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Aliun [14]
3 years ago
11

I need the answer asap

Mathematics
2 answers:
nika2105 [10]3 years ago
4 0

Answer:

-2 | -5 | global max  (vertex)

Step-by-step explanation:

Find and classify the global extrema of the following function:

f(x) = -abs(x + 2)/3 - 5

Find the critical points of f(x):

Compute the critical points of -abs(x + 2)/3 - 5

To find all critical points, first compute f'(x):

d/( dx)(-abs(x + 2)/3 - 5) = -abs(x + 2)/(3 (x + 2)):

f'(x) = -abs(x + 2)/(3 (x + 2))

f'(x) is never zero on the real line:

-abs(x + 2)/(3 (x + 2)) is never zero

f'(x) does not exist at x = -2:

x = -2

The only critical point of -abs(x + 2)/3 - 5 is at x = -2:

x = -2

The domain of -abs(x + 2)/3 - 5 is R:

The endpoints of R are x = -∞ and ∞

Evaluate -abs(x + 2)/3 - 5 at x = -∞, -2 and ∞:

The open endpoints of the domain are marked in gray

x | f(x)

-∞ | -∞

-2 | -5

∞ | -∞

The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:

The open endpoints of the domain are marked in gray

x | f(x) | extrema type

-∞ | -∞ | global min

-2 | -5 | global max

∞ | -∞ | global min

Remove the points x = -∞ and ∞ from the table

These cannot be global extrema, as the value of f(x) here is never achieved:

x | f(x) | extrema type

-2 | -5 | global max

f(x) = -abs(x + 2)/3 - 5 has one global maximum:

Answer: |  

| f(x) has a global maximum at x = -2

zheka24 [161]3 years ago
3 0

Answer:

-2 , -5

Step-by-step explanation:

y = -1/3 (x + 2) - 5

y= −1/3x +−17/3

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0.5 is the base

10 is the power

(0.5)^{10\\ = (\frac{1}{2})^{10} -- another way to write

Step-by-step explanation:

Given

(0.5)^{10\\

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Fill ion the gaps

(0.5)^{10\\ is pronounced as; 0.5 raise to the power of 10

From the above statement, we can deduce the following:

0.5 is the base

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Express 0.5 as a fraction

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<h3>Rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr</h3><h3><u>Solution:</u></h3>

Given that,

A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream

Therefore,

Upstream distance = 165 km

Upstream time = 3 hours

<h3><u>Find upstream speed:</u></h3>

speed = \frac{distance}{time}\\\\speed = \frac{165}{3}\\\\speed = 55

Thus upstream speed is 55 km per hour

Downstream distance = 510 km

Downstream time = 6 hours

<h3><u>Find downstream speed:</u></h3>

speed = \frac{510}{6}\\\\speed = 85

Thus downstream speed is 85 km per hour

<em><u>If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then</u></em>

Speed downstream = u + v km/hr

Speed upstream = u - v km/hr

Therefore,

u + v = 85 ----- eqn 1

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Solve both

Add them

u + v + u - v = 85 + 55

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<em><u>Substitute u = 70 in eqn 1</u></em>

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