Please help ASAP!! Super appreciated!!! <3

Mathematics

1 answer:

Vedmedyk [2.9K]4 years ago

5 0

The data is not linear. From (3, 1) to (7, 2), we add 4 to the x-value and add 1 to the y-value. This pattern continues for a little while, however, from (11, 3) to (18, 5), we add only 7 to the x-value even though we added 2 to the y-value. Given this information, we can determine that this is not linear data.

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Simplify the expression below:

kifflom [539]

Answer:

C. -7x^2 - 28

Step-by-step explanation:

Firstly simplify the bracket before doing anything;

4x(3x - 7) = 12x^2 - 28x

then go back to the question and substitute the expression(12x^2 - 28x) on the bracket and then work out the question;

12x^2 - 28x -19x^2...then group the values with the same exponent of x,

(12x^2 - 19x^2) - 28x

; -7x^2 - 28x

6 0

3 years ago

Without actually solving the given differential equation, find the minimum radius of convergence R of power series solutions abo

MakcuM [25]

Answer:

R1= 10.04

R2=10

Step-by-step explanation:

The differential equation is given by:

$(x^2 - 2x + 26)y'' + xy' - 4y = 0$

The minimum radius of convergence is given by the distance from the point x=a, to the nearest singularity points of the differential equation.

The singularity points are the roots of the polynomial that multiplies the second derivative of y. Thus, you have:

$x^2 - 2x + 26=0\\\\x_{1,2}=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(26)}}{2}=1\pm 10i$

the roots are in the complex plane. The radius of convergence is the distance between the points z1=0+0i, z2=1+0i (x=0 and x=1, respectively), in the complex plane, that is:

$R_1=|z_1-x_1|=\sqrt{1^2+10^2}=\sqrt{101}=10.04\\\\R_2=|z_2-x_1|=\sqrt{0^2+10^2}=\sqrt{100}=10$