A low-velocity flow over a smooth stream bed produces a

A cake is removed from a 375°F oven and placed on a cooling rack in a 63°F room. After 30 minutes the cake is 175°F. When will i

marysya [2.9K]

Answer:

The cake will be at temperature 150°F at after 37.34 minutes

Explanation:

Let T be the temperature of the cake at any time

T∞ be the temperature around the cooling rack = 63°F

T₀ be the initial temperature of the cake = 375°F

And m, c, h are all constants from the cooling law relation

From Newton's law of cooling

Rate of Heat loss by the cake = Rate of Heat gain by the environment

- mc (d/dt)(T - T∞) = h (T - T∞)

(d/dt) (T - T∞) = dT/dt (Because T∞ is a constant)

dT/dt = (-h/mc) (T - T∞)

Let (h/mc) be k

dT/(T - T∞) = -kdt

Integrating the left hand side from T₀ to T and the right hand side from 0 to t

In [(T - T∞)/(T₀ - T∞)] = -kt

(T - T∞)/(T₀ - T∞) = e⁻ᵏᵗ

(T - T∞) = (T₀ - T∞)e⁻ᵏᵗ

Inserting the known variables

(T - 63) = (375 - 63)e⁻ᵏᵗ

(T - 63) = 312 e⁻ᵏᵗ

At 30 minutes, T = 175°F

175 - 63 = 312 e⁻ᵏᵗ

112/312 = e⁻ᵏᵗ

- kt = In (112/312) = In (0.3590)

- 30k = - 1.025

k = 1.025/30 = 0.0342 /min

When the temp is 150°F,

(T - T∞) = (T₀ - T∞)e⁻ᵏᵗ

(150 - 63) = 312 e⁻ᵏᵗ

e⁻ᵏᵗ = (87/312) = 0.2788

- kt = In 0.2788 = - 1.277

t = 1.277/k = 1.277/0.0342 = 37.34 min.

7 0

4 years ago

How big is the universe I get it only God knows because he created all of it meaning everything.That is real.

deff fn [24]

god is mighty not only did he create the universe but also everything in it

but here's the answer 93 billion light years

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3 years ago

A car travels 30.25 kilometers due west and then drives 7.50 kilometers up a hill that inclines 15.0 degrees. What is the vertic

Naddik [55]

B we use soh sin15.0=o/7.50=1.91

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4 years ago

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Which of the following models shows how unpredictable electrons are?

Fantom [35]

D

The exact location of electrons in electron shells of atoms cannot be exactly ascertained. This is why VSPER atomic models represent the position of electrons (s, p, d, & f) using the probability of where they would most be expected to be found.

Explanation:

This is because merely observing electrons changes their behavior. Remember that to observe something one has to shine light on it so it bounces back to the eye. Due to the negligible mass of electrons, mere photons of light will change their direction of movement, spin or other behaviors/properties.

Learn More:

For more on electron clouds check out;

brainly.com/question/12199882

brainly.com/question/11686000

#LearnWithBrainly

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3 years ago

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Calculate the average speed and average velocity of a complete round-trip in which the outgoing 250 km is covered at 95 km/h fol

ser-zykov [4K]

To solve this problem we will apply the concepts related to the kinematic equations of linear motion. From them we will consider speed as the distance traveled per unit of time. Said unit of time will be cleared to find the total time taken to travel the given distance. Later with the calculated average times and distances, we will obtain the average speed.

PART A)

The time taken to travel a distance of 250km with a speed of 95km/h is

$t = \frac{d}{v}$