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HACTEHA [7]
3 years ago
10

Can you please help me ​

Mathematics
1 answer:
Sveta_85 [38]3 years ago
5 0

Sure....

What is your question??

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BRAINLIESTTT ASAP! PLEASE HELP ME :)
Gre4nikov [31]

Answer:

θ = 0.896 and 2.246.

Step-by-step explanation:

We will use the identity

sin²θ + cos²θ = 1

and the double angle formula

cos2θ = cos²θ - sin²θ = (1 - sin²θ) - sin²θ = 1 - 2sin²θ

1. Convert the equation to a more solvable form.

\begin{array}{rcll}\sin\theta + 1 & = & \cos2\theta &\\\sin\theta + 1& = & 1-2\sin^{2}\theta & \text{Used the double angle formula}\\f(\theta) = 2\sin^{2}\theta + \sin\theta -2 & = & 0 & \text{Moved terms to left-hand side}\\2u^2 + u - 2 & = & 0 & \text{Substituted u for }\sin\theta\\\end{array}

2. Solve the quadratic

a = 2; b = 1; c = -2

(a) Set up the equation.

u =\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\=\dfrac{-1\pm\sqrt{(1^2 - 4\times 2 \times (-2)}}{2\times2}\\\\=\dfrac{-1\pm\sqrt{1 + 16}}{4}\\\\=\dfrac{-1\pm\sqrt{17}}{4}\\

(b) Evaluate the roots

\begin{array}{rcl}u = \dfrac{-1 - 4.123}{4} & \qquad & u = \dfrac{-1 + 4.123}{4}\\\\u = -\dfrac{5.123}{4} & \qquad & u =\dfrac{3.123}{4}\\\\u = -1.281& \qquad & u =0.7808\\\end{array}

3. Solve for θ

(a) The negative root

u = sinθ = -1.281

sinθ cannot be less than -1. No solution.

(b) The positive root

If sin(x) = a, then

x = arcsin(x) + 2πn and

x = π - arcsin(a) + 2πn

(i) Case 1

u = sinθ = 0.7808

θ = arcsin(0.7808) + 2πn

θ = 0.8959 ± 2πn

If n = 0,  

θ = 0.8959

(ii) Case 2

θ = π - 0.8959 + 2πn

If n = 0,

θ = π - 0.8959 = 2.246

The solutions are θ = 0.8959 and θ = 2.246

The diagram below shows the graph of f(θ) with its roots at 0.896 and 2.246.

5 0
3 years ago
The program director at a botanical garden surveyed 75 of their annual members about the number of times they visit the gardens
Tatiana [17]

Answer: C) 165 annual members

Step-by-step explanation:

Those who will visit the garden more than 3 times in the next month will be those who visit 4, 5, and 6 or more times.

Out of the 75 surveyed, the total number of those are:

= 9 + 12 + 3

= 24

That would give a percentage of:

= 24 / 75

= 32%

This means that the best estimate for those who will visit more than 3 times is 32%.

Out of the total number of 516, that is:

= 32% * 516

= 165 members

6 0
3 years ago
Consider a graph of the equation y=x+6. What is the y intercept
Pavlova-9 [17]

Answer:

6

Step-by-step explanation:

In the slope intercept equation, y=mx+b, m stands for slope and b stands for y-intercept, therefore your y-intercept is 6.

5 0
3 years ago
Read 2 more answers
a gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket.if a bike has 36 teeth on the fr
Ber [7]

Answer:

3 : 1

Step-by-step explanation:

ratio = teeth on front sprocket : teeth on rear sprocket

       = 36 : 12 ( divide both parts of the ratio by 12 )

       = 3 : 1 ← in simplest form


5 0
3 years ago
Read 2 more answers
Write an equation of a line that is perpendicular to y=2x-3 and has a y intercept of 10
AnnyKZ [126]
The slope of a line that is perpendicular to another line is the negative reciprocal of the other.

In this case, we know that the slope of the given equation is 2.

Since we're solving for a line perpendicular to it, we simply find the reciprocal of the 2 (It turns into 1/2) and make it negative.

y = -1/2x + b

Since the given states that the new y-intercept is 10, input it into 'b'.

y = -1/2x + 10


If you'd like me to explain anything I did here, just ask :)
-T.B.
4 0
3 years ago
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