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3 years ago

Combine the like terms to make a simplified expression: - 2w - 5w=

Mathematics

2 answers:

timofeeve [1]3 years ago

5 0

Answer:

-7w

Step-by-step explanation:

-2w-5w

-2w + (-5w)

-7w

Kipish [7]3 years ago

5 0

Answer:

-7<em>w</em>

Step-by-step explanation:

If we combine like terms, we can add together all of the terms in the expression that are multiplied by <em>w</em>. In this case, we have $(-2w)+(-5w)$ , which comes to -7<em>w</em>. Hope this helped :).

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In Exercises 11-18, use analytic methods to find the extreme values of the function on the interval and where they occur. Identi

Colt1911 [192]

Answer:

Absolute maximum of 1 at x = pi/4 ; $(\frac{\pi}{4}, \ 1)$

Absolute minimum of -1 at x = 5pi/4 ; $(\frac{5\pi}{4} , \ -1)$

Local maximum of √2/2 at x = 0 ; $(0, \ \frac{\sqrt{2} }{2} )$

Local minimum of 0 at x = 7pi/4 ; $(\frac{7\pi}{4}, \ 0)$

No critical points that are not stationary points.

Step-by-step explanation:

$f(x)=sin(x+\frac{\pi}{4} ), \ 0 \leq x\leq \frac{7 \pi}{4}$

<h2>Take Derivative of f(x):</h2>

Let's start by taking the derivative of the function.

Use the power rule and the chain rule to take the derivative of f(x).

$f'(x)=\frac{d}{dx} [sin(x+\frac{\pi}{4})] \times \frac{d}{dx} (x+\frac{\pi}{4})$

The derivative of sin(x) is cos(x), so we can write this as:

$f'(x)=cos(x+\frac{\pi}{4})\times \frac{d}{dx} (x+\frac{\pi}{4})$

Now, we can apply the power rule to x + pi/4.

$f'(x)=cos(x+\frac{\pi}{4} ) \times 1$

$f'(x)=cos(x+\frac{\pi}{4} )$

<h2>Critical Points: Set f'(x) = 0</h2>

Now that we have the first derivative of $f(x)=sin(x+\frac{\pi}{4})$ , let's set the first derivative to 0 to find the critical points of this function.

$0=cos(x+\frac{\pi}{4})$

Take the inverse cosine of both sides of the equation.

$cos^-^1(0) = cos^-^1[cos(x+\frac{\pi}{4})]$

Inverse cosine and cosine cancel out, leaving us with x + pi/4. The inverse cosine of 0 is equal to 90 degrees, which is the same as pi/2.

$\frac{\pi}{2} = x +\frac{\pi}{4}$

Solve for x to find the critical points of f(x). Subtract pi/4 from both sides of the equation, and move x to the left using the symmetric property of equality.

$x=\frac{\pi}{2}- \frac{\pi}{4}$

$x=\frac{2 \pi}{4}-\frac{\pi}{4}$
$x=\frac{\pi}{4}$

Since we are given the domain of the function, let's use the period of sin to find our other critical point: 5pi/4. This is equivalent to pi/4. Therefore, our critical points are:

$\frac{\pi}{4}, \frac{5 \pi}{4}$

<h2>Sign Chart(?):</h2>

Since this is a sine graph, we don't need to create a sign chart to check if the critical values are, in fact, extreme values since there are many absolute maximums and absolute minimums on the sine graph.

There will always be either an absolute maximum or an absolute minimum at the critical values where the first derivative is equal to 0, because this is where the sine graph curves and forms these.

Therefore, we can plug the critical values into the original function f(x) in order to find the value at which these extreme values occur. We also need to plug in the endpoints of the function, which are the domain restrictions.

Let's plug in the critical point values and endpoint values into the function f(x) to find where the extreme values occur on the graph of this function.

<h2>Critical Point Values:</h2>

$f(\frac{\pi}{4} )=sin(\frac{\pi}{4} + \frac{\pi}{4} ) \\ f(\frac{\pi}{4} )=sin(\frac{2\pi}{4}) \\ f(\frac{\pi}{4} )=sin(\frac{\pi}{2}) \\ f(\frac{\pi}{4} )=1$

There is a maximum value of 1 at x = pi/4.

$f(\frac{5\pi}{4} )=sin(\frac{5\pi}{4} + \frac{\pi}{4} ) \\ f(\frac{5\pi}{4} )=sin(\frac{6\pi}{4}) \\ f(\frac{5\pi}{4}) = sin(\frac{3\pi}{2}) \\ f(\frac{5\pi}{4} )=-1$

There is a minimum value of -1 at x = 5pi/4.

<h2>Endpoint Values:</h2>

$f(0) = sin((0) + \frac{\pi}{4}) \\ f(0) = sin(\frac{\pi}{4}) \\ f(0) = \frac{\sqrt{2} }{2}$

There is a maximum value of √2/2 at x = 0.

$f(\frac{7\pi}{4} ) =sin(\frac{7\pi}{4} +\frac{\pi}{4}) \\ f(\frac{7\pi}{4} ) =sin(\frac{8\pi}{4}) \\ f(\frac{7\pi}{4} ) =sin(2\pi) \\ f(\frac{7\pi}{4} ) =0$

There is a minimum value of 0 at x = 7pi/4.

We need to first compare the critical point values and then compare the endpoint values to determine whether they are maximum or minimums.

<h2>Stationary Points:</h2>

A critical point is called a stationary point if f'(x) = 0.

Since f'(x) is zero at both of the critical points, there are no critical points that are not stationary points.

6 0

3 years ago

Mr. Dieter wants to tile the family room in his basement. He has selected a pattern of square tiles that measure 9 inches by 9 i

RUDIKE [14]

Answer:

146 ft²

21.6 tiles

1.8 boxes

Step-by-step explanation:

Please find attached an image of the family room used in answering this question

the family room has the following shapes : 2 triangles and one rectangle

the area of the family room can be determined by calculating the area of each of the shape and adding the 3 areas together

area of a rectangle = length x breadth

16 x 7 = 112 ft²

Area of a triangle = 1/2 x base x height

Area of the smaller triangle = (1/2) x 4 x 3 = 6 ft²

Area of the bigger triangle = (1/2) x 8 x 7 = 28 ft²

Sum of the areas = 112 + 6 + 28 = 146 ft²

1. First convert the area of the room to inches

1 ft = 12 in

146 x 12 = 1752 in²

2. the next step is to determine the area of the tile

area of a square = length²

9² = 81 in²

3. Divide the area of the room by the area of the tile

1752 / 81 = 21.6 tiles

c. total number of boxes that would be bought = 21.6 /12 = 1.8 boxes

6 0

3 years ago

Simplify.

a_sh-v [17]

Answer:

-9/4x -1/2

Step-by-step explanation:

hope this helps!

8 0

3 years ago

X+5 divided by 3 is less than or equal to 2

hichkok12 [17]

$\frac{x+5}{3} \leq 2$
times both sides by 3
x+5≤6
minus 5 both sides
x≤1

5 0

3 years ago

Add simplify the answer to lowest terms before entering the numerator and denominator in their boxes 11/16 + 3/16

Andrews [41]

11/16 + 3/16 = 14/16 = 7/8

The answer is 7/8

4 0

3 years ago