0.6(10m-5n) do you know this

Mathematics

1 answer:

DIA [1.3K]3 years ago

5 0

0.6*10m=6m 0.6*5n=3n rewrite 6m-3n
hope this helps have a nice nite

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Determine whether the equation x^3 - 3x + 8 = 0 has any real root in the interval [0, 1]. Justify your answer.

nikdorinn [45]

Answer:

The equation does not have a real root in the interval $\rm [0,1]$

Step-by-step explanation:

We can make use of the intermediate value theorem.

The theorem states that if $f$ is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:

If a continuous function has values of opposite sign inside an interval, then it has a root in that interval. This is also known as Bolzano's theorem.
The image of a continuous function over an interval is itself an interval.

Of course, in our case, we will make use of the first one.

First, we need to proof that our function is continues in $\rm [0,1]$ , which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval $\rm [0,1]$ , which means to evaluate the equation in 0 and 1:

$f(x)=x^3-3x+8\\f(0)=8\\f(1)=6$

Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval $\rm [0,1]$ . I attached a plot of the equation in the interval $\rm [-2,2]$ where you can clearly observe how the graph does not cross the x-axis in the interval.

6 0

3 years ago

WILL GIVE BRAINLIEST

jok3333 [9.3K]

Answer:

J'(-2,5)

K'(-7,5)

M'(-3.5,2)

L'(5.5,2)

Step-by-step explanation:

Please refer to the image attached to this answer.

Trapezoid JKLM is reflected over the x-axis, what do we notice about the ordered pairs of the original figure and the ordered pairs of its reflection over the x-axis is described below.

Point J , K L and M , when reflected over x axis , there distance from the y axis remains the same in second quadrant. the x coordinate becomes negative however the y coordinates remains the same.

The coordinates will be as shown in the image attached.