Solve the given system using elimination.

For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as a com

BartSMP [9]

F(x) = x - 2sinx

To find for what values of x graph has tangents we need to differentiate function f(x).
f'(x) = 1-2cosx
Now, if we want to have horizontal tangents we need to make function f'(x) equal to 0 because at minimum or maximum of function f(x) tangent is horizontal.

1-2cosx = 0
cosx = 1/2
x = pi/3 + 2*n*pi and
x = -pi/3 + 2*n*pi

Explanation: cosx = 1/2 for both 60° and -60°. If we make one circle cosx will be equal to 1/2 for 420 and 300 degrees. Writing degrees in radians (using pi) we can write formulas above where 2*pi represents one full circle and n is an integer which represents how many circles we made.

5 0

3 years ago

A circle's diameter is 4 feet.

Soloha48 [4]

Answer:

13

Step-by-step explanation:

The formula for cirmference is

C= π2 * r

we're using 3.14 as pi and r = radius.

the radius is always half of the diameter.

So in this case since the diamter is 4, the radius is 2. let's substitute these numbers.

C= 3.14 *2*2 and there your answer is 12.56 which rounded to the nearest tenth is 13.

Hope this helps :)

6 0

1 year ago

The landscaper charges a rate of $40 per hour to plant trees.Amelia paid a total of $725 for the trees and for the landscaper to

pickupchik [31]

23.5 hours is the anser yeteressdfdsfsjufrhhmrgijfjfxkjvnrtjeigrjiegre

8 0

3 years ago

How do you simplify radical 32

EleoNora [17]

$\sqrt{32}= \sqrt{16*2}= \sqrt{16}* \sqrt{2}=4 \sqrt{2}$

4 0

3 years ago

A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each and

Naya [18.7K]

<h2>The number of small buses used = 5</h2><h2>The number of big buses used = 4</h2>

Step-by-step explanation:

Let us assume the total number of small buses needed = x

The capacity of 1 small bus = 40

So, the capacity of x buses = 40(x) = 40 x

Let us assume the total number of big buses needed = y

The capacity of 1 big bus = 50

So, the capacity of y buses = 50(y) = 50 y

Also, the total students travelling = 400

So, the number of students traveling by (Small bus + Big bus) = 400

⇒ 40 x + 50 y = 400 ..... (1)

Also, the total number of drivers available = 9

⇒ x + y = 9 ..... (2)

Also, x ≤ 8, y ≤ 10

Now, solving both equations, we get:

40 x + 50 y = 400 ..... (1)

x + y = 9 ⇒ y = (9-x) put in (1)

40 x + 50 y = 400 ⇒ 40 x + 50 (9-x) = 400

or, 40 x + 450 - 50 x = 400

or, - 10 x =- 50

or, x = 5 ⇒ y = (9-x) = 9- 5 = 4

Hence the number of small buses used = 5

The number of big buses used = 4

8 0

3 years ago