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3 years ago

14

The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a r

ectangular prism is the product of its base area and height, what is the height of the prism?

2 answers:

olga55 [171]3 years ago

3 0

Dividing the volume by the base area, you find the height to be ...
$\frac{x^{4}+4x^{3}+3x^{2}+8x+4}{x^{3}+3x^{2}+8}=x+1-\frac{4}{x^{3}+3x^{2}+8}$

The height of the prism is $x+1-\frac{4}{x^{3}+3x^{2}+8}$

vladimir1956 [14]3 years ago

3 0

Solution:

Volume of Rectangular Prism = $x^4 + 4 x^3 + 3 x^2 + 8 x + 4$

Area of Base of Prism = $x^3 + 3 x^2 + 8$

As Given:

→→Volume of Rectangular Prism = Base Area × Height

→Height of Prism = $\frac{\text{Volume of Rectangular Prism}}{Base Area}$

→Height of Prism = $\frac{ x^4 + 4 x^3 + 3 x^2 + 8 x + 4}{x^3+3 x^2+8}$

= $\frac{(x+1)(x^3 + 3 x^2 +8) - 4}{ x^3+3 x^2+8 }\\\\=(x + 1)- \frac{4}{x^3+3x^2+8}$

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Amiraneli [1.4K]

What I always do to solve this, is find a common factor for each number first.

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3 years ago

Mariana [72]

-----------------------------------------------
Information Given:
-----------------------------------------------
ON = 7x - 9
LM = 6x + 4
MN = x - 7
OL = 2y - 7

-----------------------------------------------
Since it is a parallelogram:
-----------------------------------------------
ON = LM and
MN = OL

-----------------------------------------------
ON = LM:
-----------------------------------------------
7x - 9 = 6x + 4

-----------------------------------------------
Subtract 6x from both sides:
-----------------------------------------------
x - 9 = 4

-----------------------------------------------
Add 9 to both sides:
-----------------------------------------------
x = 13

-----------------------------------------------
MN = OL:
-----------------------------------------------
x - 7 = 2y - 7

-----------------------------------------------
Sub x = 13:
-----------------------------------------------
13 - 7 = 2y - 7

-----------------------------------------------
Simplify:
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6 = 2y - 7

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Add 7 on both sides:
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13 = 2y

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Divide by 2:
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y = 13/2

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Answer: x = 13, y = 13/2 (Answer D)
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6 0

3 years ago

Which expression represents the number 2i4−5i3+3i2+−81‾‾‾‾√ rewritten in a+bi form?

vichka [17]

Answer:

The expression $-1+14i$ represents the number $2i^4-5i^3+3i^2+\sqrt{-81}$ rewritten in a+bi form.

Step-by-step explanation:

The value of $i$ is $i=\sqrt{-1}[tex] or [tex]i^{2}=-1[\tex].Now [tex]i^{4}$ in term of $i^{2}[\tex] can be written as, [tex]i^{4}=i^{2}\times i^{2}$

Substituting the value,

$i^{4}=\left(-1\right)\times \left(-1\right)$

Product of two negative numbers is always positive.

$\therefore i^{4}=1$

Now $i^{3}$ in term of $i^{2}[\tex] can be written as, [tex]i^{3}=i^{2}\times i$

Substituting the value,

$i^{3}=\left(-1\right)\times i$

Product of one negative and one positive numbers is always negative.

$\therefore i^{3}=-i$

Now $\sqrt{-81}$ can be written as follows,

$\sqrt{-81}=\sqrt{\left(81\right)\times\left(-1\right)}$

Applying radical multiplication rule,

$\sqrt{ab}={\sqrt{a}}\sqrt{b}$

$\sqrt{\left(81\right)\times\left(-1\right)}={\sqrt{81}}\sqrt{-1}$

Now, $\sqrt{\left(81\right)=9$ and $\sqrt{-1}}=i$

$\therefore \sqrt{\left(81\right)\times\left(-1\right)}=9i$

Now substituting the above values in given expression,

$2i^4-5i^3+3i^2+\sqrt{-81}=2\left(1\right)-5\left(-i\right)+3\left(-1\right)+9i$

Simplifying,

$2+5i-3+9i$

Collecting similar terms,

$2-3+5i+9i$

Combining similar terms,

$-1+14i$

The above expression is in the form of a+bi which is the required expression.

Hence, option number 4 is correct.

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago