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alexgriva [62]
3 years ago
11

Find all solutions to 2sin(θ)=√3 on the interval 0≤θ<2π

Mathematics
1 answer:
makkiz [27]3 years ago
7 0

Answer:

2sin(3θ) - √3 = 0

Step-by-step explanation:

 sin(3θ) = √3/2

 

3θ = π/3 + 2kπ or 2π/3 + 2kπ, k = 0, ±1, ±2, ±3,...

 

θ = π/9 + 2kπ/3, 2π/9 + 2kπ/3

 

If k = 0, we get θ = π/9, 2π/9

If k = 1, we get θ = 7π/9, 8π/9

If k = 2, we get θ = 13π/9, 14π/9

 

Other values of k give values of θ lying outside of the interval [0, 2π).

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Under which condition is the sample proportion, , a point estimate of the population proportion?
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Answer:

c. the sample portion is unbaised

Step-by-step explanation:

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5 0
3 years ago
If A(1,2), B(5,-4) and (-3,2) are the vertices of a triangle, which statement holds true?
Zigmanuir [339]

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is A.

<h3>What is a triangle?</h3>

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The length of different sides are:

AB = \sqrt{(5-1)^2+(-4-2)^2} = \sqrt{16+36} = \sqrt{52}\rm\ units

BC = \sqrt{(-3-5)^2+(2+4)^2} = \sqrt{64+36} = 10\rm\ units

AC = \sqrt{(2-2)^2+(-3-1)^2} = \sqrt{16} = 4\rm\ units

Since the length of all the sides of the triangle is not equal it is a scalene triangle.

Hence, the correct option is A.

Learn more about Triangle:

brainly.com/question/2773823

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7 0
2 years ago
Read 2 more answers
Which of the following describes the image of a triangle after a dilation that has a scale factor of 5/6
Sergeeva-Olga [200]

Answer:

See example below.

Step-by-step explanation:

The image of a triangle will be 5/6 the size. It will be slightly smaller than the original. For example, if the side measurement of the triangle on one side is 12 then the image of the triangle after a dilation will be 12*5/6 = 60/6 = 10.

The new side length is 10 slightly smaller than 12.

6 0
3 years ago
A diagonal support beam is attached to the gate of a fence as shown. Which angles must be congruent in order for the top and bot
ludmilkaskok [199]

Answer:

3 and 2

Step-by-step explanation:


4 0
3 years ago
How do I solve 1 and 2?
LuckyWell [14K]
H=+15 m
v=+5 m/s
Ball hits the ground when h(t)=-15m
h(t)=-9.8t^2+vt+h
=>
-15=-9.8t^2+5t+15
9.8t^2-5t-30=0
Solve for t, using quadratic formula,
t=-1.513 or t=2.023
reject negative root due to context, so
t=2.023 seconds

2)
h(t)=-16t^2+20t+8
a. height before pitch is when t=0, or h(0)=8
b. highest point reached when h'(t)=-32t+20=0 => t=5/8 seconds
c. highest point is t(5/8)=-16(5/8)^2+20(5/8)+8=47/5=9.4 m
d. ball hits ground when h(t)=0 => solve t for h(t)=0
=> t=-0.3187 seconds or t=1.569 seconds.
Reject negative root to give
time to hit ground = 1.569 since ball was pitched.

5 0
3 years ago
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