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muminat
3 years ago
9

A bird flies directly above a submarine. The bird is in the sky at 120 feet, while the submarine is 240 feet underwater. How far

above the submarine is the bird?
Mathematics
1 answer:
IgorC [24]3 years ago
8 0

Answer:

360

Step-by-step explanation:

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a regular sheet of letter (printing) paper measrues 8.5 inches by 11 inches. you want to cut out squares from each corner that i
Juliette [100K]

Answer:

The dimensions of the square, that will result in a box of maximum volume is a square with side length of approximately 1.585 inches

Step-by-step explanation:

The  given dimension of the steel sheet are;

The width = 8.5 inches

The length = 11 inches

Let 'x' represent the side length of the squares cut out, we have;

The length of the box formed, l = 11 - 2·x

The width of the box formed, w = 8.5 - 2·x

The height of the box, h = x

The volume of the box, V = (11 - 2·x) × (8.5 - 2·x) × (x) = 4·x³ - 39·x² + 93.5·x

The maximum or minimum volume is found from dV/dx = 0 at max. or min.

dV/dx = d(4·x³ - 39·x² + 93.5·x)/dx = 12·x² - 78·x + 93.5 = 0

Which gives;

x = (78 ± √((-78)² - 4×12×93.5))/(2 ×12)

x = 4.915 or 1.585

When x = 4.915, V = 4 × 4.915³ - 39 × 4.915² + 93.5 × 4.915 = -7.65

When x = 1.585, V = 4 × 1.585³ - 39 × 1.585² + 93.5 × 1.585 = 66.15

Therefore, the local maximum occurs at x ≈ 1.585

Therefore, the dimensions of the square, 'x' that will result in a box of maximum volume is x ≈ 1.585 inches.

5 0
3 years ago
Using the Babylonian method find √600 ???????????? √235.<br><br> how?
podryga [215]

Answer:

With the Babylonian method \sqrt{600} \approx 24.494897 and \sqrt{235} \approx 15.329709.

Step-by-step explanation:

  • To find the square root of 600, do the following:

1. Make an initial guess:  Because \sqrt{576}=24 and \sqrt{625} =25 you can start with x_{0}=24 as your initial guess.

2. Apply the formula:

x_{1}=\frac{(x_{0}+\frac{x}{x_{0}})}{2} where x=600

x_{1}=\frac{(24+\frac{600}{24})}{2}\\x_{1}=24.5

The number x_{1} is a better approximation to \sqrt{600}

3. Iterate until convergence:

For this apply the formula:

x_{n+1}=\frac{(x_{n}+\frac{x}{x_{n}})}{2}

Convergence is achieved when the digits of x_{n+1} and x_{n} agree to as many decimal places as you desire.

x_{2}=\frac{(x_{1}+\frac{x}{x_{1}})}{2}\\x_{2}=\frac{(24.5+\frac{600}{24.5})}{2}\\x_{2}=24.494897

x_{3}=\frac{(x_{2}+\frac{x}{x_{2}})}{2}\\x_{3}=\frac{(24.494897+\frac{600}{24.494897})}{2}\\x_{3}=24.494897\\

Because x_{2} and x_{3} agree to six decimal places. we can say that an estimate for \sqrt{600} \approx 24.494897.

You can compare with the value that WolframAlpha gives you which is \sqrt{600} \approx 24.49489742 you can see that it agrees to six decimal places.

  • To find the square root of 235, do the following:

1. Make an initial guess:  Because \sqrt{225}=15 and \sqrt{256} =16 you can start with x_{0}=15 as your initial guess.

2. Apply the formula:

x_{1}=\frac{(x_{0}+\frac{x}{x_{0}})}{2} where x=235

x_{1}=\frac{(15+\frac{235}{15})}{2}\\x_{1}=\frac{46}{3}

3. Iterate until convergence:

Apply the formula:

x_{n+1}=\frac{(x_{n}+\frac{x}{x_{n}})}{2}

x_{2}=\frac{(x_{1}+\frac{235}{x_{1}})}{2}\\x_{2}=\frac{(\frac{46}{3}+\frac{235}{\frac{46}{3}})}{2} \\x_{2}=15.329710

x_{3}=\frac{(x_{2}+\frac{235}{x_{2}})}{2}\\x_{3}=\frac{(15.329710+\frac{235}{15.329710})}{2} \\x_{3}=15.329709

x_{4}=\frac{(x_{3}+\frac{235}{x_{3}})}{2}\\x_{4}=\frac{(15.329709+\frac{235}{15.329709})}{2} \\x_{3}=15.329709

Because x_{3} and x_{4} agree to six decimal places. We can say that an estimate for \sqrt{235} \approx 15.329709.

WolframAlpha gives you \sqrt{235} \approx 15.329709716

4 0
4 years ago
Asapppppp please i need help i need to pass
cricket20 [7]

Answer:

Option 2 which is r^6

Step-by-step explanation:

You need to apply the exponent rules.

Since the r's are the same, you can subtract the exponents.

r^9 - r^3 = r^6

Notice that the bases ("r") stayed the same.

7 0
2 years ago
Read 2 more answers
Jack and Susan bought together 28 books. Susan bought 11 books. Which one of the
Viefleur [7K]

Answer:

11 + x = 28

Step-by-step explanation:

The number of books they bought must add to 28.

3 0
2 years ago
Is - 29/8 &lt; , &gt; or = - 3.62
andreyandreev [35.5K]
When -29/8 is written as a decimal it becomes
- 3.625
Which is equivalent to -3.63, rounded to the nearest hundredth.

Now from here we will be able to tell if they're < , > or =

So, -3.63 is > -3.62

ANSWER: -29/8 > -3.62
3 0
3 years ago
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