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Svetlanka [38]
3 years ago
9

What is the average rate of change of y=cos(2x) on the interval 0 pi/2?

Mathematics
2 answers:
Snezhnost [94]3 years ago
7 0
Jesus is the answer to this 
icang [17]3 years ago
5 0

Answer:

Average rate of change (A(x)) of y=f(x) over an interval [a, b] is given by:

A(x) = \frac{f(b)-f(a)}{b-a}

As per the statement:

Given:

y=f(x)=\cos (2x) and interval [0, \frac{\pi}{2}]

At x = 0

f(0) = \cos (2(0)) = \cos (0) = 1

At x = \frac{\pi}{2}

f(\frac{\pi}{2}) = \cos (2(\frac{\pi}{2})) = \cos (\pi) =-1

Substitute the given values in [1] we have;

A(x) = \frac{f(\frac{\pi}{2})-f(0)}{\frac{\pi}{2}-0}

⇒A(x) = \frac{-1-1}{\frac{\pi}{2}}

⇒A(x) = \frac{-2}{\frac{\pi}{2}}

⇒A(x) = \frac{-4}{\pi}

Therefore, the  average rate of change of y=cos(2x) on the interval [0, pi/2] is, \frac{-4}{\pi}

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3 0
2 years ago
Cecile packages snack mix at a health food store.
Sedaia [141]
Answer:
her supply has 18 pounds

Explanation:
Assume that the number of pounds in her supply is x.
We are given that:
She uses 1/3 x in salted mix and 2/9 x in unsalted mix.
This means that:
Total amount used = 1/3 x + 2/9 x = 5/9 x of her supply

Now, we are also given that:
She used 10 pounds of her supply.
This means that:
5/9 x = 10
5x = 9*10 = 90
x = 18 pounds

Hope this helps :)
5 0
2 years ago
Read 2 more answers
How to find the slope on a table
bazaltina [42]
M= y2-y1/x2-x1

Make sure you put it in the form

Hope this helps!!:))
5 0
2 years ago
Solve the following logarithmic equations.<br> log[(x^2 + 2x − 3)^4] = 0
saw5 [17]

Answer:

The solutions are x = 1.24 and x = -3.24

Step-by-step explanation:

Hi there!

First, let´s write the equation:

log[(x² + 2x -3)⁴] = 0

Apply the logarithm property: log(xᵃ) = a log(x)

4 log[(x² + 2x -3)⁴] = 0

Divide by 4 both sides

log(x² + 2x -3) = 0

if log(x² + 2x -3) = 0, then  x² + 2x -3 = 1 because only log 1 = 0

x² + 2x -3 = 1

Subtract 1 at both sides of the equation

x² + 2x -4 = 0

Using the quadratic formula let´s solve this quadratic equation:

a = 1

b = 2

c = -4

x = [-b± √(b² - 4ac)]/2a

x =  [-2 + √(4 - 4(-4)·1)]/2 = 1.24

and

x = [-2 - √(4 - 4(-4)·1)]/2 = -3.24

The solutions are x = 1.24 and x = -3.24

Have a nice day!

4 0
3 years ago
Simplify the expressions by combining like terms<br><br> 1.5r - 3r + 8r + 2.5r
Tomtit [17]

Answer:

9r

Step-by-step explanation:

1.5r - 3r + 10.5r

10.5r + 1.5r = 12r

12r - 3r = 9r

Final Answer = 9r

5 0
3 years ago
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