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alukav5142 [94]
3 years ago
13

Write these numbers in standard notation. 3.05 x 10–3 8.92 x 106

Mathematics
2 answers:
Bad White [126]3 years ago
3 0

3.05  \times   {10}^{ - 3} =0.00305 \\8.92 \times  {10}^{6} =   8920000
Flauer [41]3 years ago
3 0

Answer:

We have been given the two numbers:

3.05 \cdot 10^{-3}

And 8.92\cdot 10^{6}

x^{-a}=\frac{1}{x^a}

10^{-3}=\frac{1}{10^3}=\frac{1}{1000}

So, 3.05 \cdot 10^{-3}=\frac{3.05}{1000}

\Rightarrow 0.00305

And 8.92\cdot 10^{6}=\frac{892}{100}\cdot {1000000}

892\cdot 10000

\Rightarrow 8920000

3.05 \cdot 10^{-3}=0.00305

8.92\cdot 10^{6}=8920000

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Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

  • A cuboid has 6 faces.
  • A cuboid contains 8 vertices.
  • A cuboid contains 12 edges .
  • The total surface area of a cuboid is

           = 2(length×breadth+breadth×height+length×height) square units

  • The dimension of a cuboid is written as length×breadth×height.
  • The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

=[x\times 2x\times (x+2)]   cubic inches

=[2x^2(x+2)]     cubic inches

=(2x^3+4x^2)     cubic inches

According to the problem,

2x^3+4x^2=192

\Rightarrow 2x^3+4x^2-192=0

\Rightarrow 2(x^3+2x^2-96)=0

\Rightarrow (x^3+2x^2-96)=0

\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0

\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0

\Rightarrow (x-4)(x^2+6x+24)=0

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

 length=(2×4) inches=8 inches

 and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

8 0
3 years ago
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