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SVEN [57.7K]
2 years ago
7

Verify that (cos²a) (2 + tan² a) = 2 - sin² a....​

Mathematics
2 answers:
Sveta_85 [38]2 years ago
7 0

Trigonometric Formula's:

\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}

\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }

Given to verify the following:

\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a

\texttt{\underline{rewrite the equation}:}

\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )

\texttt{\underline{apply distributive method}:}

\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)

\texttt{\underline{simplify the following}:}

\rightarrow \sf 2cos^2 a  + sin^2 a

\texttt{\underline{rewrite the equation}:}

\rightarrow \sf 2(1 - sin^2a )  + sin^2 a

\texttt{\underline{distribute inside the parenthesis}:}

\rightarrow \sf 2 - 2sin^2a   + sin^2 a

\texttt{\underline{simplify the following}} :

\rightarrow \sf 2 - sin^2a

Hence, verified the trigonometric identity.

Artemon [7]2 years ago
7 0

Answer:

See below ~

Step-by-step explanation:

Identities used :

⇒ cos²a = 1 - sin²a

⇒ tan²a = sin²a / cos²a

============================================================

Solving :

⇒ (cos²a) (2 + tan² a)

⇒ 2cos²a + (cos²a)(tan²a)

⇒ 2(1 - sin²a) + sin²a

⇒ 2 - 2sin²a + sin²a

⇒ 2 - sin²a [∴ Proved √]

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Answer:

The maximum height of the arrow is 125 feet.

Step-by-step explanation:

The pathway of the arrow can be represented by the equation,

h = -16t^2 +80t + 25 .....(1)

Where h is height in in feet and t is time in seconds.

It is required to find the maximum height of the arrow. For maximum height, \dfrac{dh}{dt}=0.

So,

\dfrac{d(-16t^2 +80t + 25)}{dt}=0\\\\-32t+80=0\\\\t=\dfrac{80}{32}\\\\t=2.5\ s

Put t = 2.5 s in equation (1). So,

h = -16(2.5)^2 +80(2.5) + 25\\\\h=125\ \text{feet}

So, the maximum height of the arrow is 125 feet.

6 0
3 years ago
3. Decide whether each equation is true or false, and explain how you know.
BARSIC [14]

Answer:

a.false

b.true

c.false

d.I really can't get about it.

e.false

Step-by-step explanation:

So,here;

a.9.9.3=35 is given

or,243=35 (which is false)

b.7+7+7=3+3+3+3+3+3+3

or,21=21 (which is true)

c.2/3/2=2/3

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2 years ago
Tom and Brad often play a video game. One day, they tracked the scores they each received for 10 rounds.
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Tom's median video game score is less than Brad's median video game score.

7 0
2 years ago
I REALLY need help with these 3 questions plz!!!!
Tanzania [10]

Answer:

6. No. See explanation below.

7. 18 months

8. 16

Step-by-step explanation:

6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.

Let's find the GCF of 85 and 99:

85 = 5 * 17

99 = 3^2 + 11

5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.

Answer: No because the GCF of 85 and 99 is 1.

7.

We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.

6 = 2 * 3

9 = 3^2

LCM = 2 * 3^2 = 2 * 9 = 18

Answer: 18 months

We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.

Month                Charlie          Dasha

1                          home             home

2                          home             home

3                          home             home

4                          home             home

5                          home             home

6                         trip                home

7                          home             home

8                          home             home

9                          home             trip

10                         home             home

11                         home             home

12                         trip               home

13                         home             home

14                         home             home

15                         home             home

16                         home             home

17                         home             home

18                         trip                 trip

Answer: 18 months

8.

First, we find the prime factorizations of 96 an 80.

96 = 2^5 * 3

80 = 2^4 *5

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Answer: 16

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3 years ago
Which equations represent hyperbolas?
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Try this option:
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4 0
3 years ago
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