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photoshop1234 [79]
3 years ago
6

Solve the equation (x – 2)^2 – 1 = 13 symbolically. Leave your answer in radical form.

Mathematics
1 answer:
Sliva [168]3 years ago
6 0

Answer:

x = square root of 13

Step-by-step explanation:

x^2 + 4 - 1 = 13

x^2 + 3 = 13

subtract 3

x^2 = 13

square root x^2 and 13

x = square root of 13

Hopefully this helps you understand this concept.

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If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in
Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume (V), in cubic centimeters, and surface area (A_{s}), in square centimeters, of the box with a square base are described below:

A_{s} = l^{2}+h\cdot l (1)

V = l^{2}\cdot h (2)

Where:

l - Side length of the base, in centimeters.

h - Height of the box, in centimeters.

By (2), we clear h within the formula:

h = \frac{V}{l^{2}}

And we apply in (1) and simplify the resulting expression:

A_{s} = l^{2}+ \frac{V}{l}

A_{s}\cdot l = l^{3}+V

V = A_{s}\cdot l -l^{3} (3)

Then, we find the first and second derivatives of this expression:

V' = A_{s}-3\cdot l^{2} (4)

V'' = -6\cdot l (5)

If V' = 0 and A_{s} = 30000\,cm^{2}, then we find the critical value of the side length of the base is:

30000-3\cdot l^{2} = 0

3\cdot l^{2} = 30000

l = 100\,cm

Then, we evaluate this result in the expression of the second derivative:

V'' = -600

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

V = 30000\cdot l - l^{3}

V = 2000000\,cm^{3}

The largest possible volume of the box is 2000000 cubic meters.

4 0
2 years ago
-2/3x = -1. What’s the answer?
Morgarella [4.7K]
The main Answer is X=3/2
Incase you need it in decimal point it’s X=1.5 and Mixed number form it’s X=1 1/2
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8. 20-11+m

9. 30-17=h

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What is the value of this expression? 5/6 - (1/8•3/4)
givi [52]

Answer:

71/96 or 0.74

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