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3 years ago

Simplify the following expression: -10x + 15 - 3x + 2 *

Mathematics

1 answer:

polet [3.4K]3 years ago

8 0

= -10x+15-3x+2
= -13x+17

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1. The table shows values of a function . What is the average rate of change of over the interval from x = 5 to x = 9? Show your

dmitriy555 [2]

Answer:

Average change of rate = 4

Step-by-step explanation:

The average rate of change is going to be the final value mines the initial value, divided by the change in the input of the function.

Average change of rate = (14 - (-2)) / 9 - 5 = 16/4 = 4

5 0

3 years ago

Find the equilibrium solutions of the ordinary differential equation

Mandarinka [93]

Answer:

$\dfrac{1}{2}\dfrac{sin y}{cos^2y}+\dfrac{1}{4}ln[\dfrac{siny +1}{siny-1}]=\dfrac{x^3}{3}+c$

Step-by-step explanation:

given,

y' = x² (cos y)³

solve the equation using variable separable method

$\frac{\mathrm{d} y}{\mathrm{d} x} = x^2 cos^3y\\\dfrac{dy}{(cosy)^3}= x^2 dx\\\dfrac{cos\ y}{cos^4 y}\ dy = x^2 dx\\\int \dfrac{cos\ y}{(1-sin^2 y)^2}\ dy = \int x^2dx\\\int \dfrac{1}{(t^2-1)^2}\ dt = \dfrac{x^3}{3}+c$

here sin y = t : cos y = dt

$\int(\dfrac{1}{2}{[\dfrac{1}{t-1}-\dfrac{1}{t+1}]}^2 = \dfrac{x^3}{3}+c\\\dfrac{1}{4}\int [\dfrac{1}{(t-1)^2}-\dfrac{1}{t-1}+\dfrac{1}{t-1}+\dfrac{1}{(t+1)^2}]= \dfrac{x^3}{3}+c$

$\dfrac{1}{2}\dfrac{sin y}{cos^2y}+\dfrac{1}{4}ln[\dfrac{siny +1}{siny-1}]=\dfrac{x^3}{3}+c$

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3 years ago

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Step-by-step explanation:

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7 0

3 years ago

Which of the following represents the equation with a slope of 3 and a y-intercept of 2?

Westkost [7]

Answer:

c is the correct answer

Step-by-step explanation:

7 0

3 years ago

Which of these values for p and a will cause the function f(x)=Pax to be an exponential growth function

vovikov84 [41]

The option are missing in the question. The options are :

A. P = 2, a = 1

B. $P=\frac{1}{2} ; a =\frac{1}{3}$

C. $P=\frac{1}{2} ; a =1$

D. P = 2, a = 3

Solution :

The given function is $f(x)= Pa^x$

So for the function to be an exponential growth, a should be a positive number and should be larger than 1. If it less than 1 or a fraction, then it is a decay. If the value of a is negative, then it would be between positive and negative alternately.

When the four option being substituted in the function, we get

A). It is a constant function since $2(1^x)=2$

B). Here, the value of a is a fraction which is less than 1, so it is a decay function. $f(x)=\frac{1}{2}\left(\frac{1}{3}\right)^x$

C). It is a constant function since the value of a is 1.

D). Here a = 3. So substituting, as the value of x increases by 1, the value of the function, f(x) increases by 3 times.

$f(x)=2(3)^x$

Therefore, option (D). represents an exponential function.

4 0

3 years ago