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2 years ago

IF A+B+C=Π prove that sin(3A)+sin(3B)+sin(3C)=-4cos(3A÷2)cos(3B÷2)cos(3C÷2)

Mathematics

1 answer:

Hunter-Best [27]2 years ago

4 0

Answer:

LHS of the given equation is:

sinθ+sin3θ+sin5θ+sin7θ=(sinθ+sin7θ)+(sin3θ+sin5θ)=2sin8θ2.cos6θ2+2sin8θ2.cos2θ2 [since sinC+sinD=2sinC+D2.cosC−D2=2sin4θ.cos3θ+2sin4θ.cosθ=2sin4θ.[cos3θ+cosθ] [since cosC+cosD=2cosC+D2.cosC−D2=2sin4θ.[2cos2θ.cosθ]=4cosθ.cos2θ.sin4θsinθ+sin3θ+sin5θ+sin7θ=(sinθ+sin7θ)+(sin3θ+sin5θ)=2sin8θ2.cos6θ2+2sin8θ2.cos2θ2 [since sinC+sinD=2sinC+D2.cosC-D2=2sin4θ.cos3θ+2sin4θ.cosθ=2sin4θ.[cos3θ+cosθ] [since cosC+cosD=2cosC+D2.cosC-D2=2sin4θ.[2cos2θ.cosθ]=4cosθ.cos2θ.sin4θ

any more help just ask :)

Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

A real estate agent has 19 properties that she shows. She feels that there is a 30% chance of selling any one property during a

netineya [11]

Answer:

$P(X \geq 5)=1-P(X$

We can find the individual probabilities:

$P(X=0)=(19C0)(0.3)^0 (1-0.3)^{19-0}=0.00114$

$P(X=1)=(19C1)(0.3)^1 (1-0.3)^{19-1}=0.0092$

$P(X=2)=(19C2)(0.3)^2 (1-0.3)^{19-2}=0.0358$

$P(X=3)=(19C3)(0.3)^3 (1-0.3)^{19-3}=0.0869$

$P(X=4)=(19C4)(0.3)^4 (1-0.3)^{19-4}=0.1491$

And replacing we got:

$P(X \geq 5) = 1-[0.00114+0.009282+0.0358+0.0869+0.149]= 0.7178$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=19, p=0.3)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X \geq 5)$

And we can use the complement rule:

$P(X \geq 5)=1-P(X$

We can find the individual probabilities:

$P(X=0)=(19C0)(0.3)^0 (1-0.3)^{19-0}=0.00114$

$P(X=1)=(19C1)(0.3)^1 (1-0.3)^{19-1}=0.0092$

$P(X=2)=(19C2)(0.3)^2 (1-0.3)^{19-2}=0.0358$

$P(X=3)=(19C3)(0.3)^3 (1-0.3)^{19-3}=0.0869$

$P(X=4)=(19C4)(0.3)^4 (1-0.3)^{19-4}=0.1491$

And replacing we got:

$P(X \geq 5) = 1-[0.00114+0.009282+0.0358+0.0869+0.149]= 0.7178$

4 0

3 years ago

Mary sells to her father, robert, her shares in a corp for $55,000. the shares cost mary $80,000. how much loss may mary claim f

OverLord2011 [107]

Mary Purchase shares = $80,000
Mary Sells shares = $55,000

Loss she can claim for = $80,000 - $55,000
= $ 25,000

6 0

3 years ago

Vanessa bought a house for $268,500. She has a 30 year mortgage with a fixed rate of 6.25%. Vanessa’s monthly payments are $1,59

Genrish500 [490]

Answer:

Option a - $9,314.45

Step-by-step explanation:

Cost of the house = $268,500

Time of repayment = 30 years

Repayment is done monthly, so number of repayments = 30 X 12 = 360

Monthly Payment = $1595.85

Rate of interest per payment period = $\frac{.0625}{12}$

So, Present value of monthly payments = 1595.85 X $\frac{(1+\frac{.0625}{12})^{360}-1}{(1+\frac{.0625}{12})^{360}*(\frac{.0625}{12})}$

= $259,185.55

So, Vanessa's down payment = $268,500 - $259,185.55 = $9,314.45

Hope it helps.

Thank you !!

8 0

3 years ago

IF A+B+C=Π prove that sin(3A)+sin(3B)+sin(3C)=-4cos(3A÷2)cos(3B÷2)cos(3C÷2)​

IF A+B+C=Π prove that sin(3A)+sin(3B)+sin(3C)=-4cos(3A÷2)cos(3B÷2)cos(3C÷2)