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3 years ago

Verify each identity:

2 answers:

5 0

Tan(x) + tan(y)/1 - tan(x)tan(y) = sin(x)cos(y) + cos(x)sin(y)/cos(x)cos(y) - sin(x)sin(y)

tan(x + y) = sin(x + y)/cos(x + y)
tan(x + y) = tan(x + y)

Trava [24]3 years ago

4 0

Using double angle identity in trigonometry, sin x cos y + cos x sin y is equal to the sum of x and y that is the angle inside the sine function notation. On the other hand, cos x cos y - sin x sin y is equal to cos (x+y) while (tan x + tan y) / (1 - tan x tan y) is equal to tan (x+y). Since tan (x+y) = sin (x+y)/ cos (x+y), the problem is solved

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I have the answer, 2-(3/x+2)

Marat540 [252]

Start with the answer format we want, and work your way toward forming a single fraction like so

$a + \frac{b}{x+2}\\\\a*1+\frac{b}{x+2}\\\\a*\frac{x+2}{x+2}+\frac{b}{x+2}\\\\\frac{a(x+2)}{x+2}+\frac{b}{x+2}\\\\\frac{a(x+2)+b}{x+2}\\\\\frac{ax+2a+b}{x+2}\\\\\frac{ax+(2a+b)}{x+2}\\\\$

Compare that last expression to (2x+1)/(x+2). Notice how the ax and 2x match up, so a = 2 must be the case.

Then we have 2a+b as the remaining portion in the numerator. Plugging in a = 2 leads to 2a+b = 2*2+b = 4+b. Set this equal to the +1 found in (2x+1)/(x+2) to have the terms match.

So, 4+b = 1 leads to b = -3

Therefore, a = 2 and b = -3

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An alternative route:

$\frac{2x+1}{x+2}\\\\\frac{2x+1+0}{x+2}\\\\\frac{2x+1+4-4}{x+2}\\\\\frac{(2x+4)+1-4}{x+2}\\\\\frac{2(x+2)-3}{x+2}\\\\\frac{2(x+2)}{x+2}+\frac{-3}{x+2}\\\\2-\frac{3}{x+2}\\\\$

I added and subtracted 4 in the third step so that I could form 2x+4, which then factors to 2(x+2). That way I could cancel out a pair of (x+2) terms toward the very end.

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Other alternative methods involve synthetic division or polynomial long division. They are slightly separate but related concepts.

3 0

3 years ago

Read 2 more answers

Dan has bags of candy with two pieces in each. Bill has bags of candy with five pieces in each. Bill has six more bags than Dan.

Anna35 [415]

Answer:

Bill has bags of candy with five pieces in each. The Bill has 16 bags

Solution:

Given, Dan has bags of candy with two pieces in each.

Bill has bags of candy with five pieces in each.

Bill has six more bags than Dan.

Then, number of bags with bill = 6 + number of bags with dan.

The total number of pieces candy the two boys have 100.

Now, candies with bill + candies with dan = 100

⇒ 5 pieces per bag x number of bags with bill + 2 pieces per bag x number of bags with dan = 100

⇒ 5 x (6 + number of bags with dan) + 2 x number of bags with dan = 100

⇒ 30 + 5 x number of bags with dan + 2 x number of bags with dan = 100

⇒ (5 + 2) x number of bags with dan = 100 – 30

⇒ 7 x number of bags with dan = 70

⇒ Number of bags with dan = 10

So, number of bags with bill = 6 + 10 = 16

Hence, bill has 16 bags.

7 0

4 years ago

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 oun

Ugo [173]

Answer: A) .1587

Step-by-step explanation:

Given : The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce.

i.e. $\mu=12.30$ and $\sigma=0.20$

Let x denotes the amount of soda in any can.

Every can that has more than 12.50 ounces of soda poured into it must go through a special cleaning process before it can be sold.

Then, the probability that a randomly selected can will need to go through the mentioned process = probability that a randomly selected can has more than 12.50 ounces of soda poured into it =

$P(x>12.50)=1-P(x\leq12.50)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{12.50-12.30}{0.20})\\\\=1-P(z\leq1)\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.8413\ \ \ [\text{By z-table}]\\\\=0.1587$

Hence, the required probability= A) 0.1587

6 0

3 years ago

78.84 meters= Centimeter

ValentinkaMS [17]

Answer:

7884 Centemeters

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

2. cos 0° a) sin 1° b) c) sin 90° d) tan 90° B)cos 1°

motikmotik

Answer:

sin 90

Step-by-step explanation:

cos (0)

Using the unit circle, we know that cos 0=1

sin 1 and cos 1 are not equal to 1

sin 90 =1

tan 90 = sin 90/ cos 90 = 1/0 =undefined

5 0

3 years ago