Using derivatives, it is found that regarding the tangent line to the function, we have that:
- The equation of the line is y = 962x - 5119.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:
f(x) = 5x³ + 2x + 1.
The derivative is given by:
f'(x) = 15x² + 2.
Hence the slope at x = 8 is:
m = f'(8) = 15(8)² + 2 = 962.
The line goes through the point (8,f(8)), hence:
f(8) = 5(8)³ + 2(8) + 1 = 2577.
Hence:
y = 962x + b
2577 = 962(8) + b
b = -5119.
Hence the equation is:
y = 962x - 5119.
More can be learned about tangent lines at brainly.com/question/8174665
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Answer:
19
Step-by-step explanation:
20/4 + 13
20/4 = 6
6+13 = 19
Answer:
No, the given polynomial is not prime.
Step-by-step explanation:
Given: a polynomial 
To check: whether the given polynomial is prime or not.
Solution:
A prime polynomial is a polynomial that cannot be factored into polynomials of lower degree and has integers as coefficients.
In the given polynomial, coefficients are integers.
Also, the polynomial cannot be factored further into polynomials of lower degree.
So, the given polynomial is not prime.
Answer:
Step-by-step explanation:
Vertical angles are angles on opposites sides of an intersection of two lines. Therefore, 
and 
are vertical angles. Similarly, the angle opposite to the angle marked 83 degrees is also equal to 83 degrees. Vertical angles are always equal.
Since there are 360 degrees in a circle, we have the following equation:
Since and are vertical angles and vertical angles are also equal, the measure of angle 
is also 
