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Ivan
3 years ago
12

Length = 4 + x Width = x Height = x2 + 1 What is the base area of Box 3?

Mathematics
2 answers:
Simora [160]3 years ago
8 0

Answer:

Base area of box = x^2 +4

Step-by-step explanation:

Length = 4+x

Width = x

Height = x^2 + 1

Base area of a rectangular box is a rectangle

Area of a rectangle (base area)= length times width

Length = 4+x

Width = x

Base area = (4+x) \cdot x

Multiply x inside the parenthesis

Base area of box = 4x +x^2

astraxan [27]3 years ago
3 0

Answer:

Box 3:      

Length = 4 + x

Width = x

Height = x2 + 1

The polynomial that represents the volume of Box 3 has a degree of  4

What is the base area of Box 3?  1 x2 +  4 x

What is the volume of Box 3?

B. x4 + 4x3 + x2 + 4x

Step-by-step explanation:

On Edgenuity

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\log_x(y) = \dfrac{\ln(y)}{\ln(x)}

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xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}

Use the product-to-sum identity,

\log_x(yz) = \log_x(y) + \log_x(z)

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xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}

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xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}

and simplify to

xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)

Now expand the right side:

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}

Simplify and rewrite using the logarithm properties mentioned earlier.

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1

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(C)

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