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Bad White [126]
3 years ago
11

P - 5(p+4) = p - (8-p)

Mathematics
1 answer:
zhuklara [117]3 years ago
4 0

Answer:

Simplifying 6p + 2(4 + -2p) = 3(p + 4) 6p + (4 * 2 + -2p * 2) = 3(p + 4) 6p + (8 + -4p) = 3(p + 4) ... Move all terms containing p to the left, all other terms to the right. ... When you enter an equation into the calculator, the calculator will begin by ... Similarly, 2 * (x + 5) can also be entered as 2(x + 5); 2x * (5) can be entered as 2x(5).

Step-by-step explanation:

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A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must
Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

  • (x) should be the width of the rectangle base;
  • (h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

  • the radius  \mathbf{r = \dfrac{x}{2}}  

and, the perimeter of the window can now be expressed as:

\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}

\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}

Given that the perimeter = 600 cm

∴

\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}

\mathbf{  h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}

Since h > 0, then:

\mathbf{  h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}

By rearrangement and using the inverse rule:

\mathbf{  x<  \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }

\mathbf{  x=  \dfrac{ 1200}{\Big( 2 +\pi \Big) } }

\mathbf{  x=  233.39 \ cm }

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}

\mathbf{A = x \Big [  300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ]  +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}

\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}

\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big)  \ =0}

Making x the subject of the formula, we have:

\mathbf{x = \dfrac{1200}{4 +\pi}}

x = 168.03 cm

Taking the second derivative:

\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}

\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

brainly.com/question/9964510?referrer=searchResults

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3 years ago
What is 39% of the Pacific Ocean
Cloud [144]

Answer:

.0039

Step-by-step explanation:

4 0
3 years ago
which of the following represents a relation that is not a function? a. x -8 -6 7 10 y 33 31 39 33 b. x -8 -6 0 3 y 33 31 39 33
boyakko [2]
X => -8 -6 -8 3
y => 33 31 39 33
is not a function because the x value -8 results to two different y-values 33 and 39.
8 0
3 years ago
How do you write 1 over 100 as a power of 10 with a negative exponent?
vaieri [72.5K]
I think it would look like this 1/100^-10 hope dis helped
7 0
2 years ago
Read 2 more answers
I will give BRAINLIEST to whoever answers correctly first!!!
Tatiana [17]
$3.18

Explanation: I am a cashier hahaha
7 0
2 years ago
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