You swing a 2.2 kg stone in a circle with radius 75 cm. At what speed do you need to swing it so its

Which of the following would illustrate a quadratic relation between the dependent and independent variables when graphed?

Kitty [74]

Answer: option A. a graph of the area of a circle vs. its radius r (A = πr²).

Explanation:

A quadratic relation between the dependent and independent variables shows the independent variable raised to the power of 2.

This is it is a polynomial with general form ax² + bx + c, whewre a, b, and c, named coeficients, are constants.

The function is y = ax² + bx + c, where x is the independent variable and y is the dependent variable.

As stated in the question, the area of a circle is given by A = πr².

In this case, A is the dependent variable and r is the independent variable.

π is assumed as the coefficient of the quadratic term, and the other coefficients are assumed 0, since there are no either terms on r or constants.

The equation a = 1/b is an inverse relation, not a quadratic relation.

The relation of distance vs. time for a car moving at constant speed is a linear relation of the kind v = u + st.

The mass of water vs. the volume of water in a drinking glass is a direct relation, mass = density × volume

Therefore, the only quadratic relation is shown by a graph of the area of a circle vs. its radius r.

3 0

2 years ago

You set your stationary bike on a high 80-N friction-like resistive force and cycle for 30 min at a speed of 8.0 m/s . Your body

stellarik [79]

A) The change in internal chemical energy is $1.15\cdot 10^7 J$

B) The time needed is 1 minute

Explanation:

First of all, we start by calculating the power output of you and the bike, given by:

$P=Fv$

where

F = 80 N is the force that must be applied in order to overcome friction and travel at constant speed

v = 8.0 m/s is the velocity

Substituting,

$P=(80)(8.0)=640 W$

The energy output is related to the power by the equation

$P=\frac{E}{t}$

where:

P = 640 W is the power output

E is the energy output

$t = 30 min \cdot 60 = 1800 s$ is the time elapsed

Solving for E,

$E=Pt=(640)(1800)=1.15\cdot 10^6 J$

Since the body is 10% efficient at converting chemical energy into mechanical work (which is the output energy), this means that the change in internal chemical energy is given by

$\Delta E = \frac{E}{0.10}=\frac{1.15\cdot 10^6}{0.10}=1.15\cdot 10^7 J$

B)

From the previous part, we found that in a time of

t = 30 min

the amount of internal chemical energy converted is

$E=1.15\cdot 10^7 J$

Here we want to find the time t' needed to convert an amount of chemical energy of

$E'=3.8\cdot 10^5 J$

So we can setup the following proportion:

$\frac{t}{E}=\frac{t'}{E'}$

And solving for t',

$t'=\frac{E't}{E}=\frac{(3.8\cdot 10^5)(30)}{1.15\cdot 10^7}=1 min$

Learn more about power and energy:

brainly.com/question/7956557

#LearnwithBrainly

3 0

3 years ago

Scientists suspect that modern horses have different dietary habits than horses that lived long ago. What is the most reliable s

Arte-miy333 [17]

Welllllllllll I thinkkkkkk the answer is B

6 0

3 years ago

Read 2 more answers

according to newton's second law of motion of the net force acting on the object increases while the mass of the object remains

Licemer1 [7]

Answer:

The Acceleration will increase

Explanation:

Newton's Second Law of motion: It states that the rate of change of momentum is directly proportional to the applied force and takes places along the direction of the force.

It can be expressed mathematically as,

F ∝ m(v-u)/t

Where (v-u)/t = a

F = kma.

F = force, m = mass of the body, a = acceleration, k = constant of proportionality which tend to unity for a unit force, a unit mass, and a unit acceleration.

Therefore,

F = ma.

From the equation above,

If the net force acting on a body increase, while the mass of the body remains constant, the acceleration will also increase.

4 0

3 years ago

What the planet after Venus

Aleonysh [2.5K]

Mercury and Venus are therefore closer to each other most of the time. But Earth is the planet closest to Venus. And that's why from here on Earth, Venus looks so big and luminous. Venus is the brightest thing in the night sky after the sun and the moon.

4 0

3 years ago

Read 2 more answers