Luster, hardness, color, size, and temperature are all examples of

A small balloon is released at a point 150 feet away from an observer, who is on level ground. If the balloon goes straight up a

Elza [17]

Answer:

$\dfrac{dz}{dt}=0.65\ ft/s$

Explanation:

Given that

x= 150 ft

$\dfrac{dy}{dt}= 7\ ft/s$

y= 14 ft

From the diagram

$z^2=x^2+y^2$

When ,x= 150 ft and y= 14 ft

$z^2=150^2+14^2$

$z=\sqrt{150^2+15^2}$

z=150.74 ft

$z^2=x^2+y^2$

By differentiating with respect to time t

$2z\dfrac{dz}{dt}= 2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}$

$z\dfrac{dz}{dt}= x\dfrac{dx}{dt}+y\dfrac{dy}{dt}$

Here x is constant that is why

$\dfrac{dx}{dt}=0$

$z\dfrac{dz}{dt}= y\dfrac{dy}{dt}$

Now by putting the values in the above equation we get

$150.74\times \dfrac{dz}{dt}=14\times 7$

$\dfrac{dz}{dt}=\dfrac{14\times 7}{150.74}\ ft/s$

$\dfrac{dz}{dt}=0.65\ ft/s$

Therefore the distance between balloon and observer increasing with 0.65 ft/s.

5 0

3 years ago

Explain how surface and subsurface events are integral parts of the rock cycle.

vagabundo [1.1K]

Example of surface events are erosion and weathering. Erosion is the carrying of a particle from one place to the other and weathering is the breaking down of particles. These processes help in rock formation because this allows physical changes (grouping together or breaking down) on a certain substance. Subsurface events are those which happened underground such as the flow of underground water which subsequently allow the deposition of minerals, etc.

3 0

3 years ago

The brain mass of a human fetus during a particular trimester can be accurately estimated from the circumference of the head by

Paladinen [302]

Answer:

a. If c = 20 cm, then the mass of the brain is m = 5 g.

b. At c = 20 cm, the brain's mass is increasing at a rate of 15.75 g/cm.

Explanation:

From the equation

$m\left(c\right) = \frac{c^3}{100}-\frac{1500}{c}$

we have

a. for c = 20 cm

$m\left(20\right)=\frac{20^3}{100}-\frac{1500}{20}=5,$

then the mass is m(20) = 5 g.

b. In order to find the rate of change, first we derivate

$\frac{dm}{dc}=\frac{3c^2}{100}+\frac{1500}{c^2}.$

Evaluated at c = 20 cm, we have

$\frac{dm}{dc}|_{c=20}=\frac{3\times 20^2}{100}+\frac{1500}{20^2}=15.75.$

So, at c = 20 cm, the mass of the brain is increasing at a rate of 15.75 g/cm.

3 0

3 years ago

Situations in which it is difficult for an individual to decide, either because the right course of action is not clear or becau

galina1969 [7]

Answer:

ethical dilemmas or ethical paradox

Explanation:

Ethical dilemmas or ethical paradox or moral dilemma is a situation in which a difficult choice has to be made between two or more courses of action, either because the right course of action is not clear or because the right course of action carries some negative consequences. one example is selling a bad product so as not to loose your cost.

6 0

3 years ago

In a game of basketball, a forward makes a bounce pass to the center. The ball is thrown with an initial speed of 4.8 m/s at an

tensa zangetsu [6.8K]

The equation to be used here is the trajectory of a projectile as written below:

y = xtanθ +/- gx²/2v²(cosθ)²
where
y is the vertical distance
x is the horizontal distance
θ is the angle of trajectory or launch angle
g is 9.81 m/s²
v is the initial velcity

Since the angle is below horizontal, let's use the minus equation. Substituting the values:

- 0.8 m = xtan15° - (9.81 m/s²)x²/2(4.8 m/s)²(cos15°)²
Solving for x,
x = 2.549 m

However, we only take half of this distance because it was specified that the distance asked before bouncing. Hence, the horizontal distance is equal to 1.27 m.

5 0

3 years ago