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
#SPJ1
Answer:
2x+3y-z²
Step-by-step explanation:
twice a number =2x
thrice a number =3x
minus z²
HOPE THIS HELPS!!!
Hello :) ok so to find AC you would have to use sin. It would be sin70= x/4. To find AC you would have to multiply 4 by sin70 which is 3.758 or to the nearest hundredth would be 3.76. I hope I helped, if you need a more in depth explanation lmk
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $470
r = 6% = 6/100 = 0.06
n = 1 because it was compounded once in a year.
Therefore, the equation used to determine the value of his bond after t years is
A = 470(1 + 0.06/1)^1 × t
A = 470(1.06)^t
