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ExtremeBDS [4]
3 years ago
8

An open box is to be made from a flat square piece of material 16 inches in length and width by cutting equal squares of length

x x from the corners and folding up the sides. Write the volume V V of the box as a function of x x. Leave it as a product of factors; you do not have to multiply out the factors.
Mathematics
1 answer:
vaieri [72.5K]3 years ago
7 0

Answer:

V = x(19-2x)(4-2x)

Step-by-step explanation:

We are given;

Length of flat piece of material =19 inches

Width of flat piece = 4 inches

We are told that the open box is to be made from a flat piece by cutting equal squares of length x from the corners and folding up the sides

Thus, we will now have;

length of open box = (19-2x) inches

Width of open box = (4-2x) inches

Height of box = x inches

We know that: Volume of box = length × width × height

So, plugging in the relevant values, we have;

Volume of box(V) = x(19-2x)(4-2x)

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Anestetic [448]

Step-by-step explanation:

4x - 3 + 7x + 1

Solving like terms

11x - 2

6 0
3 years ago
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A=V1-V0/t solve for V1
MA_775_DIABLO [31]
 A = V1 - V0/t.....multiply both sides by t
At = V1 - V0....add V0 to both sides
At + V0 = V1
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A storage tank contains a liquid radioactive element with a half-life of 96 years. It will be relatively safe for the contents t
PolarNik [594]

Answer:

The tank must remain intact for 1183 years.

Step-by-step explanation:

Exponential equation for decay:

The amount of a substance after t years is given by:

A(t) = A(0)e^{rt}

In which A(0) is the initial amount and r is the decay rate.

A storage tank contains a liquid radioactive element with a half-life of 96 years.

This means that A(96) = 0.5A(0), and we use this to find r.

A(t) = A(0)e^{rt}

0.5A(0) = A(0)e^{96r}

e^{96r} = 0.5

\ln{e^{96r}} = \ln{0.5}

96r = \ln{0.5}

r = \frac{\ln{0.5}}{96}

r = -0.0072

So

A(t) = A(0)e^{-0.0072t}

It will be relatively safe for the contents to leak from the tank when 0.02% of the radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?

This is t for which A(t) = 0.0002A(0). So

A(t) = A(0)e^{-0.0072t}

0.0002A(0) = A(0)e^{-0.0072t}

e^{-0.0072t} = 0.0002

\ln{e^{-0.0072t}} = \ln{0.0002}

-0.0072t = \ln{0.0002}

t = -\frac{\ln{0.0002}}{0.0072}

t = 1183

The tank must remain intact for 1183 years.

5 0
3 years ago
Find the amount withheld for Social Security weekly:
stira [4]

The amount withheld for Social Security weekly: $21.70.

<h3>Social security</h3>

Social security rate is 6.2% or 0.062

Weekly salary=$350

Using this formula

Social security=Social security rate×Weekly salary

Let plug in the formula

Social security=0.062×$350

Social security=$21.70

Therefore the amount withheld for Social Security weekly: $21.70.

Learn more about Social security here:brainly.com/question/1156607

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7 0
1 year ago
Need help with this i don't understand
Oksana_A [137]

Answer:

  1. 7
  2. see below
  3. 5
  4. the rule is not one-to-one

Step-by-step explanation:

Applying the squaring rule to each of the elements of the domain, we get ...

  \begin{array}{cc}\text{Domain}&\text{Range}\\1&1\\-3&9\\-\frac{1}{2}&\frac{1}{4}\\3&9\\2&4\\\frac{1}{4}&\frac{1}{16}\\0.5&\frac{1}{4}\end{array}

__

1. There are 7 different numbers in the Domain list.

2. See above

3. There are 5 different numbers in the Range list.

4. The rule "square me" is not "one-to-one" Two different values in the domain can result in the same value in the range. -3 and 3 both result in 9. -1/2 and 0.5 both result in 1/4.

5 0
2 years ago
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