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2 years ago

Lin's family has completed 60% of a trip. They have traveled 30 miles. How long is the whole trip?

Mathematics

2 answers:

Kaylis [27]2 years ago

7 0

Answer:

12 miles left

Step-by-step explanation:

taking 60 away from 100 is 40 and 40% of 30 is 12

tatiyna2 years ago

3 0

This one’s easy if you know how to do the fractions of 5.

The whole trip is 50 miles because 60% of 50 is 30 miles.

3/5 = 0.6

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The product of two rational numbers is 6. If one of the number is 14/3, find the other number.

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3 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:

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3 years ago

Can someone please help me find the domain, range, intercepts, and asymptotes pf this function?

marishachu [46]

1) given function

y = - 2 ^ ( -x + 2) + 1

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The exponential function is defined for all the real numbers, so the domain of the given function is all the real numbers.

3) x-intercept => y = 0

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=> - x + 2 = 0 => x = 2

The x-intercept is x = 0

4) y-intercept => x = 0

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=> The y-intercept is - 3

5) limit when x -> negative infinite

Lim f(x) when x -> ∞ = - ∞

6) limit when x -> infinite

Lim f(x) when x - > infinite = 1

=> asymptote = y = 1

7) range is the set of values of the fucntion: y

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2 years ago

Simplify the expression below.

Novay_Z [31]

Answer:

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