By applying the definition of continuity and knowing piecewise functions, we know that the solution to this system of linear equations is c = 10 and d = -8.

<h3>How to make a piecewise function continuous</h3>

According to the <em>functional</em> theory, functions are continuous for a given interval if and only if the function has an only value for each element of the interval. In the case of the <em>piecewise</em> function, we must observe these two conditions:

2 · x = c · x² + d, for x = 1 (1)

4 · x³ = c · x² + d, for x = 2 (2)

Then, we have the following system of linear equations:

c + d = 2 (1b)

4 · c + d = 32 (2b)

The solution to this system of linear equations is c = 10 and d = -8.

To learn more on piecewise functions: brainly.com/question/12561612

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4 0

2 years ago

Use the graphing method to solve the equation 5(1/2)^x=30 Round to the nearest thousandth

Daniel [21]

Answer:

x = -2.585

Step-by-step explanation:

You will have to plug this into your graphing calculator.

In y=, type 5(1/2)^x in the Y1 and type 30 in Y2.

When you hit 2nd trace and hit find intersections, you will get (-2.585, 30).

The answer is x = -2.585

5 0

3 years ago