What is 7 1/2+6 5/8 and can you show your work

stiv31 [10]

Answer:

210=75x-10x+35

Step-by-step explanation:

So we know to total profit he made is 210 dollars, in which he earned from 3 independent reasons.

The profits he made in per appointment will need a variable because we don't know how many appointments he made. So knowing that we can conclude that 75 dollars and 10 dollars per appointment has to have a variable after it. The same variable as well because both of which are money.

As of the tip, we don't need a variable because it is a one time addtion, he recieved a total of 35 dollars after all of the appointments, so no need to know how many. We already know the total.

So that leaves us to write an equation. The total=$per appointment-fee per appointment+tip. Which becomes 210=75x-10x+35.

Hope this helps!

5 0

3 years ago

F(x)=x^3+3

lawyer [7]

Answer:

(a) -3/4

(b) -0.75

(c) -0.75

Step-by-step explanation:

It's a bit hard to tell what constitutes an "iteration" when using the bisection method to approximate a polynomial root. For the purpose here, we'll say one iteration consists of ...

evaluating the function at the midpoint of the bracketing interval
choosing a smaller bracketing interval
identifying the x-value known to be closest to the solution

Thus, the result of the iteration consists of a bracketing interval and the choice of one of the interval's ends as the solution approximation.

__

(a) We observe that the graphs intersect in the interval (-1, 0). For the first iteration, we evaluate f(x)-g(x) at x=-1/2. This tells us the solution is in the interval (-1, -1/2). The x-value closest to the root is x=-1/2.

For the second iteration, we evaluate the function f(x)-g(x) at x=-3/4. This tells us the solution is in the interval (-1, -3/4). The x-value closest to the root is x=-3/4.

For the third iteration, we evaluate the function f(x)-g(x) at x=-7/8. This tells us the solution is in the interval (-7/8, -3/4). The x-value closest to the root is x=-3/4.

__

(b) The graph tells us the solution is approximately 0.7549. Rounded to 2 decimal places, the solution is approximately 0.75.

__

(c) The above solution found after 3 iterations rounded to 2 decimal places is exactly 0.75.

__

See the attached table for function values.

_____

Comment on bisection iteration

Since you cut the interval containing the root in half with each iteration, you gain approximately one decimal place for each 3 iterations. When the function value is very nearly zero at one of the interval endpoints, it can take many more iterations to achieve a better result.

Here, it takes 4 more iterations before an x-value becomes closer to the solution (x≈-97/128). And it takes one more iteration to move the end of the interval away from -3/4. After these 5 more iterations (8 total), the solution is known to lie in the interval (-97/128, -193/256). The corresponding solution approximation is -193/256. It is still only correct to 2 decimal places.