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1 year ago

Cos^3a-sin^3a/cosa-sina

Mathematics

1 answer:

KIM [24]1 year ago

8 0

Answer:

1 + cosa sina

Step-by-step explanation:

$\frac{cos^3a-sin^3a}{cosa-sina}$

cos³a - sin³a ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

cos³a - sin³a

= (cosa - sina )(cos²a + cosa sina + sin²a)

= (cosa - sina)(1 + cosa sina) [ sin²a + cos²a = 1 ]

Then

$\frac{cos^3a-sin^3a}{cosa-sina}$

= $\frac{(cosa-sina)(1+cosasina)}{cosa-sina}$ ← cancel (cosa - sina) on numerator/ denominator

= 1 + cosa sina

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3. Bob Baffert hos iwo thoroughbred horses in his bom that he brings out

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Answer:

12.5r + 200 = 12.5*2r

Step-by-step explanation:

<h3>Given</h3>

Rate of Hoppertunity = r

Rate of Dortmund = 2r as it is twice as fast

<h3>Solution</h3>

Let the distance Hoppertunity runs be d, then the distance Dortmund runs is d + 200 m

Since it took 12.5 seconds Dortmund to catch Hoppertunity, it can be expressed as:

d = 12.5r for Hoppertunity
d + 200 =12.5*2r for Dortmund

<u>By replacing d in the second equation, we get:</u>

12.5r + 200 = 12.5*2r

<u>Soving</u>:

12.5r = 200
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Hoppertunity's rate is 16 m/sec

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3 years ago

Find the area! NEED HELP ASAP!!!!!!!!

allochka39001 [22]

seperate it into a square and right triangle

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5m^2

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3 years ago

Read 2 more answers

Si agrupo mis lápices de 2 en dos me sobra 1; si lo hago de 3 en 3, también me sobra 1 y si lo hago de 5 en 5 ocurre los mismo.¿

Vinvika [58]

Answer:

31 pencils

Step-by-step explanation:

What we must do is reduce the range of responses, the first thing is to limit the numbers to the interval between 30 and 40.

If it is two by two and there is one left, it means that all the pairs are eliminated.

If it is five in five and there is one left over, the ones ending in 5 are also eliminated.

If it is three by three and there is one left over, the 33 and 39 are eliminated.

Taking this into account, the possibilities are reduced to two numbers only, 31 and 37.

37 is discarded because when it is grouped from five to five, there are 2 left over.

So the answer is 31, you have 31 pencils.

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3 years ago

Carla runs 4 miles every day. She jogs from home to the school track, which is 3/4 mile away. She then runs laps around the 1/4

julsineya [31]

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3 years ago

Help it’s slope idk how to do it

Over [174]

a. $\boxed{y-602=\frac{2}{3}(x-3)}$

b. For every month the pine tree grows about 0.67 inches.

c. <em> </em>It represents the height of the tree at the moment Ariel started to record the heights.

<h2>Explanation:</h2>

In this exercise we have that in July Ariel recorded the height of a pine tree and how quickly it was expected to grow in next several months. From the Table, we can get the following points:

$P_{1}(3,602) \\ \\ P_{2}(6,604) \\ \\ P_{3}(q,606) \\ \\ P_{4}(12,608)$

It is obvious that this problem follows a linear equation, so our goal is to find the equation that matches the Table.

The point slope form of the equation of a line is:

$y-y_{1}=m(x-x_{1}) \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{1}, y_{1}):A \ point \ on \ the \ line$

Finding (m):

$Using: \\ \\ P_{1}(x_{1},y_{1}) \rightarrow P_{1}(3,602) \\ \\ P_{2}(x_{2}, y_{2}) \rightarrow P_{2}(6,604) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{604-602}{6-3} \\ \\ m=\frac{2}{3}$

Finally, the equation of the line is:

$(x_{1}, y_{1}) \rightarrow (3,602) \\ \\ \boxed{y-602=\frac{2}{3}(x-3)}$

In this case, we have that:

The x-axis represents the <em>Number of Months </em>the pine tree was expected to grow.
The y-axis represents the <em>Height of the Tree </em>in inches.

Since the slope o a line is:

$Slope=\frac{Change \ in \ y}{Change \ in \ x}=\frac{2}{3}$

Then, this means that<em> every three months the pine tree grows two inches, </em><em>or </em><em>for every month the pine tree grows about 0.67 inches.</em>

The y-intercept can be found setting $x=0$ . So, from our equation:

$y-602=\frac{2}{3}(x-3)} \\ \\ \\ If \ x=0: \\ \\ y-602=\frac{2}{3}(0-3) \\ \\ y-602=-2 \\ \\ Solving \ for \ y: \\ \\ y=602-2 \\ \\ y=600$

So the y-intercept is $y=600$ and<em> represents the height of the tree at the moment Ariel started to record the heights.</em>

<h2>Learn more:</h2>

Slope Intercept form: brainly.com/question/4192440

#LearnWithBrainly

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3 years ago