A solid object is dropped into a pond with a temperature of 20 degrees Celsius. The function f(t) = Ce(-kt) + 20 represents the situation where t is time in minuetes, C is a constant and k = 0.0399. After 4 minutes the object has a temperature of 35 degrees Celsius. What was the initial temperature of the object

Answers

Answer 1

Given :

A solid object is dropped into a pond with a temperature of 20 degrees Celsius.

The function f(t) = Ce(-kt) + 20 represents the situation where t is time in minutes, C is a constant and k = 0.0399.

To Find :

The initial temperature of the object.

Solution :

Putting t = 4 in given equation, we get :

[tex]35 = Ce^{(-0.0399)\times 4)}+20\\\\15 = Ce^{-0.16}\\\\C = 15\times e^{0.16}\\\\C = 17.60[/tex]

Putting value of C in given equation, we get :

[tex]f(t) = 17.60e^{-0.0399t} + 20[/tex]

Now, for initial temperature is given at t=0 s .

[tex]f(t) = 17.60e^{-0.0399\times 0} + 20\\\\f(t) = 37.60^o\ C[/tex]

Therefore, the initial temperature of the object is 37.60° C.

Hence, this is the required solution.


Related Questions

Which is the equation of a line that has a slope of 4 and passes through point (2,5)?

y= 4x-2
y= 4x+6
y=4x+2
y=4x-3

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Answer:

y = 4x - 3

Step-by-step explanation:

I graphed all of them and this was the only equation that had a slope of 4 and passes through point (2,5)

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Answer:

0.1 > 10^-2

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Answer:

3,266.53

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How do I find the missing sides in the triangle?

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Answer:

x=14   y=10

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Step-by-step explanation:

3/4 x 11/11 = 44

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If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

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Answer:

What's the question you have

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Answer:

what are the questions on it say

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What is x in 7-onethirdx =11

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Answer:

[tex]\frac{-1}{3} x = 11-7\\\\\frac{-1}{3} x = 4\\\\-1x = 4*3\\-1x = 12\\\\x = -12[/tex]

apesapesapesapesapesapesapesapesapesapesapesapesapesapes

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Answer:

can you be more specific with your question?

Step-by-step explanation:

As what I understood your question to be

(a-t)^2 -(t + a)

when a is 8, and t is 3

(8-3)^2 - (8+3)

(5)^2- (11)

25- 11

= 14

Solve.

m - 15 = 20

m =

Answers

[tex]\text{Hello There!}[/tex]

[tex]\text{We are going to need to isolate the variable}[/tex]

[tex]m - 15 = 20[/tex]

[tex]\text{Add 15 to both sides.}[/tex]

[tex]\text{We do this because we need to perform inverse operations to find}[/tex] [tex]\text{the value of the variable.}[/tex]

[tex]m - 15 + 15 = 20 + 15 = 35[/tex]

[tex]\fbox{Therefore, your answer is going to be 35.}[/tex]

[tex]\rule{300}{1.5}[/tex]

Answer:

35 i guest

Step-by-step explanation:

idk ?????????

b. The total cost (1) after 8% sales tax is added to an item's price (p): 1.08p =
=f
Is there a proportional relationship

Answers

Answer:

No

Step-by-step explanation:

Yes, there is a proportional relationship between the total cost (f) after 8% sales tax is added and the item's price (p).

Here,

In this case, the total cost (f) is calculated by multiplying the item's price (p) by 1.08 (which is 100% + 8% sales tax in decimal form).

Mathematically, this can be represented as:

f = 1.08p

The equation shows that the total cost (f) is directly proportional to the item's price (p) with a proportionality constant of 1.08.

This means that as the item's price (p) increases, the total cost (f) will also increase proportionally by 8% due to the added sales tax.

Similarly, if the item's price (p) decreases, the total cost (f) will also decrease proportionally by 8%.

This relationship holds true for all values of p and f as long as the sales tax rate remains constant at 8%.

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please help i am desperate.

