Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 185 degrees Fahrenheit when freshly poured, and 3 minutes later has cooled to 167 degrees in a room at 60 degrees, determine when the coffee reaches a temperature of 137 degrees.
Answer:
9.4 secs
Step-by-step explanation:
From Newton's law of cooling;
T(t) = Ts + Do e^-kt
Where;
D0= initial temperature difference
Ts= Temperature of the surroundings
t= time
K = positive constant
Do = 185 - 60 = 125 degrees
167 = 60 + 125 e^-3k
167 - 60 = 125 e^-3k
107/125 = e^-3k
ln(e^-3k) = ln(107/125)
-3k = -0.1555
k = 0.1555/3
k = 0.0518
Substituting the value of k to find the time taken to reach 137 degrees
T(t) = Ts + Do e^-kt
137 = 60 + 125 e^-(0.0518t)
137 - 60 = 125 e^-(0.0518t)
77 = 125 e^-(0.0518t)
e^-(0.0518t)= 77/125
ln [e^-(0.0518t)] = ln(77/125)
-0.0518t = -0.4845
t = 0.4845/0.0518
t = 9.4 secs
x + 7 = 9
What does X equal?
The half-life of krypton-91 (91Kr) is 10 s. At time t = 0 a heavy canister contains 3 g of this radioactive gas. Find a function m(t) = m02−t/h that models the amount of 91Kr remaining in the canister after t seconds.
9) Linda and Maria share £200. Linda has 4 times as much money as Maria.
How much money does Maria have?
Answer:
40
Step-by-step explanation:
maria is x
linda is 4x
x+ 4x = 200
5x = 200
x= 40
What is (f o g) (3) if f (x) =3x-1 and g(x) = 4x^2 -9?
Answer:
4x+1
Step-by-step explanation:
PLEASE HELP ONE QUESTION THATS IT
Answer:
-3,2 -2,4 1,-1
Step-by-step explanation:
What is the leading coefficient of the polynomial f(x) defined below
Answer:
1
Step-by-step explanation:
The answer is simply 1 as the leading term, x^4 has a coefficient of 1.
-2x - 6 = 2 - 4x - (x - 1)
solve
Answer:
Step-by-step explanation:
-2x - 6 = 2 - 4x - x + 1
-2x - 6 = 3 - 5x
3x - 6 = 3
3x = 9
x = 3
Complete the statement to illustrate the commutative property. (PLEASE ANSWER FAST FOR BRAINLIEST!!!)
10 + (9 + 11) = 10 + (11 + ___ )
a. 11
b. 20
c. 9
d. 10
Answer:
9
Step-by-step explanation:
PLEASE HELP MEEEEEE
f(x)=4x + 5
f (-3)
Answer:
evaluate the function with -3 as x value
Step-by-step explanation:
4(-3) + 5
-12 + 5
= -7
Answer:
The answer is -7
Step-by-step explanation:
Use the given functions to set up and simplify f ( − 3 ) .
Hoped this helped!
brainly, please?
Can someone help with this problem (time sensitive)
Answer:
∠D = 52º
∠E = 32º
∠F = 96º
Step-by-step explanation:
the sum of interior angles of a triangle equals 180º
so: (x + 20) + (3x) + 32 = 180
3x + x + 20 + 32 = 180 combine like terms
4x + 52 = 180 subtract 52 from both sides
4x = 128 divide both sides by 4
x = 32
plug x into each angle measure to get them:
∠D = (32) + 20 = 52º
∠E = 32º (given)
∠F = 3(32) = 96º
si Luis ocupa una butaca de tren absorto
. luis está quiero o avanza
Answer:
quiero
Step-by-step explanation:
Combine like terms. Your answer should contain decimals.
0.5(x4-5)+12
4 is a power
Answer:
0.5x⁴ - 9.5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
0.5(x⁴ - 5) + 12
Step 2: Simplify
Distribute 0.5: 0.5x⁴ - 2.5 + 12Combine like terms: 0.5x⁴ - 9.5graph the function. Then State the domain and range. Also increasing and decreasing
Answer:
See below, I will let graphing part to yourself.
Step-by-step explanation:
First function: domain: [tex][-9,\infty)[/tex], range: [tex](-\infty, -2][/tex], decreasing
Second function: domain: [tex](-\infty, \infty)[/tex], range: [tex](-\infty, \infty)[/tex], increasing
Third function: domain: [tex][3, \infty)[/tex], range: [tex][-5,\infty)[/tex], increasing
Answer:
First function: domain: [-9,\infty)[−9,∞) , range: (-\infty, -2](−∞,−2] , decreasing
Second function: domain: (-\infty, \infty)(−∞,∞) , range: (-\infty, \infty)(−∞,∞) , increasing
Third function: domain: [3, \infty)[3,∞) , range: [-5,\infty)[−5,∞) , increasing
alguien me ordena estás fracciones 1/10 4/10 6/10 14/10 10/10 8/10 de menor a mayor porfa doy corona
Responder:
[tex]\frac{1}{10},\frac{4}{10},\frac{6}{10},\frac{8}{10},\frac{10}{10},\frac{14}{10}[/tex]
Explicación paso a paso:
Dado que los denominadores son iguales, organice los numeradores.
