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Dimas [21]
3 years ago
9

Which equation can be used to prove 1 + tan?(x) = sec2(x)?

Mathematics
1 answer:
Elodia [21]3 years ago
4 0

Answer: D

Step-by-step explanation:

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What is the circumference of the circle? Use 3.14 for Pi. A circle with radius 6.4 centimeters.
miv72 [106K]

Answer:

C≈40.21cm

Step-by-step explanation:

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Practice Question 2 - Find the Volume ​
Brrunno [24]

Answer:

112.896

Step-by-step explanation:

To calculate the volume of a triangular prism, measure the width and height of a triangular base, then multiply the base by the height by 1/2 to determine the triangle's area. Next, measure the height of the triangular prism and multiply this by the triangle's area to get the volume.

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3 years ago
an exponential function f is defined by f(x)=c^x where c is a constant greater than 1 if f (7) = 4 x f (5) what is the value of
svetoff [14.1K]

From the above, it can be seen that the nature of polynomial functions is dependent on its degree. Higher the degree of any polynomial function, then higher is its growth. A function which grows faster than a polynomial function is y = f(x) = ax, where a>1. Thus, for any of the positive integers n the function f (x) is said to grow faster than that of fn(x).

Thus, the exponential function having base greater than 1, i.e., a > 1 is defined as y = f(x) = ax. The domain of exponential function will be the set of entire real numbers R and the range are said to be the set of all the positive real numbers.

It must be noted that exponential function is increasing and the point (0, 1) always lies on the graph of an exponential function. Also, it is very close to zero if the value of x is mostly negative.

Exponential function having base 10 is known as a common exponential function. Consider the following series:

Derivative of logarithmic and exponential function 5

The value of this series lies between 2 & 3. It is represented by e. Keeping e as base the function, we get y = ex, which is a very important function in mathematics known as a natural exponential function.

For a > 1, the logarithm of b to base a is x if ax = b. Thus, loga b = x if ax = b. This function is known as logarithmic function.

Derivative of logarithmic and exponential function 2

For base a = 10, this function is known as common logarithm and for the base a = e, it is known as natural logarithm denoted by ln x. Following are some of the important observations regarding logarithmic functions which have a base a>1.

   The domain of log function consists of positive real numbers only, as we cannot interpret the meaning of log functions for negative values.

   For the log function, though the domain is only the set of positive real numbers, the range is set of all real values, i.e. R

   When we plot the graph of log functions and move from left to right, the functions show increasing behaviour.

   The graph of log function never cuts x-axis or y-axis, though it seems to tend towards them.

Derivative of logarithmic and exponential function 3

   Logap = α, logbp = β and logba = µ, then aα = p, bβ = p and bµ = a

   Logbpq = Logbp + Logbq

   Logbpy = ylogbp

   Logb (p/q) = logbp – logbq

Exponential Function Derivative

Let us now focus on the derivative of exponential functions.

The derivative of ex with respect to x is ex, i.e. d(ex)/dx = ex

It is noted that the exponential function f(x) =ex  has a special property. It means that the derivative of the function is the function itself.

(i.e) f ‘(x) = ex = f(x)

Exponential Series

Exponential Functions

Exponential Function Properties

The exponential graph of a function represents the exponential function properties.

Let us consider the exponential function, y=2x

The graph of function y=2x is shown below. First, the property of the exponential function graph when the base is greater than 1.

Exponential Functions

Exponential Function Graph for y=2x

The graph passes through the point (0,1).

   The domain is all real numbers

   The range is y>0

   The graph is increasing

   The graph is asymptotic to the x-axis as x approaches negative infinity

   The graph increases without bound as x approaches positive infinity

   The graph is continuous

   The graph is smooth

Exponential Functions

Exponential Function Graph y=2-x

The graph of function y=2-x is shown above. The properties of the exponential function and its graph when the base is between 0 and 1 are given.

   The line passes through the point (0,1)

   The domain includes all real numbers

   The range is of y>0

   It forms a decreasing graph

   The line in the graph above is asymptotic to the x-axis as x approaches positive infinity

   The line increases without bound as x approaches negative infinity

   It is a continuous graph

   It forms a smooth graph

Exponential Function Rules

Some important exponential rules are given below:

If a>0, and  b>0, the following hold true for all the real numbers x and y:

       ax ay = ax+y

       ax/ay = ax-y

       (ax)y = axy

       axbx=(ab)x

       (a/b)x= ax/bx

       a0=1

       a-x= 1/ ax

Exponential Functions Examples

The examples of exponential functions are:

   f(x) = 2x

   f(x) = 1/ 2x = 2-x

   f(x) = 2x+3

   f(x) = 0.5x

Solved problem

Question:

Simplify the exponential equation 2x-2x+1

Solution:

Given exponential equation: 2x-2x+1

By using the property: ax ay = ax+y

Hence, 2x+1 can be written as 2x. 2

Thus the given equation is written as:

2x-2x+1 =2x-2x. 2

Now, factor out the term 2x

2x-2x+1 =2x-2x. 2 = 2x(1-2)

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

2x-2x+1 = – 2x

6 1
3 years ago
Decide which title best describes all of the expressions in each column of the table. Place the correct title at the top of each
irga5000 [103]
For the first one is has greater then 3 terms
The middle one is has exactly one term
And the last one is has two terms
I believe I hope this helps
4 0
3 years ago
What part of the circumference is an arc whose measure is 30°?<br> 1/12<br> 1/10<br> 1/8<br> 1/6
GrogVix [38]

Answer:

1/12

Step-by-step explanation:

The whole circumference (i.e complete circle) is an arc which measures 360°

in our case, it is given that our arc measures only 30°

the fraction of our arc of 30° to the complete circle of 360° is

30/360

= 3/36

= 1/12

5 0
3 years ago
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