Answers

Answer:

3y +9 = perimeter

Step-by-step explanation:

Answer:

4y+9

Step-by-step explanation:

To find the perimeter , you have to add up all the 4 sides

so y + y+2 + y+4 + y+3 = 4y+ 9

hope it helps

could use some help.
35−x=8
Two-Step Equations and Properties of Equality

Answers

Answer:x=27

Step-by-step explanation:

First rearrange the terms: x+35=8

Second subtract 35 from either side:

-x=-27

Third divide both sides of the equation by the same term:

-x/1=-27/1

Fifth simplify:

X=27

Hope this helps!

what is the sum of all positive integer cubes that are less than 100

Answers

Step-by-step explanation:

2^3=8

3^3=27

4^3=64

so if you add all the positive integer cubes it will be 8+27+64=99

hence 99 is less than 100

Hence solved.

4) -4x - 10.2
I need the answer to this question asap please.


Answers

Answer: -2.55

Explanation: First add 10.2, and then the equation becomes -4x = 10.2.

Then, you just divide by -4 from both sides of the equation, and you get x = -2.55. :]

Answer:

21 - 4x

Step-by-step explanation:

Multiply 10 and 2 to get 20.

41 - 4x - 20

Subtract 20 from 41 to get 21.

21 - 4x

Camila Cabello wants to order cheesecakes over the internet. Each cheesecake costs $15.99 and shipping for the entire order is
$9.99. Camila has no more than $100 to spend. Choose the statement that best describes how many she can purchase.
She can purchase no more than 6 cheesecakes.
She can purchase no more than 5 cheesecakes.
She can purchase 6 cheesecakes.
She can purchase 5 cheesecakes.
She can purchase about 5.6 cheesecakes.
She can purchase at least 6 cheesecakes.
She can purchase at least 5 cheesecakes.

Answers

Answer:

she can purchase 5 cheesecakes

Step-by-step explanation:

15.99*5=79.95

if we add 9.99 for the shipping of thw whole order

79.95+9.99=89.94

Two forces of 17.3 pounds and 42.5 pounds act on a body with an angle of 21.9 degrees between them. The force of 42.5 pounds acts on the body in the horizontal direction. Choose the correct approximation for the direction angle the resultant vector makes with the horizontal force.
a. 6.3
b. 21.9
c. 15.7
d. 10.9

Answers

The resultant vector makes a 6.3-degree angle with the horizontal force, the correct option is A.

What is the formula for determination of angle of the resultant vector ?

The resultant angle between the vectors is given by

[tex]\rm \theta = tan^{-1} \dfrac{B sin\theta}{A +B cos\theta}[/tex]

The two forces have magnitude of 17.3 and 42.5 pounds.

The angle of the resultant vector is

[tex]\rm \rm \theta = tan^{-1} \dfrac{17.3\; sin\; 21.9}{42.5 +17.3 cos\;21.9}[/tex]

[tex]\rm \theta = tan^{-1}[/tex] (6.453/58.55)

[tex]\rm \theta[/tex] = 6.2886 degree = 6.3 degree.

Therefore, the resultant vector makes a 6.3-degree angle with the horizontal force.

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Answer:

6.3 on edge

Step-by-step explanation:

A cyclist travels 12 km from home to the park.
She leaves home at 13:00 and arrives at the park at 13:30.
What is her average speed in km/h?

Answers

Answer:

Step-by-step explanation:

12 km to the park in 30 mins so multiply the 12 km by 2 to make a whole hour.

12*2= 24 km/h

Please help! I will give brainlist, if I can

Answers

It is B glad I could help!

your awnser is C

Step-by-step explanation:

cause you'll need to multiply 1.05 × 15 then divide by 100

A certain star is 2.4 x 102 light years from the Earth. One light year is about 5.9 x 1012 miles. How far
from the earth (in miles) is the star?
TL
miles from Farth

Answers

The distance of the earth from the star is; 1.416 x 10¹⁵ miles

What are exponents?

