Mathematics: Using the polynomials q = 3 x2 + 5 x - 2, r = 2 - x2 , and s = 2 x + 5, perform the indicated operation. q - [ r + s ]

Using the polynomials q = 3 x2 + 5 x - 2, r = 2

bandithcarroyuqhi

11.03.2022

4x^2 + 3x - 9

Step-by-step explanation:

First, add together functions R(x) and S(x). Stack them vertically and combine like terms:

R(x) = 2 - x^2

S(x) = 2x + 5

(R+S)(x) = -x^2 + 2x + 7

Now subtract the above result from Q(x):

Q(x) - (R(x) + S(x)) = 3x^2 + 5x - 2 + x^2 - 2x - 7, or 4x^2 + 3x - 9

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nataliahenderso

21.12.2022

(See explanation)

Step-by-step explanation:

The differential equation for a exponential growth is:

$\frac{dn}{dt} = k\cdot n$

The formula is rearranged and integrated afterwards:

$\frac{dn}{n} = k \cdot dt$

$\int\limits_{n_{o}}^{n} {\frac{dn}{n} } = k\cdot \int\limits_{0}^{t}\, dt$

$\ln \frac{n}{n_{o}} = k\cdot t$

$\frac{n}{n_{o}} = e^{ k\cdot t}$

$n = n_{o}\cdot e^{k\cdot t}$

The exponential growth function can be used to find the montly growth function as follows:

$\ln 1.2 = k\cdot 12$

k = 0.015

The coeffcients of the expression are, respectively:

$n_{o} = 25$

k = 0.015

The exponential growth function with a monthly growth rate is:

$n(t) = 25\cdot e^{0.015\cdot t}$ , where t is measured in months.

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