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iVinArrow [24]
3 years ago
5

Simplify 27^2. please (thxx)

Mathematics
1 answer:
adoni [48]3 years ago
4 0

Answer:

729

Step-by-step explanation:

Raise 27 to the power of 2.

729

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If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid
Artist 52 [7]
Check the picture below.  Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm².  Also, recall, the base is a square, thus, length = width = x.

\bf \textit{volume of a rectangular prism}\\\\&#10;V=lwh\quad &#10;\begin{cases}&#10;l = length\\&#10;w=width\\&#10;h=height\\&#10;-----\\&#10;w=l=x&#10;\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\&#10;-------------------------------\\\\&#10;\textit{surface area}\\\\&#10;S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h&#10;\\\\\\&#10;\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\&#10;-------------------------------\\\\&#10;V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3

so.. that'd be the V(x) for such box, now, where is the maximum point at?

\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2&#10;\\\\\\&#10;\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100&#10;\\\\\\&#10;x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it.  Check the second picture below.

so, the volume will then be at   \bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3

6 0
3 years ago
-17-5(x+3)=3x plz help
katovenus [111]
  1. Start by distributing the -5 into the x and 3
  2. -17-5x-15=3x
  3. add like terms
  4. -5x-32=3x
  5. add 32 to both sides
  6. -5x=3x+32
  7. subtract 3x from both
  8. -8x=32
  9. divide both by -8
  10. x=-4

7 0
3 years ago
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Lesechka [4]

Answer:

14). 2nd quadrant

15). 1st quadrant

Step-by-step explanation:

14).Coordinates of a point → J(-8, -12)

    Coordinates of the new point J' after reflection of x-axis will follow the rule,

    (x, y) → (x, -y)

    Coordinates of J' → (-8, 12)

    Therefore, point J' will lie in 2nd quadrant.

15). Coordinates of a point → W(-6, 7)

    Rule for the rotation by 90°clockwise about the origin,

    (x, y) → (y, -x)

    Coordinates of point W → (-6, 7)

    Following this rule,

    W(-6, 7) → W'(7, 6)

    Therefore, point W' will lie in the first quadrant.

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At the mall Julie finds a sale at her favorite store. Two pair of pants will cost $42. If she wants to buy 5 pair, how much will
katovenus [111]
Divide 42 by two and then multiply by 5
5 0
3 years ago
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lesantik [10]

Answer:

so im guessing  the remainder of hw problems->

Step-by-step explanation:

24-7 =17 math problems left from doing some lunch

17-7= 10 math so its 10 math problems left

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