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ValentinkaMS [17]
2 years ago
15

2

Mathematics
1 answer:
balu736 [363]2 years ago
3 0

Answer:

increse X-inefficiency is the answer

Step-by-step explanation:  im here to help

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Help me with trigonometry
poizon [28]

Answer:

See below

Step-by-step explanation:

It has something to do with the<em> </em><u><em>Weierstrass substitution</em></u>, where we have

$\int\, f(\sin(x), \cos(x))dx = \int\, \dfrac{2}{1+t^2}f\left(\dfrac{2t}{1+t^2}, \dfrac{1-t^2}{1+t^2} \right)dt$

First, consider the double angle formula for tangent:

\tan(2x)= \dfrac{2\tan(x)}{1-\tan^2(x)}

Therefore,

\tan\left(2 \cdot\dfrac{x}{2}\right)= \dfrac{2\tan(x/2)}{1-\tan^2(x/2)} = \tan(x)=\dfrac{2t}{1-t^2}

Once the double angle identity for sine is

\sin(2x)= \dfrac{2\tan(x)}{1+\tan^2(x)}

we know \sin(x)=\dfrac{2t}{1+t^2}, but sure,  we can derive this formula considering the double angle identity

\sin(x)= 2\sin\left(\dfrac{x}{2}\right)\cos\left(\dfrac{x}{2}\right)

Recall

\sin \arctan t = \dfrac{t}{\sqrt{1 + t^2}} \text{ and } \cos \arctan t = \dfrac{1}{\sqrt{1 + t^2}}

Thus,

\sin(x)= 2 \left(\dfrac{t}{\sqrt{1 + t^2}}\right) \left(\dfrac{1}{\sqrt{1 + t^2}}\right) = \dfrac{2t}{1 + t^2}

Similarly for cosine, consider the double angle identity

Thus,

\cos(x)=  \left(\dfrac{1}{\sqrt{1 + t^2}}\right)^2- \left(\dfrac{t}{\sqrt{1 + t^2}}\right)^2 = \dfrac{1}{t^2+1}-\dfrac{t^2}{t^2+1} =\dfrac{1-t^2}{1+t^2}

Hence, we showed \sin(x) \text { and } \cos(x)

======================================================

5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]

Solving

5\,\overbrace{\frac{1-t^2}{1+t^2}}^{\cos(x)} = 12\,\overbrace{\frac{2t}{1+t^2}}^{\sin(x)}+3

\implies \dfrac{5-5t^2}{1+t^2}= \dfrac{24t}{1+t^2}+3 \implies  \dfrac{5-5t^2 -24t}{1+t^2}= 3

\implies 5-5t^2-24t=3\left(1+t^2\right) \implies -8t^2-24t+2=0

t = \dfrac{-(-24)\pm \sqrt{(-24)^2-4(-8)\cdot 2}}{2(-8)} = \dfrac{24\pm 8\sqrt{10}}{-16} =  \dfrac{3\pm \sqrt{10}}{-2}

t=-\dfrac{3+\sqrt{10}}{2}\\t=\dfrac{\sqrt{10}-3}{2}

Just note that

\tan\left(\dfrac{x}{2}\right) =  \dfrac{3\pm 8\sqrt{10}}{-2}

and  \tan\left(\dfrac{x}{2}\right) is not defined for x=k\pi , k\in\mathbb{Z}

6 0
2 years ago
For an experiment comparing two treatment conditions, an independent-measures design would obtain ____ score(s) for each subject
mrs_skeptik [129]

The score(s) that will be obtained respectively in an independent-measures design and repeated-measures design are; 1 and 2

<h3>How to interpret Experiments?</h3>

There are different ways to carry out an experiment in mathematics. This is because there are various means of research and also ways to interpret the results.

Now, when comparing two treatment conditions, an independent-measures design would always obtain 1 score for each subject. However, when a repeated-measures design is carried out on the same sample, it will obtain 2 scores.

Read more about Experiments at;  brainly.com/question/25677592

#SPJ4

5 0
1 year ago
A store has a sale for 10% off. You decide to buy a $15 t-shirt.
Elanso [62]

Answer: 1.50

10% of fifteen is 1.50

7 0
3 years ago
Read 2 more answers
Marta receive x amount dollars for helping her dad in the backyard she spent 1.77 of that amount on snacks after buying those sn
alexdok [17]

Answer:

x=15.50

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Use Greens Theorem to evaluate integral x^2ydx - xy^2dy, where C is 0 ≤ y ≤ √9-x^2 with counterclockwise orientation
Ratling [72]

Answer:

Step-by-step explanation:

a circle will satisfy the conditions of Green's Theorem since it is closed and simple.

Let's identify P and Q from the integral

P=x^2 y, and Q= xy^2

Now, using Green's theorem on the line integral gives,

\oint\limits_C {x^2ydx-xy^2dy } =\iint\limits_D {y^2-x^2} \, dA\\\\

3 0
3 years ago
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