Select the correct answer.

Determine the open intervals on which the graph of f(x) = x - 4cos x is concave upward or concave downward

bazaltina [42]

The graph of the function $f(x)$ is

concave upward, when $f''(x)>0;$
concave downward, when $f''(x)$

Find $f''(x):$

1.

$f'(x)=(x-4\cos x)'=1+4\sin x;$

2.

$f''(x)=4\cos x.$

Now:

1. when $4\cos x>0,$ the graph of the function is concave upward and this is for

$x\in \left(-\dfrac{\pi}{2}+2\pi k,\dfrac{\pi}{2}+2\pi k\right), \text{ where } k\in Z.$

2. when $4\cos x$ the graph of the function is concave downward and this is for

$x\in \left(\dfrac{\pi}{2}+2\pi k,\dfrac{3\pi}{2}+2\pi k\right), \text{ where } k\in Z.$

6 0

3 years ago

Aubrey can walk 3000 feet in 10 minutes.Walking at the same rate,how many feet can she walk in 10 seconds

Lady_Fox [76]

Speed of aubrey = 3000 ft per 10 minutes
= 3000 ft / 10 minute
= 300 ft / 1 minute
= (300 ft / 60) second
= 5 ft/second
Distance she can walk in 10 seconds = 5ft/sec
= 5 ft / seconds × 10 seconds
= 50 ft
Hence she can walk 50 ft in 10 seconds

4 0

3 years ago

The top of a tower is a cone with a radius of 12 feet. The volume of the cone is 1,506.96 cubic feet. Which of these is the heig

shepuryov [24]

<span>the question does not have the options, but this does not limit its resolution
</span>
we know that
volume of the cone=(1/3)*pi*r²*h
where
r is the radius of the cone
h is the height of the cone
r=12 ft
Volume=1506.96 ft³
h=?

clear the variable h
v=(1/3)*pi*r²*h-----> multiply by 3
3*v=pi*r²*h----> divided by (pi*r²)
h=3*v/(pi*r²)------> h=3*1506.96/(pi*12²)----> h=9.99 ft---> h=10 ft

the answer is
h=10 ft

7 0

3 years ago

Lesson 7.3 simplifying algebraic expressions

juin [17]

Answer: $19x

Step-by-step explanation:

If she bought 2 racing cars,

= $5x +$5x = $10x (Because one car is 5x)

And if she bought 3 motor cycles,

= $3x + $3x $3x = $9x

Now we get our total amount = $10x + $9x = $19x

Hope I could help! :)