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3 years ago

Kris is making cookies. He has 43 cups of sugar. He needs 23 cup of sugar to make one whole batch of cookies.

Mathematics

2 answers:

rodikova [14]3 years ago

8 0

Answer:

What's the question here?

bija089 [108]3 years ago

3 0

What’s the question even supposed to be?

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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

6 0

3 years ago

9 months before march 19 2007

elena-14-01-66 [18.8K]

June 19th 2006 specifically a monday

3 0

3 years ago

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Shirley Smith's total insurance premium is $1,050. His employer pays 50% of the total premium. How much does Shirley pay?

allsm [11]

Answer:

$525

Step-by-step explanation:

Shirley pays the other 50%, so pays ...

0.50 · $1050 = $525

8 0

3 years ago

Denise Robb's account statement shows a $210.94 unpaid balance. With a periodic rate of 1.85%, what is the finance charge? She h

Blizzard [7]

Answer:

A) 3.9 dollars

B) 126.38 dollars

Step-by-step explanation:

Given that Denise Robb's account statement shows a $210.94 unpaid balance. With a periodic rate of 1.85%

The finance charge = 1.85/100 × 210.94 = 3.9 dollars

If She had new purchases of $341.22. The new balance will be

341.22 - ( 210.94 + 3.9 )

126.38 dollars

8 0

3 years ago

6•72,749,973,947,937=?

g100num [7]

I used a calculator and got <span>4.3649984e+14</span>

7 0

3 years ago

Read 2 more answers