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Softa [21]
3 years ago
10

Find a formula for the described function. an open rectangular box with volume 9 m3 has a square base. express the surface area

sa of the box as a function of the length of a side of the base, x. sa = x2+ 36 x​ m2 state the domain of sa.
Mathematics
1 answer:
Maru [420]3 years ago
6 0

Let

x--------> the length side of the square base

h--------> the height of the box

we know that

<u>the volume of the box is equal to</u>

V=x^{2} *h\\ V=9\ m^{3}

so

x^{2} *h=9\\\\h=\frac{9}{x^{2} }

<u>the surface area of the box is equal to</u>

SA=area\ of\ the\ base+perimeter\ of\ base*height (remember that the box is open)

area of the base=(x^{2})\ m^{2}

Perimeter of the base=(4*x)\ m

height=(h) m

h=\frac{9}{x^{2}}

substitute

SA=x^{2} +4*x*h\\ \\ \\ SA=x^{2} +4*x*\frac{9}{x^{2} } \\ \\ SA=x^{2} +\frac{36}{x}

we know that

the value of x can not be negative and the denominator can not be zero

therefore

<u>the answer is</u>

the domain of  SA is x> 0

the domain is the interval-------------> (0,∞)

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-3/4x+1/3y=12
</span>Geometric figure: Straight Line
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3 years ago
Read 2 more answers
The perimeter of the triangle is 42. Find the length of all the sides.
iragen [17]
<h3>Given :-</h3>

  • Perimeter of triangle = 42

  • Side 1 of triangle = (x + 4)

  • Side 2 of triangle = (3x + 8)

  • Side 3 of triangle = (5x + 6)

<h3>To find:-</h3>

  • Length of sides

<h3>Explanation:</h3>

So to find length of sides we have to find the value of x.We can find value of x , by this formula:

\\  \\

\bigstar \boxed{ \rm perimeter \: of \triangle \:  = side_1 + side_2 + side_3}

\\  \\

So:-

\\

\dashrightarrow \tt perimeter \: of \triangle \:  = side_1 + side_2 + side_3 \\

\\  \\

\dashrightarrow \tt 42  = (x + 4) + (3x + 8)+( 5x + 6) \\

\\  \\

\dashrightarrow \tt 42  = x + 4+ 3x + 8+5x + 6 \\

\\  \\

\dashrightarrow \tt 42  = x + 3x+5x+ 4 + 8 + 6 \\

\\  \\

\dashrightarrow \tt 42  = 9x+ 4 + 8 + 6 \\

\\  \\

\dashrightarrow \tt 42  = 9x+ 18\\

\\  \\

\dashrightarrow \tt 42  - 18 = 9x \\

\\  \\

\dashrightarrow \tt 24 = 9x \\

\\  \\

\dashrightarrow \tt  9x = 24 \\

\\  \\

\dashrightarrow \tt  x = \dfrac{24}{9}  \\

\\  \\

\dashrightarrow \bf  x =2.67 \{approx \}\\

\\  \\

  • Side 1 of triangle = (x + 4)
  • Side 1 of triangle =2.67 + 4
  • Side 1 of triangle = 6.67

  • Side 2 of triangle = 3x + 8
  • Side 2 of triangle = 3 × 6.67 + 8
  • Side 2 of triangle = 20.01 + 8
  • Side 2 of triangle = 28.01

  • Side 3 of triangle = 5x + 6
  • Side 3 of triangle = 5 × 2.67 + 6
  • Side 3 of triangle = 13.35 + 6
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━━━━━━━━━━━━━━━━

~WindyMint

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Answer:

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Step-by-step explanation:

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Another way of looking at it is for the totals.  there are 550 total, so 2/5 of that is green.  2/5 of 550 is 220, while 3/5 is 330  so that means of the 550, the ratio is 220:330.  Kinda like simplifying fractions where 220/550 is the same thing as 2/5

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