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Levart [38]
3 years ago
6

Find the surface area of the cube shown below.

Mathematics
2 answers:
sashaice [31]3 years ago
8 0

Answer:

37.5 or 37 1/2

Step-by-step explanation:

The formula for finding surface area in a cube is A=6a^2

substituting 2.5 instead of a will result in this equation. A=6(2.5)^2

solving algebraically will then get you to your answer of 37.5

Ghella [55]3 years ago
8 0

Answer:

<h2>S.A. = 37.5</h2>

Step-by-step explanation:

Each cube has six faces. All faces are congruent and each of them is a square.

The fromula of an area of a square is:

A=s^2

<em>s - </em><em>length of a side of a square</em>

<em />

We have

s=2\dfrac{1}{2}

Convert it to a decimal

s=2\dfrac{1}{2}=2.5

Substitute to the formula of an area of a square:

A=(2.5)^2=(2.5)(2.5)=6.25

The Surface Area of a cube:

S.A.=6A

Substitute:

S.A.=6\cdot6.25=37.5

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Answer:

  1.3363

Step-by-step explanation:

The basic idea here is to find an expression for the direction vector between a point on L1 and a point on L2. Then, solve for the points on L1 and L2 that make that vector perpendicular to both lines L1 and L2. (The dot product of direction vectors is zero.) The distance between the points found is the shortest distance between the lines.

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Let P be a point on L1. Then the parametric equation for P is ...

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Let Q be a point on L2. The direction vector for L2 is given by the difference between the given points. It is (4-1, 1-(-1), 6-1) = (3, 2, 5). Then the parametric equation for Q is ...

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The direction vector for PQ is ...

  Q -P = (3s+1-6t, 2s-1, 5s+1+t)

The dot product of this and the two lines' direction vectors will be zero:

  (3s+1-6t, 2s-1, 5s+1+t)·(6, 0, -1) = 0 = 13s -37t +5 . . . perpendicular to L1

  (3s+1-6t, 2s-1, 5s+1+t)·(3, 2, 5) = 0 = 38s -13t +6 . . . perpendicular to L2

The solution to these equations is ...

  s = -157/1237

  t = 112/1237

Then (Q-P) becomes (94, -1551, 564)/1237, and its length is ...

  |PQ| = √(94² +1551² +564²)/1237 ≈ 1.3363

The distance between the two lines is about 1.3363 units.

8 0
3 years ago
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Elanso [62]
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3 years ago
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BaLLatris [955]
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3 years ago
3x^2+7x+3<br> + 5x^2+12x
Dvinal [7]

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Step-by-step explanation:

Simplify the expression by combining like terms. Terms which look a like and sound a like should be added together.

3x^2+7x+3+5x^2+12x

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Suppose y varies directly as x, and y =15 when x = 3. Find the constant of variation (k).
vovangra [49]

Answer:

k = 5

Step-by-step explanation:

y = kx

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k = 15/3

k = 5

8 0
3 years ago
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