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3 years ago

12

Two fish are put in a man-made lake with no other fish in it. Each month, the fish population triples. Which model and equation

best represents this plan?

1 answer:

aleksandr82 [10.1K]3 years ago

8 0

Answer:

Step-by-step explanation:

The basic model for this growth is the exponential function: y = a(b)^c, where a is the initial value, b is the growth rate and c is the time.

Here we have P = fish population = (2 fish)(3)^t

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

pickupchik [31]

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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What is the value of |B| – |A|? <br><br> A. 4<br> B. –10<br> C. 10<br> D. –4

Elena L [17]

Answer:

A. 4

Step-by-step explanation:

We can look at the number line and find B and A

we get

B=-7

A=3

now, we can find |B| and |A|

$|B|=|-7|=7$

$|A|=|3|=3$

now, we can find

|B|-|A|

now, we can plug values

$|B|-|A|=7-3$

$|B|-|A|=4$

So,

option-A

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