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3 years ago

Which function has the greater rate of change?

Mathematics

1 answer:

Gnoma [55]3 years ago

3 0

Answer:

Function 1

Step-by-step explanation:

Function 1:

$y=\dfrac{5}{6}x+10$

The rate of change of the function 1 is:

$\dfrac{5}{6}\approx 0.83$

Function 2:

The rate of change of the function 2 is:

$\dfrac{15.75-14.25}{1-(1)}=\dfrac{1.5}{2}=0.75$

Hence, the greater rate of change has function 1.

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Find the equation of the exponential function represented by the table below:

UNO [17]

Answer:

Step-by-step explanation:

If this is an exponential function, it is of the form

$y=a(b)^x$ where x and y are coordinates from your table, a is the intial value, and b is the growth/decay rate. To find out what the equation is that represents this data, choose 2 points and solve first for a and then for b. Just a hint: If at all possible, choose the coordinate that gives you an x of 0. You'll see why in a minute.

I chose the first 2 points from your table: (0, .2) and (1, .8). Solving first for a:

$.2=a(b)^0$ The reason to choose the x of 0 as one of your points is because anything raised to the power of 0 is 1. So our equation then becomes:

$.2=a(1)$ so

a = .2 Easy enough.

Now use that value along with the other coordinate to solve for b:

$.8=.2(b)^1$ b to the first is just b, so,

.8 = .2b

Divide both sides by .2 and you'll get that

b = 4

The equation, then, is

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3 years ago

Find the surface area of the prism Show all the work I'll mark you brainiest

Trava [24]

Answer:

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Step-by-step explanation:

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3 years ago

The graph shows the dilation of ΔABC with the origin as its center. Which rule describes this transformation? A) (x, y) → (2x, 2

podryga [215]

Note: Since, you have not added the graph. So, I will give you a general overview of the concept of dilation, the understanding of which will make you clear your concept.

Step-by-step explanation:

We know that a dilation is the kind of transformation which produces an image which has the same shape as the original object, but having a different size.

Here are some key factors regarding dilation:

Enlargement occurs when a dilation does create a larger image.

Reduction occurs when a dilation does create a smaller image.

A dilation shrinks or stretches the original object.
If the scale factor > 1, the image will be a stretch (enlargement)
If the scale factor is between 0 and 1, the image will be shrunk (reduction)
If the scale factor = 1, the original object and the image will be congruent

Here is the impact of dilation when (x, y) → (2x, 2y):

Dilation with scale factor 2, will have the rule as (x, y) → (2x, 2y). The image will be a stretch (enlargement) as the scale factor > 1.
The location of the new coordinates of the image can be obtained by multiplying the coordinates of the original figure by 2.

For example, the coordinates of the image of a point A(4, 8) will be A'(2×4, 2×8) or A'(8, 16) after the dilation of scale 2 at the origin.

Here is the impact of dilation when (x, y) → (0.5x, 0.5y):

Dilation with scale factor 0.5, will have the rule as (x, y) → (0.5x, 0.5y). The image will be shrunk (reduction) as the scale factor < 1.
The location of the new coordinates of the image can be obtained by multiplying the coordinates of the original figure by 0.5.

For example, the coordinates of the image of a point A(4, 8) will be A'(0.5×4, 0.5×8) or A'(2, 4) after the dilation of scale 0.5 at the origin.

Keywords: dilation, transformation, enlargement, reduction

Learn more about dilation from brainly.com/question/13846651

#learnwithBrainly

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3 years ago

50 POINTS FOR CORRECT ANSWER @PlatoNation REPORTED IF INCORRECT

aleksandrvk [35]

Answer:

About 2614 years.

Step-by-step explanation:

We are given k, and the information that N/N0 = 0.77, so the C-14 function becomes:

$N=N_0\cdot e^{-kt} \\0.77N_0 = N_0\cdot e^{-kt}\\0.77 = e^{-0.0001 t}$

and we can solve for t:

$0.77 = e^{-0.0001 t}\\\ln0.77 = \ln e^{-0.0001 t}\\\ln 0.77 = -0.0001 t\implies\\t = -\frac{\ln0.77}{0.0001}=2613.65\approx 2614\,\,\,\mbox{years}$

The estimated age of the bird skeleton is 2614 years.

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4 years ago