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hichkok12 [17]
3 years ago
13

The dimensions of a rectangular prism can be expressed as width w,length w+4, and height 5-w.What is the approximate width (w) t

hat will maximize the volume of the tank?

Mathematics
2 answers:
Alenkinab [10]3 years ago
8 0

Answer:

The approximate value of w that maximize the volume

V = -w³ + w² + 20w

is w = 3 units

Step-by-step explanation:

Volume of rectangular prism is given by the formula:

V = Bh

B is the base, and

B = lw

Where l is the length of the rectangle, and w is the width.

B = w(w + 4)

= w² + 4w

V = Bh

= (w² + 4w)(5 - w)

= 5w² - w³ + 20w - 4w²

V = -w³ + w² + 20w

To obtain the approximate value of w that maximizes the volume, let us solve:

-w³ + w² + 20w = 0

w(-w² + w + 20) = 0

w = 0

Or

-w² + w + 20 = 0

Using the quadratic formula,

w = [-b±√(b² - 4ac)]/2a

Where a = -1, b = 1, and c = 20.

w = {-1 ±√[(1 - 4(1)(20)]}/2(-1)

= (-1 ±√25)/(-2)

= 1/2 ± -5/2

w = 1/2 + 5/2

= -4/2 = -2

w = 1/2 - 5/2

= 6/2 = 3

Now we have the following values for w.

w = 0 or -2 or 3

The maximum of these is 3, and it is what we are looking for.

k0ka [10]3 years ago
5 0

The solution is in the attachment

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Write a numerical expression that matches the phrase: 8 more than the product of 3 and 2.
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Answer:

8+3(2)

Step-by-step explanation:

8 more than indicates addition, so that makes the first part of the expression 8+.

The product of 3 and 2 indicates multiplication, since product means the result of multiplication. That finishes the expression with 3(2).

In conclusion, a numerical expression that matches the states phrase is 8+3(2). You can also do 8+3×2 too, as they equal the same thing.

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Can anyone help? thanks in advance!
Kipish [7]

Answer:

B(2,4)

Step-by-step explanation:

A(-1,-9)

M(0.5,-2.5)

with M we can find x₂ and y₂

x = 0.5

x = x₁+x₂/2

0.5 = (-1 + x₂)/2

(x₂ -1)/2 = 0.5

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x₂-1=1

x₂=2

for y₂

y= -2.5

y=(y₁+y₂)/2

y=(-9+y₂)/2

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Answer the questions below about Line 1 and Line 2 shown below.
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  1. The expression was rewritten using the commutative law of addition.
  2. Line 1 says 3 + 4, which could be represented using dots as ••• + •••• for a total of 7 dots.
  3. Line 2 says 4 + 3, which could be represented using dots as •••• + ••• for a total of 7 dots.

<h3>What is the commutative law of addition?</h3>

The commutative law of addition is also referred to as the law of cumulative addition and it states that if two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.

This ultimately implies that, the sum of addends would always be the same (equal) regardless of their arrangement in accordance with the commutative law of addition. Mathematically, the commutative law of addition can be represented using the following formula:

A + B = B + A.

In this context, we can reasonably infer and logically deduce that the given expression was rewritten using the commutative law of addition.

In conclusion, Line 1 says 3 + 4, which could be represented using dots as ••• + •••• for a total of 7 dots. Line 2 says 4 + 3, which could be represented using dots as •••• + ••• for a total of 7 dots.

Read more on commutative law of addition here: brainly.com/question/778086

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