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slega [8]
3 years ago
13

Determine which function has the greatest rate of change as x approaches infinity.

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
3 0

Answer: h(x) = 3*x^2 - 7*x + 8

Step-by-step explanation:

The rate of change of a function is equal to the derivate:

remember that a derivate of the form:

k(x) = a*x^n is k'(x) = n*a*x^(n-1)

Then we have:

f(x) = 2*x - 10

f'(x) = 1*2* = 2

g(x) = 16*x - 4

g'(x) = 1*16 = 16

h(x) = 3*x^2 - 7*x + 8

h'(x) = 2*3*x - 1*7 = 6*x - 7

So the only that increases as x increases is h(x), this means that the greates rate of change as x approaches inffinity is the rate of change of h(x)

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6(5)-7
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3 years ago
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Soap films and bubbles are colorful because the interference conditions depend on the angle of illumination (which we aren't cov
mylen [45]

Answer:

56.39 nm

Step-by-step explanation:

In order to have constructive interference total optical path difference should be an integral number of wavelengths (crest and crest should be interfered). Therefore the constructive interference condition for soap film can be written as,

2t=(m+\frac{1}{2} ).\frac{\lambda}{n}

where λ is the wavelength of light and n is the refractive index of soap film, t is the thickness of the film, and m=0,1,2 ...

Please note that here we include an additional 1/2λ phase shift due to reflection from air-soap interface, because refractive index of latter is higher.

In order to have its longest constructive reflection at the red end (700 nm)

t_1=(m+\frac{1}{2} ).\frac{\lambda}{2.n}\\ \\ t_1=\frac{1}{2} .\frac{700}{(2)*(1.33)}\\ \\ t_1=131.58\ nm

Here we take m=0.

Similarly for the constructive reflection at the blue end (400 nm)

t_2=(m+\frac{1}{2} ).\frac{\lambda}{2.n}\\ \\ t_2=\frac{1}{2} .\frac{400}{(2)*(1.33)}\\ \\ t_2=75.19\ nm

Hence the thickness difference should be

t_1-t_2=131.58-75.19=56.39 \ nm

7 0
3 years ago
Please help and explain <br><br> question 12
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The sunflower is 2.387 meters tall.

The question is asking: which rounding will result in the greatest value?

To see, we need to round 2.387 to meter, tenth meter, and hundredth meter.

Meter - 2 meters

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Hundredth meter - 2.39 meters

As you see, rounding to the tenth meter gives the greatest value of 2.4. Therefore, Bahir should use a decimal rounded to the tenth meter.

3 0
3 years ago
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Answer:

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Step-by-step explanation:

Dilation of any image changes its size and the shape remains same.

The scale factor is the ratio of dilated image to original image.

Dilation rule: (x, y) → (kx, ky), where k is the scale factor.

It means k = x₂/x₁ or y₂/y₁

K = -5/20 = -1/4 or K = -4/16 = -1/4.

<u>The negative value of scale factor (K) indicates dilations with 180 degree rotation of the dilated image.</u>

Hence the scale factor is K = -1/4.

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Step-by-step explanation:

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