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4 years ago

Find tan2θ if θ terminates in Quadrant IV and cosθ =3/5 .

Mathematics

1 answer:

Liula [17]4 years ago

6 0

Answer:

The answer to your question is $\frac{-8}{3}$

Step-by-step explanation:

Data

cos Ф = 3/5

tan2Ф = ?

Quadrant IV

Process

1.- Remember that tanФ = $\frac{Opposite side}{Adjacent side}$ and cos Ф = $\frac{adjacent side}{hypotenuse}$

then, adjacent side = 3 and hypotenuse = 5

2.- Calculate opposite side

O² = h² - a²

O² = 5² - 3²

O² = 25 - 9

O² = 16

O = 4

3.- Calculate the tan 2Ф

tan 2Ф = 2( $\frac{-4}{3}$ ) The opposite side is negative in the fourth

quadrangle

tan 2Ф = $\frac{-8}{3}$

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4 years ago

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What is the sum or difference?

dlinn [17]

1. Ans: Option (B) $-6x^4$

Explanation:
Given: $2x^4 - 8x^4$
Take the common out:
=> $x^4(2 - 8)$

Hence: => $[tex]-6x^4$ [/tex] (Option B)

2. Ans: Option (D) $-3y^5$

Explanation:
Given: $6y^5 - 9y^5$
Take the common term(s) out:
=> $y^5(6-9)$

Hence: => $-3y^5$ (Option D)

3. Ans: Option (B) $9x^2 - 12x + 6$ quadratic trinomial

Explanation:
Given: $6 - 12x + 13x^2 - 4x^2$

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> $13x^2 - 4x^2 - 12x + 6$
=> $9x^2 - 12x + 6$ (Option B)

4. Ans: Option (C) $7.3x^2 + 0.8x + 1.3$

Explanation:
In order to find the total number of Common and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

Common guppies: $3.1x^2 +6.0x + 0.3$ 
Endler's guppies: $4.2x^2 - 5.2x + 1.0$
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Total number: $7.3x^2 +0.8x + 1.3$
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Hence the ans is Option(C) $7.3x^2 + 0.8x + 1.3$

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Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = $266x^2$

Now the area of the circular fountain:
Area of the Circular Fountain = $\pi r^2$
Since, r=6x
Therefore,
Area of the Circular Fountain = $\pi (6x)^2 = 36 \pi x^2$

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = $266x^2$ - $36 \pi x^2$
=> Final area of the Yard = $2x^2(133 - 18 \pi)$ (Option D)

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Explanation:
First let's find the total area of the lot:
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