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

We are given that 1 light year ≈ 5.9 x  10¹² miles

so: the Coefficients for the problem are mathematically given a

Coefficients =2.4 x 5.9

Coefficients = 14.16

For Exponents;

Exponents=   10² x 10¹² = 10⁽²⁺¹²⁾

Exponents =10¹⁴

In conclusion, we put them together once again to produce a scientific notation;

14.16 x 10¹⁴

1.416 x 10¹⁵ miles

The distance of the earth from the star is; 1.416 x 10¹⁵ miles

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Find the value of the following expression

(2^8 5^-5 19^0) x [5^-2 over 2^3]^4 x 2^28 (5 points)

Write your answer in simplified form. Show all of your steps. (5 points)

Answers

Looks like the expression is

(2⁸ • 5⁻⁵ • 19⁰) • (5⁻² / 2³)⁴ • 2²⁸

First, any positive number raised to 0 is 1:

(2⁸ • 5⁻⁵ • 1) • (5⁻² / 2³)⁴ • 2²⁸

(2⁸ • 5⁻⁵) • (5⁻² / 2³)⁴ • 2²⁸

Exponents in a denominator can be rewritten as negative exponents in the numerator:

(2⁸ • 5⁻⁵) • (5⁻² • 2⁻³)⁴ • 2²⁸

Distribute the 4th power across the product 5⁻² • 2⁻³ :

(5⁻² • 2⁻³)⁴ = 5⁻⁸ • 2⁻¹²

so we have

(2⁸ • 5⁻⁵) • (5⁻⁸ • 2⁻¹²) • 2²⁸

Multiplication is associative, so we can ignore the parentheses. Combine factors with equal bases and simplify the exponents:

2⁸ • 5⁻⁵ • 5⁻⁸ • 2⁻¹² • 2²⁸

2⁸⁻¹²⁺²⁸ • 5⁻⁵⁻⁸

2²⁴ • 5⁻¹³

Rewrite the negative exponent as a positive one:

2²⁴ / 5¹³

PLEASE HELP ME! THANK YOU!!

Answers

It's obviously the second one

This is really hard can anyone help it's due in 20 minutes

Answers

Answer:

The answer would be B if right mark brainliest

Answer:

I believe it's A

Step-by-step explanation:

What is the domain of the function p(t)=-8t+100

Answers

Answer:

Step-by-step explanation:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{x|x∈R}

{xlx∈R} means -We write x ∈ X if x is an element of the set X and x /∈ X if x is not an element of X. If the definition of a “set” as a “collection” seems circular, that's because it is. ... then P ⊂ N, and N ⊂ R. The empty set ∅ and the whole set X are subsets of any ... We assign the starting point x1 to a subset in the following way: (a) x1 ∈ XX if.

What is 3÷4? Draw a diagram that explains how you know.

Answers

Answer:

3 divided by 4 is 0.75

Step-by-step explanation:

Answer:

Answer: 3 divided by 4 is 0.75 .

Step-by-step explanation:

4 ( y+2 ) = 2( y+4 )

Answers

Answer:

y=0

Step-by-step explanation:

8=8

What is the slope and y-intercept of the function:
y=9x

Answers

Answer:

slope= 9

y-intercept= 0

Step-by-step explanation:

Because 9 is in the m spot and bis 0

a² + b -c for a = 2 b = (-9) c = 4

Answers

Answer:

-9

Step-by-step explanation:

4+(-9)-4

4+(-13)

-9

Answer:

-9

4 + -9 - 4

4 + -9 + -4

4 + -13 = -9

David mixes 2 liters of lemon juice with 9 liters of water to make lemonade. Which ratio of liters of lemon juice to liters of water will make the same concentration of lemonade?
F: 3 : 10
G: 10 : 72
H: 14 : 63
J: 27 : 6​

Answers

Answer:

J

Step-by-step explanation:

Asapppp, plssss help meee :(

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D because the x coordinate 1 has multiple y’s

Monty buys hats in bulk to sell at his store. His cost for each hat is $17. He marks up the hats 45%. What is retail price per hat?

I need help!

Answers

Answer:

I think it's $24.65

Step-by-step explanation:

45% of $17 is $7.65.

17 + 7.65 = 24.65

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