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1 year ago

Determine f(x+a)−f(x) for the following function. f(x)=x−9‾‾‾‾‾√+6

Mathematics

1 answer:

Darina [25.2K]1 year ago

3 0

The value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)

<h3>How to evaluate the function value?</h3>

The function definition is given as

f(x) = √(x - 9) + 6

We start by calculating the function f(x + a)

So, we have

f(x + a) = √(x + a - 9) + 6

The function definition f(x + a) - f(x) is calculated as

f(x + a) - f(x) = √(x + a - 9) + 6 - (√(x - 9) + 6)

Open the bracket

So, we have

f(x + a) - f(x) = √(x + a - 9) + 6 - √(x - 9) - 6

Evaluate the difference

So, we have

f(x + a) - f(x) = √(x + a - 9) - √(x - 9)

Hence, the value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)

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Analyze the conditional statement below and complete the instructions that follow. You will receive the trophy if you win the ch

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This is a problem of logic. So we need to identify what the conditional statement means. In logic, there are several operators, one of them is the conditional operator. As the name implies, the conditional operator creates a compound statement that sets up a condition for something to be true. If the condition is met, the statement is true.

Symbol: →

Parts of Conditional: Two simple statements joined by the conditional symbol. The first simple statement in a conditional is called the antecedent and the second simple statement is called the consequent.

So let's analyze each case:

Case 1. Analyze the conditional statement and complete the instructions that follow.

Statement: You will receive the trophy if you win the championship match.

We can rewrite this in a standard form of the conditional operator, that is:

A→B: If you win the championship match then you will receive the trophy

A: You win the championship match
B: You will receive the trophy

Hypothesis: You win the championship match
Conclusion: You will receive the trophy

Case 2.

According to the problem we have:

Hypothesis: You will receive the trophy.
Conclusion: You win the championship match

A: You will receive the trophy.
B: You win the championship match

We can rewrite this in an standard form of the conditional statement, that is:

A→B: If you will receive the trophy then you win the championship match

Case 3.

According to the problem we have:

Hypothesis: You do not win the championship match.
Conclusion: You will not receive the trophy

A: You do not win the championship match.
B: You will not receive the trophy

We can write this in a conditional statement:

A→B: If you do not win the championship match then you will not receive the trophy

Case 4.

According to the problem we have:

Hypothesis: You win the championship match
Conclusion: You will receive the trophy

We can rewrite this in a conditional statement:

A: You win the championship match
B: You will receive the trophy

We can write this in a conditional statement:

A→B: If you win the championship match then you will receive the trophy

Case 5.

According to the problem we have:

Hypothesis: You will not receive the trophy
Conclusion: you do not win the championship match

A: You will not receive the trophy
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We can write this in a conditional statement:

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finlep [7]

Answer:

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Lee: 2+2√5 days ≈ 6.47 days

Step-by-step explanation:

Let L represent the number of days it takes Lee to frame a cabin. Then it take L+4 days for Ron to frame it. Working together, they take 4 days. Then their rates, in cabins per day, add up as ...

1/L + 1/(L+4) = 1/4

Multiplying by the product of denominators, we get ...

4(L+4) +4L = L(L+4)

Subtracting the left side gives ...

L^2 -4L -16 = 0

Completing the square, we can write this as ...

L^2 -4L +4 = 20

(L -2)^2 = 20

L = 2 + √20 = 2 +2√5 ≈ 6.47

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Ron takes 6+2√5 ≈ 10.47 days to frame a cabin.

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