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butalik [34]
3 years ago
10

What is the domain of the function?

Mathematics
1 answer:
dusya [7]3 years ago
4 0
The function domain: x<0 or 0<x<4 or x>4 (?) I believe....
You might be interested in
Find , , and if and terminates in quadrant .
ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

,

• cos2x

,

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})=\frac{12}{13}

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\  \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

\tan 2x=\frac{2\tan x}{1-\tan ^2x}=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}=\frac{\frac{4}{3}}{1-\frac{4}{9}}=\frac{\frac{4}{3}}{\frac{9-4}{9}}=\frac{\frac{4}{3}}{\frac{5}{9}}=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}

OR

\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0
1 year ago
The distance a spring will stretch varies directly with how much weight is attached to the spring. if a spring stretches 9 inche
Tcecarenko [31]
9/100 = x/90
Cross multiply to get 810 = 100x
Divide both sides by 100 to get x = 81 inches
6 0
2 years ago
Solve the equation.-7=y/7
ad-work [718]

Answer:

y = -49

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

-7 = y/7

<u>Step 2: Solve for </u><em><u>y</u></em>

  1. Multiply 7 on both sides:                    -49 = y
  2. Rewrite:                                               y = -49
7 0
3 years ago
How many home runs did each player hit the season
olya-2409 [2.1K]
Let Peter's hit be x and Alice's runs be y.
x = 2(y - 6) . . . (1)
x + y = 18 . . . (2)

Putting (1) into (2) gives,
2y - 12 + y = 18
3y = 18 + 12 = 30
y = 30/3 = 10
x = 2(10 - 6) = 2(4) = 8

Therefore, Peter hit 8 home runs and Alice hit 10 home runs.
3 0
3 years ago
Hamza bought 8 gallons of brown paint to paint his kitchen and dining room. Unfortunately, when
dalvyx [7]

Answer:

4 gallons of white paint

Step-by-step explanation:

Let

x -----> quantity of gallons of white paint that  Hamza has to buy

we know that

A gallon of white paint must mixed with 2 gallons of brown paint

using proportion

\frac{1}{2}\frac{gallon\ white}{gallons\ brown} =\frac{x}{8}\frac{gallons\ white}{gallons\ brown}\\\\x=8/2\\x=4\ gallons\ white

3 0
3 years ago
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