Answer:
[tex]\frac{1}{10} ,\frac{4}{10}, \frac{6}{10}, \frac{8}{10}, \frac{10}{10}, \frac{14}{10}[/tex]
¡Espero que ayude!
Lo siento si es mal español. No soy un hablante nativo. :P
Step-by-step explanation:
what is 6/5÷7/1 can u tell me pls
Answer:
6/35
Step-by-step explanation:
6/5÷7/1=6/5 x 1/7 = 6/35
Answer:
6/35
Step-by-step explanation:
In the diagram below of parallelogram ROCK, m angle is 70 degrees and m angle ROS is 65 what is the value of x
Answer:
135
Step-by-step explanation:
The measure of the angle KSO is 135°
What is a parallelogram?A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
Given that, In the diagram below of parallelogram ROCK, m angle is 70 degrees and m angle ROS is 65
We know that, opposite angles of a parallelogram are equal,
Therefore, ∠ ORK = 70°
In triangle, SRO, ∠ ORK and ∠ ROS are interior angles, and ∠ KSO is an exterior angle,
We know, The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
Therefore, ∠ KSO = ∠ ORK + ∠ ROS
∠ KSO = 135°
Hence, The measure of the angle KSO is 135°
For more references on parallelogram, click;
https://brainly.com/question/29147156
#SPJ2
Find the equation of the exponential function represented by the table below:
Answer:
[tex]f(x)=5(4)^x[/tex]
Step-by-step explanation:
The exponential function is [tex]f(x)=ab^x[/tex]. [tex]a[/tex] is the initial value of the function, or the y-value when x=0. In this case, [tex]a[/tex]=5. If we enter that into the equation:
[tex]f(x)=5b^x[/tex]
Then we can use another point to solve for [tex]b[/tex].
[tex]20=5b^1[/tex]
Since anything raised to the power of 1 remains the same, we can continue to solve algebraically.
[tex]20=5b\\\frac{20}{5}=\frac{5b}{5}\\b=4[/tex]
Now that we have both the [tex]a[/tex] and [tex]b[/tex] value, we can return to the exponential function and fill in the blanks.
[tex]f(x)=5(4)^x[/tex]
I hope this helps!
13/5 ÷ 4/5 = ??????????
I need help fast I’ll really appreciate it.
Answer:
11 : 8
Step-by-step explanation:
3 + 8 = 11
Answer:
11:8
Step-by-step explanation:
I think i may be wrong I hope this is right
4
Write an exponential decay
equation with a rate of 25% and
an initial value of 6.
Suppose y varies directly as x. If x = 24 when y = 8, then what is the constant of variation
Direct variation is represented by the formula [tex]\frac{y}{x} = k[/tex]
where k is the constant of variation.
So here, since we know that x = 24 and y = 8,
the constant of variation must be equal to 8/24.
if we write 8/24 in lowest terms, we have 1/3.
So 1/3 = k.
Eva is going to the amusement park, where she has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money Eva will spend is given by the equation y=26+1.5x. , where y represents the total amount of money, in dollars and cents, and represents the number of rides Eva goes on . What could the number 1.5 represent in the equation ?
Answer:
B. The change in the total amount if money for every one additional ride she goes on
Step-by-step explanation:
Given,
y = 26 + 1.5x, where,
y = total amount of money Eva will spend
x = number of rides Eva rides on
Thus,
Set price of admission into the amusement park = $26
Price per ride = $1.5
Therefore, the 1.5 I'm the equation can be said to be "the change in the total amount if money for every one additional ride she goes on".
Drag steps in the given order to evaluate this expression,
-3(-3+2) - 6
Answer:-3
Step-by-step explanation:
Maria needs $2.35 to buy a magazine. The only money she has is a jar of nickels and dimes. Write an equation in standard form for the different amounts of nickels and dimes she could use.
Answer:
Step-by-step explanation:
sorry need the points
0.2 =% yssssssssssssssssssssssssssssssssssssssssss
Answer:
20%
Step-by-step explanation:
If it was 0.3 it would be 30% or if it was .35 it would be 35%.
0.3 is another way of writing 0.30 but since it's just a zero, you don't really have to write 30.
Answer:
Good luck your so lucky
Step-by-step explanation:
PLEASE HELP!!
Questions and directions are in image!
Step-by-step explanation:
this is what I use go to your app store and get Math. way and type your answer in
Answer:
a) (c + 2)²
b) (x + 2)(x - 4)
c) (g + 2)(g + 6)
d) (x + 2)(x - 9)
e) (r + 9)(r + 1)
f) (x - 6)(x - 4)
Step-by-step explanation:
The model below is shaded to represent 9/10
Answer:
0.9
Step-by-step explanation:
Solve the linear equation 3+5x=3
Step-by-step explanation:
the answer is
3+5x=3
5x=0
x=0
early says that m ×(-1) is always equal to m ÷(-1) for all rational values of m. is he correct
Answer:
The equation are true.
Step-by-step explanation:
Given
[tex]m * (-1) = m / (-1)[/tex]
Required
True or false?
We solve this question from right to left:
[tex]m * (-1) = m / (-1)[/tex]
Express / as *
[tex]m * (-1) = m * 1/(-1)[/tex]
[tex]m * (-1) = m * (-1)[/tex]
The expression on both sides of the equation are true.