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4 years ago

Complete the identity. (sin(\alpha +\beta ))/(cos\alpha cos\beta )

Mathematics

1 answer:

Irina18 [472]4 years ago

7 0

Answer:

$\frac{sin\alpha.cos\beta +cos\alpha.sin\beta}{cos\alpha.cos\beta}=tan\alpha +tan\beta$

Explanation:

Here are the steps to simplify the expression and obtain the identity.

1) Given:

$\frac{si(\alpha+\beta)}{cos(\alpha)cos(\beta)}$

2) Use the identity sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

$\frac{sin\alpha.cos\beta +cos\alpha.sin\beta}{cos\alpha.cos \beta}$

3) Distributive property of division:

$\frac{sin\alpha.cos\beta}{cos\alpha.cos \beta}+\frac{cos\alpha.sin\beta}{cos\alpha.cos \beta}$

4) Simplify common factors in numerators and denominators

$\frac{sin\alpha}{cos\alpha }+\frac{sin\beta}{cos \beta}$

5) Definition of tangent ratio

tanα + tanβ

6) Conclusion

$\frac{sin\alpha.cos\beta +cos\alpha.sin\beta}{cos\alpha.cos \beta}=tan\alpha +tan\beta$

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. Find the smallest value of k such that 3240k is a perfect cube.

Stels [109]

The product of multiple perfect cubes is also a perfect cube.
Proof for two:
n^3 * p^3 = nnnppp = npnpnp = (np)^3
And any integer whose exponent is a multiple of 3 is a perfect cube.
We will use this here:

Prime factorize 3240:
3240 = 405 * 2^3 = 2^3 * 3^4 * 5^1
We need to multiply this by k, to make all the exponents divisible by 3
The exponents not divisible by 3 are 4 and 1.
So let's fix that:
2^3 * 3^4 * 3*2 * 5^1 * 5^2
So, k is 3^2 * 5^2 = 225
(3240*225)^(1/3) = 90

8 0

3 years ago

5. Jazmin goes to her locker every 15 minutes during gym. Cathy goes to her locker every 20 minutes. If they both just went to t

postnew [5]

1 hour or 60 minutes bcuz 15×4=60 and 20×3=60

3 0

3 years ago

Resolver para x <br><br> 141-x=291

yarga [219]

Answer:

x= 291-141= 150

x=150

Hope that helped! :D

5 0

3 years ago

Read 2 more answers

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The m

marshall27 [118]

Answer:

1. 0.0000454

2. 0.01034

3. 0.0821

4. 0.918

Step-by-step explanation:

Let X be the random variable denoting the number of passengers arriving in a minute. Since the mean arrival rate is given to be 10,

$X \sim Poi(\lambda = 10)$

1. Requires us to compute

$P(X = 0) = e^{-10} \frac{10^0}{0!} = 0.0000454$

2. We need to compute $P(X \leq 3) = P(X =0) + P(X =1) + P(X =2) + P(X =3)$

$P(X =1) = e^{-10} \frac{10^1}{1!} = 0.000454$

$P(X =2) = e^{-10} \frac{10^2}{2!} = 0.00227$

$P(X =3) = e^{-10} \frac{10^3}{3!} = 0.00757$

$P(X \leq 3) =0.0000454+ 0.000454 + 0.00227 + 0.00757 = 0.01034$

3. The expected no. of arrivals in a 15 second period is = $10 \times \frac{1}{4} = 2.5$ . So if Y be the random variable denoting number of passengers arriving in 15 seconds,

$Y \sim Poi(2.5)$

$P(Y=0) = e^{-2.5} \frac{2.5^0}{0!} = 0.0821$

4. Here we use the fact that Y can take values $0,1, \dotsc$ . So, the event that "Y is either 0 or $\geq$ 1" is a sure event ( i.e it has probability 1 ).

$P(Y=0) + P(Y \geq 1) = 1 \implies P(Y \geq 1) = 1 -P(Y=0) = 1 - 0.0821 = 0.918$

3 0

3 years ago

Cassidy says that capacity is the same as the amount. Do you agree? Explain why or why not.

telo118 [61]

The capacity is the same as the amount because it refers to the amount of what is inside the object. Lets say you have a bag of chips it refers to the amount inside the bag of chips.

6 0

3 years ago