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Zinaida [17]
3 years ago
11

Explain how to write a composite function to find the area of the region at time t.

Mathematics
1 answer:
andrey2020 [161]3 years ago
5 0

Answer:

The composite function is:a(r(t)) = π (0.5 + 2t)²After simplification it becomes:a(r(t)) = π (0.25 + 2t + 4t²)Step-by-step explanation:Here is the complete function:a circular oil spill continues to increase in size. the radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. the area of the circular region is given by the function a(r) = πr², where r is the radius of the circle at time t.  Explain how to write a composite function to find the area of the region at time t.Solution:The composite function is written by applying one function to another. The requirement of this question is to write a composite function to find are of region at time t.Leta(r) = πr²is function 1andr(t) = 0.5 + 2tis function 2ThenThis means that function r(t) should be applied to a(r) and it should be inside function a(r)Then composite function becomes:a(r(t))Now put the value of r(t) = 0.5 + 2t into a(r) = πr²a(r(t)) = π (0.5 + 2t)²So this is the composite function to find area of the region at time tSimplifying this equation we get:a(r(t)) = π (0.5 + 2t)²        = π (0.5 + 2t) (0.5 + 2t)       =  π [(0.5 * 0.5)+ (0.5 * 2t) + (2t * 0.5) + (2t *2t)]       = π (0.25 + 1t +  1t + 4t²)       = π ( 0.25 + t + t + 4t²)       = π (0.25 + 2t + 4t²)a(r(t)) = π (0.25 + 2t + 4t²)

Step-by-step explanation:

Hope it helps you ✌️

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Suppose you and a friend each choose at random an integer between 1 and 8, inclusive. For example, some possibilities are (3,7),
Bezzdna [24]

Answer and explanation:

Given : Suppose you and a friend each choose at random an integer between 1 and 8, inclusive.

The sample space is

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)  (1,7) (1,8)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)   (2,7) (2,8)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)   (3,7) (3,8)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)   (4,7) (4,8)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)   (5,7) (5,8)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)   (6,7) (6,8)

(7,1) (7,2) (7,3) (7,4) (7,5) (7,6)   (7,7) (7,8)

(8,1) (8,2) (8,3) (8,4) (8,5) (8,6)   (8,7) (8,8)

Total number of outcome = 64

To find : The following probabilities ?

Solution :

The probability is given by,

\text{Probability}=\frac{\text{Favorable outcome }}{\text{Total outcome}}

a) p(you pick 5 and your friend picks 8)

The favorable outcome is (5,8)= 1

\text{Probability}=\frac{1}{64}

b) p(sum of the two numbers picked is < 4)

The favorable outcome is (1,1), (1,2), (2,1)= 3

\text{Probability}=\frac{3}{64}

c) p(both numbers match)

The favorable outcome is (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8) = 8

\text{Probability}=\frac{8}{64}

\text{Probability}=\frac{1}{8}

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

Here is the complete question:

Dylan scored a total of 48 points in first 4 games of the basketball season. Which equation can be used to find g, the average number of points he scores per game?

a. 48÷4=g

b. 4÷48=g

c. g÷4=g

d. 4÷g=48

The average number of points Dylan scores per game which has been represented by g will be the total points scored divided by the number of game played. This will be:

g = total point scored ÷ number of games played

g = 48 ÷ 4

Therefore, option A is the right answer.

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Step-by-step explanation:

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