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3 years ago

Please help im confused\

Mathematics

1 answer:

Bad White [126]3 years ago

8 0

The slope-point form: y - y₁ = m(x - x₁).

The slope-intercept form: y = mx + b.

$k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have:

$k:y-3=-4(x+2)\to m_1=-4$ and the point (-5, 7)

therefore $m_2=-\dfrac{1}{-4}=\dfrac{1}{4}$

$y-7=\dfrac{1}{4}(x-(-5))\\\\\boxed{y-7=\dfrac{1}{4}(x+5)}\to\boxed{B.}$

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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

The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?

Assoli18 [71]

Answer:16pie

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

64 divided by 0.4 and explain how you did it please i don't wanna be stuck on this all night

Brrunno [24]

Okay so 0.4 is equal to 4/10 (hopefully you know that!) & anything over 1 is itself so i would but 64 over 1.

so now you hace 2 fractions & when dicing fractions you alwas flip the second fraction upside down & then just multiply across.

so if you have
64 4
---- / ----
1 10

you would switch the 2nd one so the 10 would be on top.

so that would give you 64*10 over 1*4

which equals 640/4

& when you simplify that you get 160

so that's your answer(:

7 0

3 years ago

Billy was counting the number of wheels and bike seats at the playground. He saw tricycles and bicycles. He counted 79 wheels an

mart [117]

I think the answer is 25.5. Although, I don't know how you would have half a bike unless there was a 3 wheel bike which would make the answer 24.

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3 years ago

Which line is represented by y = 3/2x - 3?

const2013 [10]

Answer:

The answer is the third picture

Step-by-step explanation: