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alisha [4.7K]
3 years ago
6

Brayden and Aubrey are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Brayde

n is 280 miles away from the stadium and Aubrey is 340 miles away from the stadium. Brayden is driving along the highway at a speed of 30 miles per hour and Aubrey is driving at speed of 40 miles per hour. Let
B
B represent Brayden's distance, in miles, away from the stadium
t
t hours after noon. Let
A
A represent Aubrey's distance, in miles, away from the stadium
t
t hours after noon. Graph each function and determine the number hours after noon,
t
,
t, when Brayden and Aubrey are the same distance from the stadium.

Mathematics
1 answer:
USPshnik [31]3 years ago
4 0

Answer:

B(t) = -30t + 280

A(t) = -40t + 340

(Screenshot of graph is attached below)

They will be the same distance away from the stadium after 6 hours.

Step-by-step explanation:

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Monica [59]

Using derivatives, it is found that regarding the tangent line to the function, we have that:

  • The slope is of 962.
  • 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

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2 years ago
Pls help I’ll brainlest ASAP
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So, and, but, but, or, nor, so. Im pretty sure this is correct.
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