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4 years ago

If a = b and the supplementary of

Mathematics

1 answer:

shusha [124]4 years ago

8 0

It all equals ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

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Here we will study the function f (x) = e ^ x sin (x), where x ∈ [0, 2π]. a) Determine where the function is decreasing and incr

Semmy [17]

fff

$f(x) = e^x sin (x)$

To find increasing and decreasing intervals we take derivative

$f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)$

Now we set the derivative =0 and solve for x

$e^x(sinx+cosx)=0$

sinx + cosx =0

divide whole equation by cos x

$\frac{sinx}{cosx} + \frac{cosx}{cosx} =0$

tanx +1 =0

tanx = 1

$x=\frac{3\pi }{4}$ and $x=\frac{7\pi}{4}$

Now we pick a number between 0 to $\frac{3\pi }{4}$

Lets pick $\frac{\pi }{2}$

Plug it into the derivative

$f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))$

= 4.810 is positive

So the graph of f(x) is increasing on the interval [0, $x=\frac{3\pi }{4}$ )

Now we pick a number between $\frac{7\pi}{4}$ to 2pi

Lets pick $\frac{11\pi}{6}$

Plug it into the derivative

$f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))$

= 116 is positive

So the graph of f(x) is increasing on the interval $(\frac{7\pi }{4}, 2\pi)$

Increasing interval is $(0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)$

Decreasing interval is $(\frac{3\pi}{4}, \frac{7\pi}{4})$

(b)

The graph of f(x) increases and reaches a local maximum at $x=\frac{3\pi}{4}$

The graph of f(x) decreases and reaches a local minimum at $x=\frac{7\pi}{4}$

(c)

f(0) = 0

$f(2\pi)=0$

$f(\frac{3\pi }{4})=7.46$

$f(\frac{7\pi}{4})=-172.64$

Here global maximum at $x=\frac{3\pi}{4}$

Here global minimum at $x=\frac{7\pi}{4}$

3 0

3 years ago

Read 2 more answers

Bill is making accessories for the soccer team. He uses 611.66 inches of fabric on headbands for 31 players and 3 coaches. He al

Sliva [168]

Answer:

26.8 inches of fabrics was used on headband and wristband for each player

Step-by-step explanation:

Headbands for 31 players and 3 couches = 611.66 inches of fabric

Total number of people = 31 players + 3 couches

= 31 + 3

= 34 people

Fabrics per person's headbands = Total inches of fabrics for headbands / total number of people

= 611.66 inches of fabric / 34 people

= 17.99 inches of fabrics per person

Wristband for 31 players = 273.11 inches of fabric

Fabric per person's wristband = total inches of fabrics for wristband / number of players

= 273.11 inches of fabric / 31

= 8.81 inches per person

How much fabric was used on a headband and wristband for each player?

= Fabrics per person's headbands + Fabric per person's wristband

= 17.99 inches + 8.81 inches

= 26.8 inches of fabrics was used on headband and wristband for each player

4 0

3 years ago

Solve for x -3+8×-5=-8

Art [367]

Answer:

x is 0

Step-by-step explanation:

subtract the number 3 5 and 8 then combine like terms and 8 on both sides of the equation then simplify after that divide both sides of the equation by the same term then simplify

5 0

3 years ago

A line with a slope of – 2 is written in the form y = mx + b.

sp2606 [1]

Answer:

the value of b would be -7

Step-by-step explanation:

8 0

3 years ago

The graph of a line gets _____ as the absolute value of the slope gets bigger.

Usimov [2.4K]

The slope of a line is defined as rise by run i.e. how much y value changes with respect to the change in x value. So the slope gives the steepness of the line.

Slope 0 indicates there is no change in y when the x value is changed and so the line with slope 0 is a horizontal line. A line with slope 1 shows with 1 unit change in x, y changes by 1 unit. Likewise slope equal 2 indicates with 1 unit change in x, y changes by 2 units.

We can see as the absolute value of slope is increasing, the change in y with respect to x is increasing i.e. the line is becoming more tilted or steep.

Hence, we can conclude that:
The graph of a line gets Steeper as the absolute value of the slope gets bigger.
C is the correct answer.

6 0

3 years ago

Read 2 more answers