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Nata [24]
1 year ago
14

Use a graph in a (-2π, 2π, π/2) by (-3, 3, 1) viewing rectangle to complete the identity.

Mathematics
1 answer:
yaroslaw [1]1 year ago
8 0

First, notice that:

2\tan (\frac{x}{2})=2\cdot(\pm\sqrt[]{\frac{1-cosx}{1+\cos x})}

And in the denominator we have:

1+\tan ^2(\frac{x}{2})=1+\frac{1-\cos x}{1+\cos x}=\frac{1+cosx+1-\cos x}{1+cosx}=\frac{2}{1+\cos x}

then, we have on the original expression:

\begin{gathered} \frac{2\tan(\frac{x}{2})}{1+\tan^2(\frac{x}{2})}=\frac{2\cdot\pm\sqrt[]{\frac{1-\cos x}{1+cosx}}}{\frac{2}{1+\cos x}}=\frac{2\cdot(\pm\sqrt[]{1-cosx})\cdot(1+\cos x)}{2\cdot(\sqrt[]{1+cosx})} \\ =(\sqrt[]{1-\cos x})\cdot(\sqrt[]{1+\cos x})=\sqrt[]{(1-\cos x)(1+\cos x)} \\ =\sqrt[]{1-\cos^2x}=\sqrt[]{\sin^2x}=\sin x \end{gathered}

therefore, the identity equals to sinx

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The city of Anville is currently home to 16000 people, and the population has been growing at a continuous rate of 4% per year.
Nesterboy [21]

Answer

After 13.15 years the population of both towns will become equal.

Step-by-step explanation:

Population of the city Anville is given by using the compound interest formula  

The formula of compound interest

A = p( 1+r/n)^n*t

using this we get

P1 = 16000 (1 +\frac{0.04}{1}) ^1*t

Population of the city of Brinker will be

P2 = 11000( 1  + \frac{0.07}{1}) ^1*t

now to make equal population in both towns

P1=P2

16000 (1 +\frac{0.04}{1}) ^1*t = 11000( 1  + \frac{0.07}{1}) ^1*t

(\frac{1.04}{1.07} )^t = \frac{11}{16}

t = 13.15 years

5 0
3 years ago
I need help! What’s the best answer choice??
borishaifa [10]
The awnser is F) This account earns 4% compounding interest.
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4 0
3 years ago
Read 2 more answers
The sum of Rayson and his brother’s age is 29. If Rayson is 4 years older than his brother 7 years ago. How old is Rayson and hi
Neko [114]

Answer:

16 years, 13 years

Step-by-step explanation:

Let their ages be x, 29-x

Equation formed:-

(x - 7) + 4 = 29 - x

→ 2x = 29 + 3

→ x = 16 years

Answer: 16 years, 13 years

7 0
3 years ago
linda thinks of a two digit number. the sum of the digits is 8. if she reverses the digits, the new number is 26 greater than he
antoniya [11.8K]
<span>Let
x = the 10s digit
y = the units
N1----------> original number
</span>N2----------> new number
<span>N2=N1+36--------- >N2-N1=36
y+x=8------------- > equation (I)
then
10x + y = N1
10y+x=N2

(10y+x)-(10x+y)=36- -----> 9y-9x=36------- > y-x=4----------- > equation (II)

resolving (I) and (II)
</span> y+x=8
 y- x=4<span>
-----------------
2y+0x=12--------------- >y=6
then
x=8-y=8-6=2----------> x=2

N1=26 and N2=62

the two digit number is 26</span>
7 0
4 years ago
At Pizza Company, Lee made 50 pizzas one day. There were 110 pizzas sold that day. What fraction of the pizzas did Lee make? Sim
sineoko [7]

Answer:

50/110 or 5/11

Step-by-step explanation:

Use 5/11 as your final answer

8 0
3 years ago
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