Dadas las funciones f(x) = x + 3, g(x)= x(cuadrada)+ 5x + 6,r(x) = x+2, s(x) = x(cuadrada) - 3x - 10

Mathematics

1 answer:

Aleksandr [31]3 years ago

5 0

So the answer is D hope this would help you

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I don't understand what I'm supposed to do here. I have a test on this tomorrow so if you explain how to do it that would be gre

VladimirAG [237]

Here is a little tip for this: The unit above cancels the unit below. So in this problem you are asked to convert pounds to ounce. So your equation will look like this.

ounce = 2.93 pounds $( \frac{16 ounces}{1 pounds} ) = 46.88$
Your ratio should involve the conversion factor. So 16 and 1 is involved canceling A and D. Then, Notice that you started with poubls. Then the ratio must have pounds at the bottom to cancel the units leaving ounces.

7 0

3 years ago

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.