Can you solve E=MC2?

An object is taken from an oven at 350o F and left to cool in a room at 70o F. If the temperature fell to 250o F in one hour, wh

Oksana_A [137]

Answer:

117.83° F

Explanation:

Using Newton's Law of Cooling which can be expressed as:

$\dfrac{dT}{dt}= k(T-T_1)$

The differential equation can be computed as:

$\dfrac{dT}{dt}= k(T-70)$

$\dfrac{dT}{(T-70)}= kdt$

$\int \dfrac{dT}{(T-70)}= \int kdt$

$In|T-70| = kt +C$

$T- 70 = e^{kt+C} \\ \\ T = 70+e^{kt+C} \\ \\ T = 70 + C_1e^{kt} --- (1)$

where;

$C_1 = e^C$

At the initial condition, T(0)= 350

$350 = 70 C_1^{k*0}$

$350 -70 = C_1$

$280 = C_1$

replacing $C_1$ = 280 into (1)

Hence, the differential equation becomes:

$T(t) = 70 + 280 e^{kt}$

when;

time (t) = 1 hour

T(1) = 250

Since;

$250 = 70 + 280 e^{k*1}$

$180 = 280e^k \\ \\ \dfrac{180}{280}= e^k$

$k = In (\dfrac{180}{280})$

k = -0.4418

Therefore;

T(t) = 70 + 280e^{(-0.4418)}t

After 4 hours, the temperature is:

T(t) = 70 + 280e^{(-0.4418)}4

T(4) = 117.83° F

7 0

3 years ago

A flash of red light and a flash of blue light enter a glass cube perpendicular to its surface at the same time. after passing t

Wewaii [24]

A flash of red light and a flash of blue light enter a glass cube perpendicular to its surface at the same time. after passing through the block, the red light pulse exits first.

For any medium, other than vacuum, the index of refraction for red light is slightly lower (closer to 1 ) than that for blue light. This means that when light goes from vacuum (or air) into glass, the red light deviates from its original direction less than does the blue light. Also, as the light reemerges from the glass into vacuum (or air), the red light again deviates less than the blue light. If the two surfaces of the glass are parallel to each other, the red and blue rays will emerge traveling parallel to each other, but displaced laterally from one another.

what is refractive index?

The ratio between the speed of light in medium to speed in a vacuum is the refractive index. When light travels in a medium other than the vacuum, the atoms of that medium continually absorb and re-emit the particles of light, slowing down the speed light.

learn more about refractive index from here: brainly.com/question/28203787

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7 0

2 years ago

The gyri and sulci on the brain greatly increase the brain’s surface area. How do you think this increase in surface area relate

MrRa [10]

Answer:

Increase in surface area leads to more chances for connections between neurons hence more possible learning

Explanation:

The brain appears wrinkled due to the presence of gyri and sulci. Sulci are the grooves in the brain while gyri are the folds. The two major functions of gyri and sulci are to lead to formation of brain divisions and increase the surface area of cerebral cortex. The formation of brain divisions is done by creating boundaries between the brain lobes thereby leading to division of the brain into two hemispheres. Moreover, by increasing the surface area of the brain, the cortex processes more information since more neurons are formed.

8 0

4 years ago

Does pressure change faster as you move horizontally or vertically? explain reasoning

ANTONII [103]

Answer:

Vertically

Explanation:

Pressure changes faster as we move vertically because as we go to the height from the surface of the earth. The density of air becomes lesser in comparison with the surface of the earth. So, as we move vertically pressure moves faster than in comparison with the vertical movement.

The best example that describes the above statement is the hill station.

3 0

3 years ago

How big is this restoring force compared with the tensile force stretching the spring?

madam [21]

The restoring force on the spring is found to have exactly the same magnitude as the stretching force. Option D

<h3>What is the restoring force?</h3>

The restoring force is the force that seeks to restore the spring to its equilibrium position. It has the same magnitude as the stretching force but acts in opposite direction.

Thus, the restoring force on the spring is found to have exactly the same magnitude as the stretching force.

Learn more about restoring force:brainly.com/question/12162527

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4 0

2 years ago