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The value of k such that the graph of f and the graph of g only intersect one is equal to 2.
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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Answer:
Its a right angle triangle so trigonometry is used.
a is the hypotenuse, b is the adjacent.
Use sin to find a. Use tan to find b.
By applying Exponential laws, option no. c which is, stands correct.
What are exponents?
- A number's exponent indicates how many times that number has been multiplied by itself.
- However many times multiplying a given number is indicated by its exponent. Powers and indices are other names for exponents.
- An indication of the action of elevating to a power that is printed above and on the side of a mathematical form
- Exponent-related problems are solved using the rules of exponents or the properties of exponents. These characteristics are regarded as fundamental exponents rules that must be adhered to when solving exponents.
Given that,
Applying the law of exponents to the given expression,
Putting the given value in the above expression, we get,
Hence, by applying Exponential laws, option no. c which is, stands correct.
Learn more about exponents here:
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