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.
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
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)
Answer: D
Step-by-step explanation:
help me thanks . please
Answer:
0.1 > 10^-2
(I'm pretty sure I'm right. sorry if im wrong :(
Divide. Round your answer to the nearest tenth.
39,527 = 7
HELPPP MEEEE
Answer:
3,266.53
Rounded to the nearest 0.01 or
the Hundredths Place.
Step-by-step explanation:
How do I find the missing sides in the triangle?
Answer:
x=14 y=10
Step-by-step explanation:
Please help me with this
Step-by-step explanation:
3/4 x 11/11 = 44
7/12 x 5/5 = 35/60
18/72 = 6/6 x 3/12
Topic: Fractions
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
I need the answers by midnight helppp
Answer:
What's the question you have
Step-by-step explanation:
Answer:
what are the questions on it say
Step-by-step explanation:
What is x in 7-onethirdx =11
Answer:
[tex]\frac{-1}{3} x = 11-7\\\\\frac{-1}{3} x = 4\\\\-1x = 4*3\\-1x = 12\\\\x = -12[/tex]
apesapesapesapesapesapesapesapesapesapesapesapesapesapes
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 =
[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
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.
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
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
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.
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.
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
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.
To know more about Resultant vector angle
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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?
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
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
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
Learn more about exponentiation here:
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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)
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!!
This is really hard can anyone help it's due in 20 minutes
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
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.
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 )
Answer:
y=0
Step-by-step explanation:
8=8
What is the slope and y-intercept of the function:
y=9x
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
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
Answer:
J
Step-by-step explanation:
Asapppp, plssss help meee :(
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!
Answer:
I think it's $24.65
Step-by-step explanation:
45% of $17 is $7.65.
17 + 7.65 = 24.65