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Novosadov [1.4K]
3 years ago
14

An astronaut drops a rock into a crater on the moon. The distance, d(t), in meters, the rock travels after t seconds can be mode

led by d(t)=0.8t^2. What is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?
Mathematics
1 answer:
jek_recluse [69]3 years ago
5 0
Given:
d(t) = 0.8t²

d(5) = 0.8*5² = 0.8 * 25 = 20
d(10) = 0.8*10² = 0.8 * 100 = 80

Average speed = distance traveled / time of travel
Average speed = 20 meters / 5 seconds = 4 meters per second

Average speed = 80 meters / 10 seconds = 8 meters per second

4 mps + 8 mps = 12 mps 
12 mps / 2 = 6 mps the average speed in meters per second between 5 and 10 seconds. 
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Answer:

12 mathletes is needed to solve 30 problems in 5 minutes

Step-by-step explanation:

8 athletes can solve 20 problems in 10 minutes

30-20=10

now we need 10 more problems to be solved so

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yan [13]

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2 years ago
Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)
Svetlanka [38]

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17. The polynomial is in standards when has the form p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}, where n is the order of the polynomial. The example has the following information:

n = 3, a_{0} = 17, a_{1} = -6, a_{2} = 2, a_{3} = 5.

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials p_{1} and p_{2} such that:

p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i} and p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}, where m \geq n

p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be p_{1} a polynomial such that:

p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}

And \alpha an scalar. If the polynomial is multiplied by the scalar number, then:

\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}

Lastly, the following expression is constructed by distributive property:

\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}

Hence, polynomials are closed with respect to multiplication.

4 0
3 years ago
The rabbit population in a certain area is 200​% of last​ year's population. There are 900 rabbits this year. How many were ther
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Answer:

Sum means to ADD in the math world

Step-by-step explanation:

So your answer would be d + 9

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