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.
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Answer:
The bottle of orange juice will have higher amounts of vitamin C per serving, as it will have 125 mg against 90 mg of the cranberry juice.
Step-by-step explanation:
To determine the amount of vitamin C in each serving of fruit juice, knowing that the bottle of orange juice contains 750 mg of vitamin C and 6 servings, while the bottle of cranberry juice contains 135 mg and 1.5 servings, you must perform the following calculation:
Orange: 750/6
Orange: 125 mg per serving
Cranberry: 135 / 1.5
Cranberry: 90 mg per serving
Thus, the bottle of orange juice will have higher amounts of vitamin C per serving, as it will have 125 mg against 90 mg of the cranberry juice.
∑ Hey, petalssquad10 ⊃
Answer:
( 10 x + 10 ) = 110
Step-by-step explanation:
As you can see this following diagram shown a vertical angles which are angles that are opposite of each other when two lines cross. You can also see it kind of look like a "x". Vertical angles also means that they have the same angle measure. A example is if this angle is "110" then the other sides equal to "110''.
Hence, the equation we can be used to solve for x in the following diagram is:
( 10 x + 10 ) = 110
You can also refer to the image below:
<u><em>xcookiex12</em></u>
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<em>8/18/2022</em>
The general solution of the given system of odes is


In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.
the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.
It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.
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