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antoniya [11.8K]
2 years ago
7

Prove that \displaystyle \frac{\cos \theta}{1 + \sin \theta} = \frac{1 - \sin \theta}{\cos \theta}

Mathematics
1 answer:
Bogdan [553]2 years ago
7 0

Answer:

sin^2(θ)+cos^2(θ)=1

Step-by-step explanation:

We know that the statement above is true because of the Pythagorean identity theorem, which states the aforementioned equation. If you solve the equation for 1 you get the same equation.

To do this first multiply both sides by cos(θ), this gives you (cos^2θ)/1+sinθ = 1-sinθ

Then, multiply both sides by sinθ. This equals cos^θ=1-sin^2θ.

Finally, add sin^2θ to both sides. This equals the final answer of cos^2θ+sin^2θ=1. Which is true.

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If y= 3x + 6, what is the minimum value of (x^3)(y)?
Rainbow [258]

Answer:

Given the statement: if y =3x+6.

Find the minimum value of (x^3)(y)

Let f(x) = (x^3)(y)

Substitute the value of y ;

f(x)=(x^3)(3x+6)

Distribute the terms;

f(x)= 3x^4 + 6x^3

The derivative value of f(x) with respect to x.

\frac{df}{dx} =\frac{d}{dx}(3x^4+6x^3)

Using \frac{d}{dx}(x^n) = nx^{n-1}

we have;

\frac{df}{dx} =(12x^3+18x^2)

Set \frac{df}{dx} = 0

then;

(12x^3+18x^2) =0

6x^2(2x + 3) = 0

By zero product property;

6x^2=0   and 2x + 3 = 0

⇒ x=0 and x = -\frac{3}{2} = -1.5

then;

at x = 0

f(0) = 0

and  

x = -1.5

f(-1.5) = 3(-1.5)^4 + 6(-1.5)^3 = 15.1875-20.25 = -5.0625


Hence the minimum value of (x^3)(y) is, -5.0625






3 0
3 years ago
From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be cond
Vladimir79 [104]

Answer:

The mean and standard deviation of the number preferring the incumbent is mean = 330, standard deviation = 10.59.

Step-by-step explanation:

We are given that From previous polls, it is believed that 66% of likely voters prefer the incumbent.

A new poll of 500 likely voters will be conducted. In the new poll the proportion favoring the incumbent has not changed.

Let p = probability of voters preferring the incumbent = 66%

n = number of voters polled = 500

<u>So, the mean of the number preferring the incumbent is given by;</u>

         Mean = n \times p = 500 \times 0.66

                                = 330 voters

<u>And, standard deviation of the number preferring the incumbent is given by;</u>

          Variance =  n \times p\times (1-p)  

                          =  500 \times 0.66 \times (1-0.66)

                          =  112.2

So, Standard deviation =  \sqrt{Variance}

                                       = \sqrt{112.2}  = 10.59

7 0
2 years ago
The floor plan of a proposed auditorium shows a stage that measures 1.75 inches in width . The scale of the floor plan is 1 in =
Nikolay [14]

Answer:

31.5

Step-by-step explanation:

so if they say that every inch is realy 18 ft and u have 1.75 inches then multiply 8 by 1.75 to get the width of the stage

8 0
2 years ago
Find the length of side xx to the nearest tenth.<br> 30°<br> 60°<br> x<br> 9
otez555 [7]

Answer:

yes I am the only one that has a lil before I go to

4 0
2 years ago
162 ⋅ 90 238·56 238 ⋅ 34 =
ollegr [7]

1572455566080 is your answer! Hope I helped! :D

6 0
3 years ago
Read 2 more answers
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