3. Who set up their equation correctly for the following question?
1 answer:
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Answer:
See below
Step-by-step explanation:
<h3>Continuation of the question</h3><u>Data in the table:</u>
<u>PH 4 5 6 7 8 9 10 11 </u>
<u>Bacteria 116 120 131 136 141 151 148 163</u>
- <em>Create a scatter plot to represent the data: Based on the data and your scatter plot, what do you think a good linear function would be to represent the data?</em>
<em>See attached for scatter plot</em>
We can see the chart is close to linear function. Let's build one based on data in the table
<u>The line will be in the form of:</u>
- y = mx + b
<u>If we use two points and get the equation</u>
- (4, 116) and (8, 141)
<u>Finding the slope:</u>
- m = (141-116)/(8-4) = 25/4 = 6.25
<u>Then, finding y-intercept:</u>
- 116 = 6.25*4 + b
- b = 116 - 25 = 91
<u>So the line is:</u>
- y = 6.25x + 91
<em>Note: This is approximate best fit graph and it is attached as well. Exact formula for the line is built by using different method and is very close to the one above</em>
The given <span>expression is 
</span>
So, we have 3 square roots.
The number under a square root sign must be Non negative.
Beside that the denominator must be not equal zero.
For the term ⇒⇒⇒
∴ x > 0 ⇒⇒⇒ x ∈ (0,∞)
For the term ⇒⇒⇒
∴x+1 ≥ 0 ⇒⇒⇒ x ≥ -1 ⇒⇒⇒ ∴ x ∈ [-1,∞)
For the term ⇒⇒⇒
∴ 1-x ≥ 0 ⇒⇒⇒ x ≤ 1 ⇒⇒⇒ x ∈ (-∞,1]
So, The values of x which make the <span>expression well defined
</span>
<span>∴ x ∈ { </span><span>(0,∞) ∪ </span><span>[-1,∞) ∪ </span><span>(-∞,1] }
</span><span>
</span><span>∴ x ∈ [-1,0) ∪ (0,1]
</span><span>
</span><span>OR can be written as ⇒⇒ x ∈ [-1,1] - {0}
</span>
</span>
So, we have 3 square roots.
The number under a square root sign must be Non negative.
Beside that the denominator must be not equal zero.
For the term ⇒⇒⇒
∴ x > 0 ⇒⇒⇒ x ∈ (0,∞)
For the term ⇒⇒⇒
∴x+1 ≥ 0 ⇒⇒⇒ x ≥ -1 ⇒⇒⇒ ∴ x ∈ [-1,∞)
For the term ⇒⇒⇒
∴ 1-x ≥ 0 ⇒⇒⇒ x ≤ 1 ⇒⇒⇒ x ∈ (-∞,1]
So, The values of x which make the <span>expression well defined
</span>
<span>∴ x ∈ { </span><span>(0,∞) ∪ </span><span>[-1,∞) ∪ </span><span>(-∞,1] }
</span><span>
</span><span>∴ x ∈ [-1,0) ∪ (0,1]
</span><span>
</span><span>OR can be written as ⇒⇒ x ∈ [-1,1] - {0}
</span>