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slega [8]
3 years ago
7

An open box is to be made from a flat piece of material 14 inches long and 6 inches wide by cutting equal squares of length xfro

m the corners and folding up the sides. Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors.
Mathematics
1 answer:
Ludmilka [50]3 years ago
6 0

Answer:

f(x)=x(14-2x)(6-2x)

Step-by-step explanation:

We are given that

Length of flat piece of material=14 in

Width of flat piece of material=6 in

We have to find the volume of box as a  function of x.

An open box is made from flat piece of material by cutting equal squares of length x from the corner and folding up the sides.

Therefore, Height of box=x in

Length of box=14-2x in

Width of box=6-2x in

We know that volume of box=length\times breadth\times height

Using the formula

Volume of box=f(x)=x(14-2x)(6-2x)

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Which is the equation of a hyperbola centered at the origin with x-intercept +\- 3 and asymptote y=2x
Radda [10]

Answer:

{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}

Step-by-step explanation:

The hyperbola has x-intercepts, so it has a horizontal transverse axis.

The standard form of the equation of a hyperbola with a horizontal transverse axis is  \dfrac{(x - h)^{2}}{a^{2}} - \dfrac{(y - k)^{2}}{b^{2}} = 1

The center is at (h,k).

The distance between the vertices is 2a.

The equations of the asymptotes arey = k \pm \dfrac{b}{a}(x - h)

1. Calculate h and k. The hyperbola is symmetric about the origin, so  

h = 0 and k = 0

2. For 'a': 2a = x₂ - x₁ = 3 - (-3) = 3 + 3 = 6

a = 6/2 = 3  

3. For 'b': The equation for the asymptote with the positive slope is  

y = k + \dfrac{b}{a}(x - h) = \dfrac{b}{a}x

Thus,  asymptote has the slope of

\begin{array}{rcl}m& =& \dfrac{b}{a}\\\\2& =& \dfrac{b}{3}\\\\b& =& \mathbf{6}\end{array}

4.  The equation of the hyperbola is

\large \boxed{\mathbf{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}}

The attachment below represents your hyperbola with x-intercepts at ±3 and asymptotes with slope ±2.

7 0
3 years ago
a shape with rotational symmetry can be rotated around a point so that all of its characteristics are maintained
kirza4 [7]

The correct answer to this is “True”.

Symmetry signifies balance and form. An object with rotational symmetry will still look the same after a rotation. Since it maintains its shape and figure after being rotated, therefore its characteristics such as length of the diagonals, the angles of each corner, or parallelism of opposite sides will remain the same.

4 0
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Evgesh-ka [11]
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Explanation:

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There are 3600 x 24 = 86400s in 1 day

And one month = 30 days

86400 x 30 = 2, 592, 000s in 1 month

Write in scientific notation:

2, 592, 000 = 2.592 x 10^6

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Nicola claims that the product of any fraction and 1616 will always be less than 1616. complete the sentences below about nicola
LUCKY_DIMON [66]
Can't see the answer choices but Nicola is wrong. 16 * (12/8) = 24>16
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Answer:

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