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Tcecarenko [31]
3 years ago
7

What is the product of the polynomials below

Mathematics
1 answer:
Scrat [10]3 years ago
8 0

Answer:

B. 15x^{4} + 2x³ - 8x² - 22x - 15

Step-by-step explanation:

1. (3x² - 2x - 3)(5x² + 4x +5)

15x^{4} + 12x³ + 15x² - 10x³ - 8x² - 10x - 15x² - 12x - 15

2. Combine like terms

15x^{4} + 2x³ - 8x² - 22x - 15

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A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha
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To model this situation, we are going to use the decay formula: A=Pe^{rt}
where 
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P is the initial population 
e is the Euler's constant
r is the decay rate 
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A. We know for our problem that the initial population is 1,250, so P=1250; we also know that after a year the population is 1000, so A=1000 and t=1. Lets replace those values in our formula to find r:
A=Pe^{rt}
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e^{r}= \frac{1000}{1250}
e^{r}= \frac{4}{5}
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Now that we have r, we can write a function to model this scenario:
A(t)=1250e^{-0.2231t}.

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C. 
- The function is decreasing
- The function doe snot have a x-intercept 
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- Since the function is decaying, it will have a maximum at t=0: 
A(0)=1250e^{(-0.2231)(0)
A_{0}=1250e^{0}
A_{0}=1250
- Over the interval [0,10], the function will have a minimum at t=10:
A(10)=1250e^{(-0.2231)(10)
A_{10}=134.28

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: m= \frac{A(0)-A(10)}{10-0}
where 
m is the rate of change 
A(10) is the function evaluated at 10
A(0) is the function evaluated at 0
We know from previous calculations that A(10)=134.28 and A(0)=1250, so lets replace those values in our formula to find m:
m= \frac{134.28-1250}{10-0}
m= \frac{-1115.72}{10}
m=-111.572
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

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