Multiply the two fractions (1/2)(2/5). Simplify your answer.

docker41 [41]

The vertical shifts in graphs are caused by a constant added to the output (y - axis).

<h3>What is vertical shift in a graph?</h3>

Vertical shifts are outside changes that affect the output (y- axis) values and shift the function up or down (vertical direction).

Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right

<h3>The cause of vertical shift in a graph</h3>

The vertical shift results from a constant added to the output (y - axis). The graph will move up if the constant added is positive OR it will move down if the constant is negative.

Thus, the vertical shifts in graphs are caused by a constant added to the output (y - axis).

Learn more about vertical shifts in graph here: brainly.com/question/27653529

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8 0

1 year 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

In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 .

kondaur [170]

<span>The diagonals of a parallelogram bisect each other. So we just equate the two equations BE and DE 2x^2 - x = x^2 + 6 2x^2 - x - x^2 - 6 = 0 x^2 - x - 6 = 0 This is quadratic eqn. So we obtain. (x - 3) ( x + 2) = 0 Setting each to 0 and solving for x, we have that x = 3 and x = -2 So we have two possible values for BD. But Since BE = DE then we can simply double each If x = 3 BD = 2 (2(3)^2 - 3) = 2 ( 18 - 3) = 30 units If x = - 2 BD = 2((-2)^2 -3 ) = 2 (8 - 3) = 10 units</span>

8 0

2 years ago

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An object is dropped from 43 feet below the tip of the pinnacle atop a 527-ft tall building. The height h of the object after t

Marizza181 [45]

Answer:

5.5 seconds

Step-by-step explanation:

The function that gives the height of the object after t seconds falling is:

h = -16t^2 + 484.

To find the time when the object reaches the ground, we just need to use the value of h = 0 in the equation, and then find the value of t:

0 = -16t^2 + 484.

16t^2 = 484

t^2 = 30.25

t = 5.5 seconds

So the object will reach the ground after 5.5 seconds

5 0

2 years ago

Read 2 more answers

Fill in the bubble completely to show your answer.

adell [148]

Answers :D18

Step-by-step explanation:

Because I did the marh

4 0

2 years ago