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Stells [14]
3 years ago
5

Find all solutions to 4tan(3x)=-4 between 0° and 360°​

Mathematics
1 answer:
jeyben [28]3 years ago
6 0

Divide both sides by 4 to get

\tan(3x)=-1

Recalling the definition of tangent as ratio between sine and cosine, we have

\tan(3x)=-1 \iff \dfrac{\sin(3x)}{\cos(3x)}=-1 \iff \sin(3x)=-\cos(3x)

The sine and cosine of an angle are opposite only if the angle is

\alpha = 135+180k,\quad k \in \mathbb{Z}

So, we have

3x=135+180k \iff x = 45+60k,\quad k \in \mathbb{Z}

So, the solutions are

\alpha \in \{45,\ 105,\ 165,\ 225,\ 285,\ 345\}

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Please help me with this pleaseee
torisob [31]

Answer:

x = 88.2

Step-by-step explanation:

The angle at the top of the triangle = 90° - 10° = 80°

and the left side of the triangle is x ( opposite sides of a rectangle )

Using the tangent ratio in the right triangle

tan80° = \frac{opposite}{adjacent} = \frac{500}{x}

Multiply both sides by x

x × tan80° = 500 ( divide both sides by tan80° )

x = \frac{500}{tan80} ≈ 88.2

5 0
3 years ago
Evaluate f(x) = 8.4x + 3.8 when x = 9.1. Type the number only for auto grade to work correctly. Round your answer to 2 decimal p
vova2212 [387]
The answer is 80.24.
3 0
3 years ago
Which statement best describes the polynomial 3x^2-6+4x^4
Elanso [62]
<span>fourth degree polynomial with three terms
the degree is the highest exponent the term are separated by plus or minus  </span>
8 0
4 years ago
Leila, Charlie, and Joe have a total of $144 in their wallets. Joe has 4 times what Leila has. Charlie has $6 more than Leila. H
ollegr [7]

Answer:

The amounts of money each has are:

Joe = $92

Charlie = $29

Leila = $23

Step-by-step explanation:

To solve this, we will convert the statements into an equation, and use that to solve for the unknowns, as follows:

total amount = $144

Let Leila's share be S

Joe's share = 4 times Leila's = 4S

Charlie's share = $6 + Leila's share = 6 + S

Joe's share + Charlie's Share + Leila's Share = $144

4S + (6 + S) + S = 144

4S + 6 + S + S = 144

4S + 2S + 6 = 144

6S + 6 = 144

6S = 144 - 6 = 138

S = 138 ÷ 6 = $23

Therefore Leila's share 'S' = $23

Joe share= 4S = 4 × 23 = $92

Charlie's share = 6 + 23 = $29

8 0
3 years ago
Let ​ x^2+18x=44 .​ What values make an equivalent number sentence after completing the square?
Lostsunrise [7]
To find the final term to compete the square you need to divide the 'x' term by 2 then square it

x^2 +18x + = 44+ \\ x^2+18x+( \frac{18}{2} )^2=44+( \frac{18}{2} )^2 \\ x^2+18x+9^2=44+9^2 \\ x^2+18x+81=44+81 \\ (x+9)^2=125 - equivalent equation
6 0
4 years ago
Read 2 more answers
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