Como se relacionan los valores de los ochos en 880

A box in the shape of a rectangular prism has a volume of 96 cubic feet. The box has a length of (x+8) feet, a width of x feet,

anygoal [31]

96=(x+8)*x*(x-2)=x^3 +6x^2 -16x. Solve to get x= -6,-4,4. Negative distance doesn't make sense, so x=+4. Therefore, length is (x+8)=(4+8)= 12, width=x=4, and height=(x-2)=(4-2)=2.

3 0

3 years ago

The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expect

Liula [17]

Answer:

After 25 years the population will be:

Australia: 22271200
China: 1580220878
Mexico: 157380127
Zaire: 112794819

Step-by-step explanation:

Growth rate problem that has a growth rate proportional to the population size can be solved using the equation:

P(t) = P₀eʳᵗ

t is your unit of time. It could be days, or hours, or minutes. It changes depending on each problem. In this problem, t is measured in years because you're jumping from 2000 to 2025. Years just makes the most sense to measure that leap in time.

P(t) is the population at time t. An example in this problem could be P(20) would be the population 20 years after the initial count. or maybe P(12) would be the population 12 years after the initial count. or P(0) would be the initial count of the population.

P₀ is the initial population at P(0)
r is the growth rate. Don't forget to convert the percentage to its decimal form

Now that everything is set out, lets use the equation to solve for our answer.

P(t) = P₀eʳᵗ

Australia:

$P(t)=(19169000)e^{(0.006)t}$

after 25 years

$P(25)=(19169000)e^{(0.006)(25)}=22271200.6$

China:

$P(t) = (1261832000)e^{(.009)t}$

after 25 years:

$P(25)=(1261832000)e^{(.009)(25)}=1580220878$

Mexico:

$P(t) = (100350000)e^{(0.018)t}$

after 25 years:

$P(25)=(100350000)e^{(0.018)(25)}=157380127.8$

Zaire:

$P(t) = (51965000)e^{(0.031)t}$

after 25 years:

$P(25)=(51965000)e^{(0.031)(25)}=112794819.9$

6 0

4 years ago

Hello, Brainly community!

ioda

Answer:

(B) $\displaystyle \frac{W(3.1) - W(2.9)}{0.2}$

General Formulas and Concepts:

Calculus

Limits

Derivatives

The definition of a derivative is the slope of the tangent line.

Derivative Notation

Instantaneous Rates

Tangent Line: $\displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}$

Step-by-step explanation:

Since we are trying to find a rate at which W(t) changes, we must find the derivative at t = 3.

We are given 2 close answer choices that would have the same numerical answer but different meanings:

(A) $\displaystyle \lim_{t \to 3} W(t)$
(B) $\displaystyle \frac{W(3.1) - W(2.9)}{0.2}$

If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the rate at which the volume would be changing and it is not a derivative.

If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a derivative at t = 3, and a derivative tells us what rate something is changing.

∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

8 0

3 years ago

5(-3x - 2) - (x - 3) = -4 (4x +5) + 13

S_A_V [24]

Start off by distributing the numbers into the parentheses:

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
-15x - 10 - (x - 3) = -16x - 20 + 13

(Note: It's super important to be careful when opening up negative parentheses! -(x-3) is not just - x - 3, it is actually -x + 3 since the negative is distributed in every number!)

-15x - 10 - x + 3 = -16x - 20 + 13
-16x - 7 = -16x - 7
-16x = -16x
0 = 0

There is an infinite number of solutions in this equation.

(When you get 0=0 when solving for a variable, that means that said variable will have infinite solutions, that is, any number plugged into the equation will work)

4 0

3 years ago

Read 2 more answers

The value, V (t), in dollars, of a stock t months after it is purchased is modeled by the following equation.

11Alexandr11 [23.1K]

Answer:

Step-by-step explanation: $V(t)= 42(1-e ^{1.5t} ) +36$ is given value in dollars of a stock in t months after it is purchased.