The table of ordered pairs (x,y) gives an exponential function.

Mathematics

1 answer:

Andreyy891 year ago

8 0

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 8):

8 = ab⁰

a = 8

At point (1, 32):

32 = 8b

b = 4

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

Find out more on equation at: brainly.com/question/2972832

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erica [24]

Circumference + perimeter =38
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(38-x) is perimeter
then
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6 0

3 years ago

HELP ASAP FOR BRAINLIEST!

salantis [7]

Answer:

make sure calculator is in "radians" mode
use the cos⁻¹ function to find cos⁻¹(.23) ≈ 1.338718644

Step-by-step explanation:

A screenshot of a calculator shows the cos⁻¹ function (also called arccosine). It is often a "2nd" function on the cosine key. To get the answer in radians, the calculator must be in radians mode. Different calculators have different methods of setting that mode. For some, it is the default, as in the calculator accessed from a Google search box (2nd attachment).

The third attachment shows a graph of the cosine function (red) and the value 0.23 (dashed red horizontal line). Everywhere that line intersects the cosine function is a value of A such that cos A = 0.23. There are an infinite number of them. You need to know about the symmetry and periodicity of the cosine function to find them all, given that one of them is A ≈ 1.339.

The solution in the 4th quadrant is at 2π-1.339, and additional solutions are at these values plus 2kπ, for any integer k.

Also in the third attachment is a graph of the inverse of the cosine function (purple). The dashed purple vertical line is at x=0.23, so its intersection point with the inverse function is at 1.339, the angle at which cos(x)=0.23. The dashed orange graph shows the inverse of the cosine function, but to make it be single-valued (thus, a function), the arccosine function is restricted to the range 0 ≤ y ≤ π (purple).

_____

So, the easiest way to answer the problem is to use the inverse cosine function (cos⁻¹) of your scientific or graphing calculator. (Always make sure the angle mode, degrees or radians, is appropriate to the solution you want.) Be aware that the cosine function is periodic, so there is not just one answer unless the range is restricted.

I keep myself "unconfused" by reading cos⁻¹ as the angle whose cosine is. As with any inverse functions, the relationship with the original function is ...

cos⁻¹(cos A) = A

cos(cos⁻¹ a) = a