All categories

2 years ago

Martha states that –6 is a rational number. Which is a correct explanation for this statement?

Mathematics

2 answers:

bonufazy [111]2 years ago

6 0

Answer:

Step-by-step explanation:

-6 is rational because it can be written as a ratio -6/1 for example

oee [108]2 years ago

3 0

Answer:

Step-by-step explanation:

You might be interested in

Given the second order homogeneous constant coefficient equation y′′−4y′−12y=0 1) the characteristic polynomial ar2+br+c is r^2-

Vitek1552 [10]

Answer:

The initial value problem $y(x) = 4 e^{-2x} -3 e^{6 x}$

Step-by-step explanation:

Step1:-

a) Given second order homogenous constant co-efficient equation

$y^{ll} - 4y^{l}-12y=0$

Given equation in the operator form is $(D^{2} -4D-12)y=0$

Step 2:-

b) Let f(D) = $(D^{2} -4D-12)y$

Then the auxiliary equation is $(m^{2} -4m-12)=0$

Find the factors of the auxiliary equation is

$m^{2} -6m+2m-12=0$

m(m-6) + 2(m-6) =0

m+2 =0 and m-6=0

m=-2 and m=6

The roots are real and different

The general solution $y = c_{1} e^{-m_{1} x} + c_{2} e^{m_{2} x}$

the roots are $m_{1} = -2 and m_{2} = 6$

The general solution of given differential equation is

$y = c_{1} e^{-2x} + c_{2} e^{6 x}$

Step 3:-

C) Given initial conditions are y(0) =1 and y1 (0) =-26

The general solution of given differential equation is

$y(x) = c_{1} e^{-2x} + c_{2} e^{6 x}$ .....(1)

substitute x =0 and y(0) =1

$y(0) = c_{1} e^{0} + c_{2} e^{0}$

$1 = c_{1} + c_{2}$ .........(2)

Differentiating equation (1) with respective to 'x'

$y^l(x) = -2c_{1} e^{-2x} + 6c_{2} e^{6 x}$

substitute x= o and y1 (0) =-26

$-26 = -2c_{1} e^{0} + 6c_{2} e^{0}$

$-2c_{1} + 6c_{2} = -26$ .............(3)

solving (2) and (3) by using substitution method

$substitute c_{2} =1- c_{1}$ in equation (3)

$-2c_{1} + 6(1-c_{1}) = -26$

on simplification , we get

$-2c_{1} + 6(1)-6c_{1}) = -26$

$-8c_{1} = -32$

dividing by'8' we get $c_{1} =4$

substitute $c_{1} =4$ in equation $1 = c_{1} + c_{2}$

so $c_{2} = 1-4 = -3$

now substitute $c_{1} =4 and c_{2} =-3$ in general solution

$y(x) = c_{1} e^{-2x} + c_{2} e^{6 x}$

$y(x) = 4 e^{-2x} -3 e^{6 x}$

now the initial value problem

$y(x) = 4 e^{-2x} -3 e^{6 x}$

7 0

3 years ago

A 20 foot long flag pool casts a 8 foot long shadow. At the same time the oak tree casts a 12 foot shadow. How tall is Is the oa

Orlov [11]

It depends on where the sun is but the answer is 22 but my math could be wrong

3 0

2 years ago

Identify the points corresponding to p and q. Help needed!!

givi [52]

Answer:

The points corresponding to P=(3,4) and Q=(6,7), so the answer is D.

Step-by-step explanation:

Ok, in mathematics, given two sets X and Y, the collection of all the ordered pairs (X, Y), formed with a first element in X and a second element in Y, is called the Cartesian product of X and Y. The Cartesian product of sets allows define relationships and functions. In this case, it is a function that contains two points, denoted P and Q. Given, the ordered pair of each, first read the one corresponding to the X axis and then to the Y axis.

For P: you read X and you see that it is on 3 (between 2 and 4), and then the Y axis is on 4 (between 3 and 5).

For Q: you read X and you see that it is on 6 (between 5 and 7) and then the Y axis is on 7 (between 6 and 8)

8 0

2 years ago

Given the replacement set {0,1,2,3,4} .solve 6x-3=3

Vsevolod [243]

This statement is false

4 0

2 years ago

The probability of drawing a yellow or green marble out of a bag containing 3 blue, 2 green , 8 yellow , 4 red , and 3 orange ma

WINSTONCH [101]

Answer:

$\frac{10}{23}$

Step-by-step explanation:

add green and yellow which is 10 over the whole thing which is 23

5 0

3 years ago