Consider the following equation, bh + hr = 25 Solve the equation for h

a bookstore packs 6 books in a box. the total weight of the books is 14 1/4 pounds. if each book has the same weight, what is th

Sunny_sXe [5.5K]

$\frac{1}{4}$ = .25
$\frac{14.25}{6}$
=2.375 pounds

3 0

3 years ago

Are the points B, F, and W coplanar?

harina [27]

Answer:

yes

Step-by-step explanation:

Because the point lie on the plane they are coplanar

7 0

2 years ago

Find n for which the nth iteration by the Bisection Method guarantees to approximate the root of f(x) = 2x^2 − 3x − 2 on [−2, 1]

Lady_Fox [76]

Answer:

n = 29 iterations would be enough to obtain a root of $f(x)=2x^2-3x-2$ that is at most $10^{-8}$ away from the correct solution.

Step-by-step explanation:

You can use this formula which relates the number of iterations, n, required by the bisection method to converge to within an absolute error tolerance of ε starting from the initial interval (a, b).

$n\geq \frac{log(\frac{b-a}{\epsilon} )}{log(2)}$

We know

a = -2, b = 1 and ε = $10^{-8}$ so

$n\geq \frac{log(\frac{1+2}{10^{-8}} )}{log(2)}\\n \geq 29$

Thus, n = 29 iterations would be enough to obtain a root of $f(x)=2x^2-3x-2$ that is at most $10^{-8}$ away from the correct solution.

You can prove this result by doing the computation as follows:

From the information given we know:

$f(x)=2x^2-3x-2$
$\epsilon = 10^{-8}$

This is the algorithm for the Bisection method:

Find two numbers a and b at which f has different signs.
Define $c=\frac{a+b}{2}$
If $b-c\leq \epsilon$ then accept c as the root and stop
If $f(a)f(c)\leq 0$ then set c as the new b. Otherwise, set c as the new a. Return to step 1.