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3 years ago

What are the values of x in the equation x(x-6)=4(x=6)?

Mathematics

1 answer:

Klio2033 [76]3 years ago

7 0

X=6....6(6-6)=4(6=6) 6(0)=0....0=\=4 6=6

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Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2

Sergeu [11.5K]

Answer:

The work is in the explanation.

Step-by-step explanation:

The sine addition identity is:

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$ .

The sine difference identity is:

$\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(a)$ .

The cosine addition identity is:

$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$ .

The cosine difference identity is:

$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$ .

We need to find a way to put some or all of these together to get:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$ .

So I do notice on the right hand side the $\sin(a+b)$ and the $\sin(a-b)$ .

Let's start there then.

There is a plus sign in between them so let's add those together:

$\sin(a+b)+\sin(a-b)$

$=[\sin(a+b)]+[\sin(a-b)]$

$=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]$

There are two pairs of like terms. I will gather them together so you can see it more clearly:

$=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]$

$=2\sin(a)\cos(b)+0$

$=2\sin(a)\cos(b)$

So this implies:

$\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)$

Divide both sides by 2:

$\frac{\sin(a+b)+\sin(a-b)}{2}=\sin(a)\cos(b)$

By the symmetric property we can write:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$

3 0

3 years ago

The door code to gain access to a top-secret laboratory is 6 digits. The first 3 digits of the code are all odd, and the last 3

WINSTONCH [101]

5 odd numbers and 5 even numbers
since they can be repeated
5*5*5=first 3 digits
5*5*5=last 3 digits
in all
5*5*5*5*5*5=15625 ways

3 0

2 years ago

How to factor this equation

KIM [24]

Answer:

Step-by-step explanation:

x2=256

By taking Square root we get

x=16

7 0

2 years ago

Tonys bill at the restaurant was $9.52. If he wants to leave a 20% tip, how much is that?

postnew [5]

Answer:

11.42 dollars

Step-by-step explanation: since you are adding a percentage turn 20% into a decimal. if you do this you will get .2. Next, multiple .2 by 9.52 and you will get 20% of 9.52. Now add this value to 9.52 and you will get 11.42 dollars.

6 0

3 years ago

Each person in a group of college students was identified by graduating year and asked when he or she preferred taking classes:

swat32

Answer:

Step-by-step explanation:

The frequency table is attached below.

We have to calculate, the probability that the student preferred morning classes given he or she is a junior.

i.e $P(\text{Morning }|\text{ Junior})$

We know that,

$P(A\ |\ B)=\dfrac{P(A\ \cap\ B)}{P(B)}$

So,

$P(\text{Morning }|\text{ Junior})=\dfrac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}$

Putting the values from the table,

$\dfrac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}=\dfrac{\frac{16}{143}}{\frac{26}{143}}=\dfrac{16}{26}=0.615$

3 0

3 years ago