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romanna [79]
2 years ago
14

I) Solve the equation sin2x + 3cos2x = 0 (for 0 till 360°)

Mathematics
1 answer:
galina1969 [7]2 years ago
7 0
Get rid of cos2x by dividing both the values. So Sin2x/cos2x +3cos2x/cos2x.
Tan2x = 3
2x = -71.5 so x is -35.6
Use the quadrant method and add 360 twho the two values tou get.
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Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i
jenyasd209 [6]

Answer:

If the limit that you want to find is \lim_{x\to \infty}\dfrac{P(x)}{Q(x)} then you can use the following proof.

Step-by-step explanation:

Let P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0} and Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0} be the given polinomials. Then

\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}

Observe that

\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}

and

\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}

Then

\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}

3 0
2 years ago
Arlene sleeps for
True [87]

Answer:

50.40

Step-by-step explanation:

7 hours and 20 minutes times 7= 50 hours and 40 minutes

And then you have to change it into a mixed number and it is 50.40

7 0
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The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of
Yakvenalex [24]
Hey there! First, set up the equation y = mx + b<span>. Next, we're going to subtract b from both sides, leaving us with </span>y - b = mx. After that, divide the equation by x to isolate the variable "m". The answer is y-b / x = m. I hope this helps!
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A firm has a revenue function that can be represented by r (x)=700x-0.35x^2, where r (x) is the total revenue (in dollars) and x
Fudgin [204]

Answer:

How many units need to be sold to produce the maximum revenue? 1000 units

How many in dollars is the maximum revenue when the maximum of units are sold? $350,000

Step-by-step explanation:

We get max value of a function if we differentiate it and set it equal to 0.

We need to differentiate r(x) and set it equal to 0 and solve for x.

<u><em>That would be number of units sold to get max revenue.</em></u>

<u><em /></u>

<u>Then we take that "x" value and substitute into r(x) to get the max revenue amount.</u>

<u />

Before differentiating, we see the rules shown below:

f(x)=ax^n\\f'(x)=n*ax^{n-1}

Where

f'(x) is the differentiated function

Now, let's do the process:

r (x)=700x-0.35x^2\\r(x)=700-2*0.35x\\r(x)=700-0.7x\\0=700-0.7x\\0.7x=700\\x=1000

So, 1000 units need to be sold for max revenue

Now, substituting, we get:

r (x)=700x-0.35x^2\\r(1000)=700(1000)-0.35(1000)^2\\r(1000)=350,000

The max revenue amount is $350,000

5 0
2 years ago
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
Elena-2011 [213]

<u>Given</u>:

The length of the segment of the chord DB is 8.2 units.

The length of the segment AB is 6.9 units.

The length of the radius AC be x units.

We need to determine the value of x.

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Since, we know the property that, "if a radius is perpendicular to the chord, then it bisects the chord".

Thus, applying the above property, we have;

DB ≅ BC

8.2 = BC

Thus, the length of BC is 8.2 units.

<u>Value of x:</u>

Since, ∠B makes 90°, let us apply the Pythagorean theorem to determine the value of x.

Thus, we have;

AC^2=AB^2+BC^2

Substituting the values, we have;

x^2=6.9^2+8.2^2

x^2=47.61+67.24

x^{2} =114.85

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Thus, the value of x is 10.7 units.

Hence, Option A is the correct answer.

4 0
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