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3 years ago

After heating up in a teapot, a cup of hot water is poured at a temperature of

Mathematics

1 answer:

xxTIMURxx [149]3 years ago

3 0

Answer:

k ≈ 0.060
T(4) ≈ 178 °F

Step-by-step explanation:

The desired formula parameters for Newton's Law of Cooling can be found from the given data. Then the completed formula can be used to find the temperature at the specified time.

<h3>Given:</h3>

$T(t)=T_a+(T_0-T_a)e^{-kt}\\\\T_a=68,\ T_0=208,\ (t,T)=(3,185)$

T(4)

<h3>Solution:</h3>

Filling in the given numbers, we have ...

185 = 68 +(208 -68)e^(-k·3)

117/140 = e^(-3k) . . . . . subtract 68, divide by 140

ln(117/140) = -3k . . . . . . take natural logarithms

k = ln(117/140)/-3 ≈ 0.060

The temperature after 4 minutes is about ...

T(4) = 68 +140e^(-0.060·4) ≈ 68 +140·0.787186

T(4) ≈ 178.205

After 4 minutes, the final temperature is about 178 °F.

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Si camilo tiene 6 años mas que juan, juan tiene 7 años menos que andrés y andrés tiene 35 años

lidiya [134]

Answer:

Part a) Camilo is 34 years old and Juan is 28 years old

Part b) The difference between Camilo's age and Juan's age is 6 years

Part c) The sum of the ages of Camilo and Juan not coincide with the age of Andres' grandmother

Step-by-step explanation:

<u><em> The question in English is</em></u>

If Camilo is 6 years older than Juan, Juan is 7 years younger than Andrés and Andrés is 35 years old .

Part a) How old is Camilo and how old is Juan? raises the equation.

Part b) What's the difference between Camilo's age and Juan's age?

Part c) If Andres's grandmother is 65 years old, does the sum of the ages of Camilo and Juan coincide with the age of Andres' grandmother?

Part a) How old is Camilo and how old is Juan? raises the equation.

Let

x -----> Camilo's age

y -----> Juan's age

z -----> Andres's age

we know that

$x=y+6$ -----> equation A

$y=z-7$ -----> equation B

$z=35$ -----> equation C

<em>Find the value of y</em>

substitute the value of z in the equation B

$y=35-7=28$

<em>Find the value of x</em>

substitute the value of y in the equation A

$x=28+6=34$

therefore

Camilo is 34 years old and Juan is 28 years old

Part b) What's the difference between Camilo's age and Juan's age?

Subtract Juan's age from Camilo's age

$x-y=34-28=6\ years$

Part c) If Andres's grandmother is 65 years old, does the sum of the ages of Camilo and Juan coincide with the age of Andres' grandmother?

Adds Camilo's age and Juan's age

$x+y=34+28=62\ years$

$62\ years\neq 65\ years$

therefore

The sum of the ages of Camilo and Juan not coincide with the age of Andres' grandmother

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3 years ago

Below is the graph of y=b^x. Find b.

omeli [17]

Y = <span>b^x

when x = 1
y = b^1
y = b

Therefore, the value of b is the same as the value of y when x =1
From the graph,
When x = 1, y = 0.5
Therefore, b = 0.5

To confirm this

From the graph,

When x = -1, y = 2
Since </span>y = b^x<span>
2 = </span>b^-1
2 = 1/b
2b = 1
b = 0.5

When x = -2, y = 4
Since y = b^x
4 = b^-2
4 = 1/(b^2)
b^2 = 1/4
b = √(1/4)
b = 1/2
b = 0.5

Therefore, it is conformed that b = 0.5

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3 years ago

Read 2 more answers

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bezimeni [28]

Answer:

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Step-by-step explanation:

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