All categories

1 year ago

Luigi incorrectly solved the following equation. Explain the error in Luigi's work.

Mathematics

2 answers:

neonofarm [45]1 year ago

7 0

Answer:

the error(s) is from the step 2

Step-by-step explanation:

3r - 12 = 2r - 3 +4r

3r - 4r -2r = 12 - 3

-3r = 9

r = 9 : (-3)

r = -3

--------------------------

the error(s) is from the step 2

ruslelena [56]1 year ago

6 0

Answer:

235

Step-by-step explanation:

You might be interested in

What point is 9 units right and 3 units up from point (3,4)?

Tomtit [17]

Answer: (6,12)

Step-by-step explanation:

3+3=6

4+9=12

4 0

2 years ago

Read 2 more answers

Luke and Inga are riding the Prince Charming Carousel at Disney World. Luke is on a horse 17 feet from the center. Inga is on a

wlad13 [49]

Answer:

Luke's angular speed = 188.49 rad/sec

Inga's angular speed = 188.49 rad/sec

Step-by-step explanation:

Data provided in the question:

Distance between the center and Luke = 17 feet

Distance between the Inga and center = 25 feet

Frequency of rotation, f = 30 rpm

Now,

Angular speed, ω is given as = 2πf

thus,

ω = 2π × 30

ω = 188.49 rad/s

here the angular speed is independent of radius

Therefore,

Luke's angular speed = 188.49 rad/sec

Inga's angular speed = 188.49 rad/sec

7 0

2 years ago

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

2 years ago

A bulletin board can be covered completely by 30 square pieces of paper without any gaps or overlaps. If each piece of paper has

9966 [12]

Can you help me please I need help with a couple of questions

7 0

2 years ago

Need help checking my answers thanks!!

Hitman42 [59]

Answer:

They are correct good job!

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers