The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

<h3>How to find the value of the constant k of a system of two polynomic equations</h3>

Herein we have a system formed by two <em>nonlinear</em> equations, a <em>quadratic</em> equation and a <em>cubic</em> equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4 (1)

g(x) - x² - k · x = x³ + 2 · k (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

To learn more on polynomic functions: brainly.com/question/24252137

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7 0

1 year ago

The surface of the ground at Drake's well is 1,200 ft above sea level. To reach oil, Drake first drilled through gravel to a poi

Aneli [31]

Answer:

1176

Step-by-step explanation:

All you have to do is add 1168 plus 38 would be 1176.

3 0

3 years ago

Recall that a conflict of interest scenario was presented to a sample of 200 marketing researchers and that 109 of these researc

Tju [1.3M]

Answer: Null hypothesis: $p\leq0.50$

Alternative hypothesis: $p>0.50$

Step-by-step explanation:

A null hypothesis is a type of hypothesis that states that there is no difference between a particular parameter of a population whereas an alternative hypothesis states that there is a difference.

Given: p = Proportion of all marketing researchers who disapprove of the actions taken in the conflict of interest scenario.

n= 200

Sample proportion = $\hat{p}=\dfrac{109}{200}=0.545$

Claim : p>0.50

Null hypothesis: $p\leq0.50$

Alternative hypothesis: $p>0.50$

4 0

2 years ago