Answer:
In order to maximize
, the cow must stand 3.74 ft away from the billboard, approximately.
Explanation:
The vertical angle subtended by the billboard at the cow's eye can be calculated from
![\theta = \arctan{\frac{7}{x}} - \arctan{\frac{2}{x}}.](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Carctan%7B%5Cfrac%7B7%7D%7Bx%7D%7D%20-%20%5Carctan%7B%5Cfrac%7B2%7D%7Bx%7D%7D.)
Now, maximaxing
, we have
![\theta_{max} = \frac{d\theta}{dx}|_{x=x_0}=0\\-\frac{7}{x_0^2+49} - \left(\frac{2}{x_0^2+4}\right) = 0\\\frac{7}{x_0^2+49} - \frac{2}{x_0^2+4} = 0.](https://tex.z-dn.net/?f=%5Ctheta_%7Bmax%7D%20%3D%20%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%7C_%7Bx%3Dx_0%7D%3D0%5C%5C-%5Cfrac%7B7%7D%7Bx_0%5E2%2B49%7D%20-%20%5Cleft%28%5Cfrac%7B2%7D%7Bx_0%5E2%2B4%7D%5Cright%29%20%3D%200%5C%5C%5Cfrac%7B7%7D%7Bx_0%5E2%2B49%7D%20-%20%5Cfrac%7B2%7D%7Bx_0%5E2%2B4%7D%20%3D%200.)
Solving the equation for ![x_0](https://tex.z-dn.net/?f=x_0)
![x_0 = \pm\sqrt{14} \approx 3.74.\\](https://tex.z-dn.net/?f=x_0%20%3D%20%5Cpm%5Csqrt%7B14%7D%20%5Capprox%203.74.%5C%5C)
Which can be interpretated as the cow standing either one or the other side from the billboard. The next plot confirms that
's positive root, gives a maximum for the angle
.
Answer: b. Throw it directly away from the space station.
Explanation:
According to <u>Newton's third law of motion</u>, <em>when two bodies interact between them, appear equal forces and opposite senses in each of them.</em>
To understand it better:
Each time a body or object exerts a force on a second body or object, it (the second body) will exert a force of equal magnitude but in the opposite direction on the first.
So, if the astronaut throws the wrench away from the space station (in the opposite direction of the space station), according to Newton's third law, she will be automatically moving towards the station and be safe.
Answer:
3.2N
Explanation:
Given parameters:
Coefficient of kinetic friction = 0.43
Weight of box = 7.4N
Unknown:
Force of kinetic friction = ?
Solution:
The force of kinetic friction is given as:
Force of kinetic friction = UN
U is the coefficient of friction
N is the weight
Force of kinetic friction = 0.43 x 7.4 = 3.2N
Answer:
Explanation:
Given
there is fix Quantity of gas i.e. mass of gas is constant
From ideal gas Equation
PV=nRT
(a) volume always increases is not true as Pressure can also be increased .
(b)If Pressure is constant along with mass then as Temperature increases, Volume also increases.
(c)true , Product of Pressure and volume depends upon temperature thus it also increases with temperature.
(d)Density of gas may or may not increases
As density is ![\frac{mass}{volume}](https://tex.z-dn.net/?f=%5Cfrac%7Bmass%7D%7Bvolume%7D)
volume may increase or decrease as temperature increase .
(e)false
as it clearly stated that quantity of fixed therefore there is no change in gas
C. The number of F atoms in the reactants equals the number of F atoms in the products.