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3 years ago

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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Solve by substitution 3x-4y=-4 y=2x-4

dybincka [34]

Answer:

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Step-by-step explanation:

From first function we have:

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And from the second one:

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2 years ago

Lim->infinity 4n^2/n^2+10000n

dybincka [34]

let P(n)=4n² / n²+10000n
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3 years ago

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timama [110]

Use the change-of-basis identity,

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

to write

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

Use the product-to-sum identity,

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

to write

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

Redistribute the factors on the left side as

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

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.

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

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

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2 years ago