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Luda [366]
3 years ago
14

How to solve arctan[tan(7pi /4)] ...?

Physics
1 answer:
Svet_ta [14]3 years ago
7 0
Well, 
arctan is a bijection from R into (-pi/2 , pi/2)*and 
pi is a period of tangent function: 
so 
as we have : tan(7pi/4) = tan(pi - pi/4) = - tan(pi/4) 
we finally get : 

<span>arctan(tan(7pi/4)) = artan(tan(- pi/4)) = - pi/4 
</span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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A truck covered 2/7 of a journey at an average speed of 40
sertanlavr [38]

Answer:

The amount of time for the whole journey is 8 hours.

Explanation:

A truck covered 2/7 of a journey at an average speed of 40  mph. Representing 1 the total of the trip traveled, then the rest of the distance traveled is calculated as: 1-\frac{2}{7} =\frac{5}{7}

So if the truck covered the remaining 200 miles at \frac{2}{7}, this means that \frac{5}{7} of the trip represents the 200 miles. So, to calculate the total distance traveled by the truck, you apply the following rule of three: if \frac{5}{7} of the route represents 200 miles, the integer 1 (which represents the total of the route), how many miles are they?

miles=\frac{1*200miles}{\frac{5}{7} } =\frac{7}{5} *200 miles

miles= 280

So the total distance traveled is 280 miles. Since speed is the relationship between the space traveled by an object and the time used for it (speed=\frac{distance}{time}), then if the average of the entire trip was 35 mph and the distance traveled 280 miles, the time is calculated as:

time=\frac{distance}{speed}=\frac{280 miles}{35 mph}

time= 8 h

<u><em> The amount of time for the whole journey is 8 hours.</em></u>

<u><em /></u>

6 0
3 years ago
A book, that has a mass of 0.5 grams, is pushed across a table with a force of 20 newtons. What is the acceleration of the book?
Bas_tet [7]

Answer:

4\cdot 10^4 m/s^2

Explanation:

The acceleration of an object is given by Newton's second law:

a=\frac{F}{m}

where

F is the net force applied on the object

m is the mass of the object

For the book in the problem, we have:

m=0.5 g =5\cdot 10^{-4} kg is the mass

F=20 N is the force applied

Substituting into the formula, we find the acceleration:

a=\frac{20 N}{5\cdot 10^{-4} kg}=4\cdot 10^4 m/s^2

6 0
3 years ago
Suppose that a planet were discovered between the sun and Mercury, with a circular orbit of radius equal to 2/3 of the average o
Musya8 [376]

Explanation:

It is given that,

A planet were discovered between the sun and Mercury, with a circular orbit of radius equal to 2/3 of the average orbit radius of Mercury.

Mass of the Sun, M=1.99\times 10^{30}\ kg

Radius of Mercury's orbit, r=5.79\times 10^{10}\ m

Radius of discovered planet, R=\dfrac{2}{3}r

R=\dfrac{2}{3}\times 5.79\times 10^{10}\ m=3.86\times 10^{10}\ m

Let T is the orbital period of such a planet. Using Kepler's third law of planetary motion as :

T^2\propto R^3

T^2=\dfrac{4\pi^2R^3}{GM}

T^2=\dfrac{4\pi^2\times (3.86\times 10^{10})^3}{6.67\times 10^{-11}\times 1.99\times 10^{30}}

T=\sqrt{1.71\times 10^{13}}

T = 4135214.625 s

or

T = 47.86 days

So, the orbital period of such a planet is 47.86 days. Hence, this is the required solution.

6 0
3 years ago
What does it mean for a reaction to be endothermic? choose 2 of the following
Rainbow [258]

Answer: I would choose options C and D

Explanation:

3 0
2 years ago
Read 2 more answers
Please answer this<br> No links please
Sladkaya [172]
Your answer is- amplitudes
6 0
3 years ago
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