# Jason is covering an ottoman with fabric. The ottoman is in the shape of a rectangular prism that is 37 cm long, 21 wide, and 30 cm high. How much fabric is needed to cover the sides and top of the ottoman? Explain your strategy.

2 months ago

## Solution 1

Guest #3322
2 months ago
We know that
we need to calculate the surface area including only one base

surface area=area of the base+perimeter of the base*height

area of the base=37*21----> 777 cm
²

perimeter of the base=2*[37+21]----> 116 cm

height of the prism=30 cm
surface area=777+116*30-----> 4257 cm²

4257 cm²

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What logarithmic equation has the same solution as x-4=2^3
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What logarithmic equation has the same solution as x-4=2^3

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x-4=2³

x-4=2*2*2

x-4=8

TO solve for x, Let us add 4 on both sides

x-4+4=8+4

x+0=12

So, x=12

But, x=12 is not a logarithmic equation and there are no options

So, an equation like, x=㏒

As log has base 10,

So, x=㏒ =12

So, logarithmic equation like x=log has same solution as x-4=2³

Solution 2

is required lograthmic equation.

Step-by-step explanation:

Given: Given equation, x - 4 = 2³

To find: Logarithmic function whose solution is same as given equation.

First we find the solution of given Equation.

consider,

x - 4 = 2³

x - 4 = 8        ( ∵ 2³ = 2×2×2 = 8 )

x = 8 + 4       ( Transposing 4 to RHS )

x = 12

Now we find the logarithmic equation whose solution is also x = 12.

( There exist many such equations )

Lets say one of them is,

Now we find its solution to check if it is same or not.

(using lograthmic rule,)

⇒ 2 × ( x + 2 ) = 28  (using lograthmic rule, )

⇒ 2x + 4 = 28

⇒ 2x = 28 - 4     (transposing 4 to RHS)

⇒ 2x = 24          (transposing 2 to RHS)

⇒ x = 12

Therefore, is required lograthmic equation.

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