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kompoz [17]
3 years ago
13

What does tan^2(theta) mean?

Mathematics
1 answer:
Luda [366]3 years ago
5 0
It is the square of \tan{\theta}.

\tan^2{\theta}=(tan{\theta})^2
You might be interested in
A 6-pack of batteries cost $10.50.what is the unit price
IRINA_888 [86]

Answer:

Unit price = $1.75

Step-by-step explanation:

In order to determine the unit price of the batteries, divide the $10.50 total price for the 6-pack of batteries by 6:

$10.50 ÷ 6 = $1.75

Therefore, the unit price of each battery is $1.75.

4 0
3 years ago
Read 2 more answers
If(x) = x + 2 and h(x) = x-1, what is f • h](-3)?
deff fn [24]

Answer/Step-by-step explanation:

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

1

x

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

1

x

) = 3(x

2 +

1

x

) + 4 (12)

f(x

2 +

1

x

) = 3x

2 +

3

x

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

3

x + 4.

Let’s try one more composition but this time with 3 functions. It’ll be exactly the same but

with one extra step.

• Find (f ◦ g ◦ h)(x) given f, g, and h below.

f(x) = 2x (14)

g(x) = x

2 + 2x (15)

h(x) = 2x (16)

(17)

We wish to find f(g(h(x))). We will first find g(h(x)).

h(x) = 2x (18)

g( ) = ( )2 + 2( ) (19)

g(h(x)) = (h(x))2 + 2(h(x)) (20)

g(2x) = (2x)

2 + 2(2x) (21)

g(2x) = 4x

2 + 4x (22)

Thus g(h(x)) = 4x

2 + 4x. We now wish to find f(g(h(x))).

g(h(x)) = 4x

2 + 4x (23)

f( ) = 2( ) (24)

f(g(h(x))) = 2(g(h(x))) (25)

f(4x

2 + 4x) = 2(4x

2 + 4x) (26)

f(4x

2 + 4x) = 8x

2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

2 + 8x.

4 0
2 years ago
For each function, do the following: a) state the name of the function, b) identify the independent and dependent variable, c) i
Lostsunrise [7]

Answer:

Given the function in the question

f(x) = |x-3| + 2

a) state the name of the function

  Absolute value function

  since it is similar to f(x) = |x|

b) identify the independent and dependent variable  

x = independent variable (input variable)

f(x) or y = dependent variable  (output variable)

The variable which we assign the value we call the independent variable,    and the other variable is the dependent variable, since it value depends on  the independent variable.

c) identify the rule

A function is an equation that has only one answer for y for every x.

d) evaluate the function

given x = -5

 f(-5) = |-5 - 3| + 2

        = |-8| + 2

        = 8 +2

        = 10

8 0
2 years ago
What is the average rate of change from x = −4 to x = 1?
kati45 [8]

Answer:

What is the average rate of change from x = −4 to x = 1? x= -4 x + 5

5 0
2 years ago
Of all college degrees awarded in the United States, 50% are bachelor's degrees, 59% are earned by women, and 29% are bachelor's
Natasha2012 [34]

Answer:

  P(W|B) = 0.58

Step-by-step explanation:

The conditional probability formula tells you ...

  P(W | B) = P(W&B) / P(B)

  = 0.29/.050

  = 0.58

7 0
3 years ago
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