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Masteriza [31]
2 years ago
6

The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than 4 and greater than 1.5.

Model the normal range of pH values of lemon juice, using a compound inequality.
1.5 > x > 4
1.5 < x < 4
1.5 ≤ x ≤ 4
1.5 ≥ x ≥ 4
Mathematics
1 answer:
castortr0y [4]2 years ago
8 0

Let's say x is J because it's Lemon Juice.

It's said that the pH of J is less than 4 so: pH(J) < 4 and pH(J) is greater than 1.5 so: pH(J) > 1.5

Now we can construct:

1.5 < pH(J) \wedge pH(J) < 4

Or simply:

1.5 < pH(J) < 4

We can also write this with an interval:

pH(J)\in(1.5, 4)

Hope this helps.

r3t40

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B) We have 26 letters from which to choose 2, and 10 digits from which to choose 4:
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C) We have 26 letters from which to choose 5, and 10 digits from which to choose 2:
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A rectangular area is formed having a perimeter of 40 cm. Determine the length and breadth of the rectangle if it is to enclose
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Let x and y be the dimensions of the rectangle. If the perimeter is 40, we have

2(x+y)=40 \iff x+y=20

We can expression one variable in terms of the others as

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Since the area is the product of the dimensions, we have

xy=(20-y)y=-y^2+20y

This is a parabola facing down, so it's vertex is the maximum:

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So, the maximum is

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And since we know that x+y=20, we have x=10 as well.

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The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit in
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Answer:

\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})

And when we apply the limit we got that:

\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1

Step-by-step explanation:

Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"

We have the following formula in order to find the sum of cubes:

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We can express this formula like this:

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And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2

\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2

If we operate and we take out the 1/4 as a factor we got this:

\lim_{n\to\infty} \frac{n^2(n+1)^2}{n^4}

We can cancel n^2 and we got

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We can reorder the terms like this:

\lim_{n\to\infty} (\frac{n+1}{n})^2

We can do some algebra and we got:

\lim_{n\to\infty} (1+\frac{1}{n})^2

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And when we apply the limit we got that:

\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1

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