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ddd [48]
3 years ago
5

An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places w

here appropriate. If there is no solution, enter NO SOLUTION.)
sin(θ/2) − 1 = 0
(a) Find all solutions of the equation.
(b) Find the solutions in the interval [0, 2π).

Mathematics
1 answer:
vredina [299]3 years ago
3 0

Answer:

(a) θ = π + 4πn

(b) θ = π

Step-by-step explanation:

(a) sin(θ/2) − 1 = 0

sin(θ/2) = 1

θ/2 = π/2 + 2πn

θ = π + 4πn

(b) Try different values of n.

n = -1, θ = -3π

n = 0, θ = π

n = 1, θ = 5π

If 0 < θ < 2π, then θ = π.

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a country's population in 1990 was 242 million, in 1999 it was 244 million. estimate the population in 2013
Free_Kalibri [48]

Answer:

247.12 million

Step-by-step explanation:

Given:

In 1990, population=242 million

In 1999, population=244 million

estimated population in 2013=?

Estimated growth is calculated by:

P(t)= Po*e^(kt)

where Po is original population

k is growth rate

t is the time in year

Now putting the values of Po=242, P(t)=244, t=9 (t=1999-1990=9) we have:

244=242e^(9k)

(244/242)=e^(9k)

ln(244/242)=9k

k=1/9ln(244/242)

k=0.00091

Now Putting k=0.00091, Po=242, and t=23 (t=2013-1990=23) we have:

P(t)=242e^(23*0.00091‬)

P(t)=247.12 million

the population in 2013 estimated to be 247.12 million!

3 0
3 years ago
a new car worth 37000 is depreciating in value by 2000 per year. how many years will the car be worth 17000
dangina [55]
37000 (total price of the car) - 17000 (the target value) = 20,000 (the difference)

20,000 (difference) / 2000 (how much it depreciates per year) = 10 (the amount of years it will take)

Verify:

17000 + (2000 * 10) = 37000? Yes.
4 0
4 years ago
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is form
kolbaska11 [484]

h=(a)(sinC)=19(sin37)

That means h ≈11.43

Since c<h, There is no triangle

6 0
3 years ago
Read 2 more answers
The set {3, 5, ?} could not be the sides of a triangle.<br><br> 2<br> 7<br> 3<br> 5
tresset_1 [31]
7 and 2 cannot be the lengths as on a triangle they're two equal side so two 3s or two 5s
6 0
3 years ago
Read 2 more answers
1st Question:
liq [111]

Answer:

1) 3/4 = x

Step-by-step explanation:

1) 3/x -4 >0

=3/x -4+4>0 +4

=3/x> 4

switch 4 with x

x = 3/4

so literally the ans is x< 4

sorry but I don't know how to do the second question ☹️☹️

4 0
3 years ago
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