700.
f(5)=700
P
=700
57=700
57=700/-----2
Equating 1&2
95/=700/
=7.36
=7.36
=
equating both sides
4r=2
r=0.5
put the value of t=21 in the exponential equation
f(21)=57
=57
=57*36315.5
=2069983.5
Hence the population on 21st march is 2069983.5.
Learn more about equation at brainly.com/question/2972832
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