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2 years ago

Distinguish between directly proportional and inversely proportional with an example of each

1 answer:

4 0

Consider two variables said to be "inversely proportional" to each other. If all other variables are held constant, the magnitude or absolute value of one inversely proportional variable decreases if the other variable increases, while their product (the constant of proportionality k) is always the same.

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A tortoise can move with a speed of 10.0cm/s, while a rabbit can move 10 times faster. In a race, both of them started at the sa

Xelga [282]

Answer:

C. 199.9 s

Explanation:

3 minutes = 3×60 = 180 seconds.

the turtle moves in that time 180×10 = 1800 cm.

in other words the rabbit gave it that much head-start (it does not matter if that was at the begin of in the middle of the race).

the rabbit moves with 10×10cm/s = 100cm/s.

the rabbit needs therefore 1800/100 = 18 seconds for the

1800 cm.

at that time the turtle has added another 18×10 = 180 cm.

for which the rabbit needs 180/100 = 1.8 seconds.

during that time the turtle has added 1.8×10 = 18 cm.

and so on.

in formal mathematics this looks like this :

1800 + 10x = 100x

after x seconds of the rabbit running both will have run the same distance, and it is a tie.

1800 = 90x

x = 20 seconds

so, at that point, the rabbit was actively running for 20 seconds and raced 20×100 = 2000 cm

and the turtle was actively running for 180 + 20 = 200 seconds, and also covered 200×10 = 2000 cm.

but our question tells us that the turtle won by 10 cm.

so, the race was over a little bit before these 200 seconds (for a tie).

this means, the rabbit could not run the last 10 cm for the tie (because the race was over and the turtle had won).

the rabbit would have needed 10/100 seconds for these 10 cm.

as speed = distance/time

we need to divide distance by speed

distance/1 / distance/time

to get time.

so,

10cm/1 / 100cm/s = 10s/100 = 1/10 s

so, we need to deduct this 1/10 s from the 200 seconds of the turtle (and also from the 20 seconds for the rabbit).

the race lasted of course the whole time the turtle was running (while the rabbit was resting, officially still participating in the race with speed 0 for 3 minutes).

and so, the race was 199.9 s long.

8 0

11 months ago

What is the magnitude of the electric field at the dot in the figure? (figure 1)

blondinia [14]

The magnitude of the electric field at the dot is : 10⁴ v/m

<h3>What is electric field?</h3>

Electric field is a region around a charged particle or object within which a force would be exerted on other charged particles or objects.

Given that there are three equipotential lines with equal spacing,we will apply the the relationship between P.D and electric field

Determine the magnitude of the electric field at the dot

change in voltage = E .d

$100 - 0 = E \times ( 1 \times 10^{-2}\ m ) ----- ( 1 )$

From equation ( 1 )

The magnitude of electric field will be given as

$E = \dfrac{100 }{ ( 1 \times 10^{-2})\ }$

$E = 10^4\ \ \frac {v}{ m}$

Hence we can conclude that The magnitude of the electric field at the dot is : 10⁴ v/m

Learn more about electric field :

brainly.com/question/14372859

#SPJ4

5 0

1 year ago

A 210-kg woorden raft floats on a lake. When a 75-kg man stands on the raft, it sinks 5.0 cm deeper into the water. When he step

GaryK [48]

Answer:

A: The frequency of the vibration is 1.3329 Hz

B: The total energy of the vibration is 18.39375 J

Explanation:

The force of the man his weight causes the raft to sink, and that causes the water to put a larger upward force on the raft. This extra force is a restoring force, because it is in the opposite direction of the force put on the raft by the man. Then when the man steps off, the restoring force pushes upward on the raft, and thus the raft – water system acts like a spring, with a spring constant found as follows:

k= F/x = ((75 kg) * (9.81 m/s²))/(5*10^-2 m) = 14715 N/m

The frequency of the vibration is determined by the spring constant (k) and the mass of the raft (210kg).

fn = 1/2π * √(k/m) = 1/2π * √(14715 / 210) = <u>1.3329 Hz</u>

<u>The frequency of the vibration is 1.3329 Hz</u>

<u />

Since the gravitational potential energy can be ignored, the total energy will be :

Etot = 1/2 k* A² = 1/2 * (14715 )*(0.05)² = 18.39375 J

<u>The total energy of the vibration is 18.39375 J</u>

7 0

2 years ago

What will happen to the speed of an object if the net force is in the direction of the motion?

nata0808 [166]

The speed increases

6 0

2 years ago

Read 2 more answers

Question 11 (1 point)

Ainat [17]

Answer:

gravitational potential energy.

Explanation:

Gravitational potential energy (GPE) can be defined as an energy possessed by an object or body due to its position above the earth surface.

Mathematically, gravitational potential energy is given by the formula;

$G.P.E = mgh$

Where,

G.P.E represents gravitational potential energy measured in Joules.

m represents the mass of an object.

g represents acceleration due to gravity measured in meters per seconds square.

h represents the height measured in meters.

This ultimately implies that, anytime there is height, the object must have gravitational potential energy.

Hence, an object possesses gravitational potential energy due to its height (position) and the earth's gravitational force.

8 0

1 year ago