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never [62]
2 years ago
10

The volume of a rectangular prism (shown below) is 48x^3+56x^2+16x Answer the following questions:

Mathematics
1 answer:
pickupchik [31]2 years ago
8 0

Answer:

(a)

Length = 8x\\Width = 3x + 2\\Height = 2x + 1

(b)

P(2) = 640

(c)

Length= 16

Width = 8

Height =5

(d)

Volume = 640

Step-by-step explanation:

Given

P(x) = 48x^3 + 56x^2 + 16x

Solving (a): The prism dimension

We have:

P(x) = 48x^3 + 56x^2 + 16x

Factor out 8x

P(x) = 8x(6x^2 + 7x + 2)

Expand 7x

P(x) = 8x(6x^2 + 4x + 3x + 2)

Factorize

P(x) = 8x(2x(3x + 2) +1( 3x + 2))

Factor out 3x + 2

P(x) = 8x(3x + 2)(2x + 1)

So, the dimensions are:

Length = 8x\\Width = 3x + 2\\Height = 2x + 1

Solving (b): The volume when x = 2

We have:

P(x) = 48x^3 + 56x^2 + 16x

P(2) = 48 * 2^3 + 56 * 2^2 + 16 * 2

P(2) = 640

Solving (c): The dimensions when x = 2

We have:

Length = 8x\\Width = 3x + 2\\Height = 2x + 1

Substitute 2 for x

Length=8*2

Length= 16

Width = 3*2+2

Width = 8

Height = 2*2 + 1

Height =5

So, we have:

Length= 16

Width = 8

Height =5

Solving (d), the volume in (c)

We have:

Volume = Length * Width * Height

Volume = 16 * 8 * 5

Volume = 640

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the general solution has a form of,

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\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}

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r3t40

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3 years ago
A coordinate grid with 2 lines. The first line is labeled g(x) and passes through the points (negative 3, 0) and (0, 2). The sec
Snezhnost [94]

The correct answer is option c i.e. (0, 2)

<h3>What is Linear Equation?</h3>

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Here, The solution to this Linear System is already shown by the graph. This is also called the Graph Method. The Solution of this Linear System is this common point in this case, (0,2).

Since each equation is represented by a line. So We have  g(x) for the red line, and f(x) for the blue one. Each line is a set of points, We know that from the Euclidean Geometry and its common point (0,2) solves this system.

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Learn more about linear equation from:

brainly.com/question/11897796

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Mars2501 [29]

Answer:

The answer to -8 1/2 + 4 1/14 = -4 3/7

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Step-by-step explanation:

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