The line shown represents the amount of money Ben owes on his lunch account.

Mathematics

1 answer:

nasty-shy [4]3 years ago

7 0

Answer:

y=2x-1

Step-by-step explanation:

Remeber to put no spaces on the test

and it is this answer bc he owes one dollar evryday and owing is negative

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CALCULUS EXPERT WANTED

Vlad [161]

a. Use the mean value theorem. 16 falls between 12 and 20, so

$v'(16)\approx\dfrac{v(20)-v(12)}{20-12}=\dfrac{240-200}8=5$

(Don't forget your units - 5 m/min^2)

b. $v(t)$ gives the Johanna's velocity at time $t$ . The magnitude of her velocity, or speed, is $|v(t)|$ . Integrating this would tell us the total distance she has traveled whilst jogging.

The Riemann sum approximates the integral as

$\displaystyle\int_0^{40}|v(t)|\,\mathrm dt=12\cdot200+8\cdot240+4\cdot220+16\cdot150=7600$

If you're not sure how this is derived: we're given 5 sample points, so we can cut the interval [0, 40] into 4 subintervals. The lengths of each subinterval are 12, 8, 4, and 16 (the distances between each sample point), and the height of the rectangle approximating the area under the plot of $|v(t)|$ is determined by the value of $v(t)$ at each sample point, 200, 240, |-220| = 220, and 150.

c. Bob's velocity is given by $B(t)$ , so his acceleration is given by $B'(t)$ . We have