Answer:
The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.
Step-by-step explanation:
dy/dt = y(1/t - k)
separating the variables, we have
dy/y = (1/t - k)dt
dy/y = dt/t - kdt
integrating both sides, we have
∫dy/y = ∫dt/t - ∫kdt
㏑y = ㏑t - kt + C
㏑y - ㏑t = -kt + C
㏑(y/t) = -kt + C
taking exponents of both sides, we have
[tex]\frac{y}{t} = e^{-kt + C} \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt} (A = e^{C})\\y = Ate^{-kt}[/tex]
when t = 1 hour, y = 15 grams. So,
[tex]y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}[/tex](1)
when t = 3 hours, y = 30 grams. So,
[tex]y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k}[/tex] (2)
dividing (2) by (1), we have
[tex]\frac{30}{15} = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}[/tex]
taking natural logarithm of both sides, we have
-2k = ㏑(2/3)
-2k = -0.4055
k = -0.4055/-2
k = 0.203
From (1)
[tex]A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36[/tex]
Substituting A and k into y, we have
[tex]y = 18.36te^{-0.203t}[/tex]
The maximum value of y is obtained when dy/dt = 0
dy/dt = y(1/t - k) = 0
y(1/t - k) = 0
Since y ≠ 0, (1/t - k) = 0.
So, 1/t = k
t = 1/k
So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours
[tex]y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g[/tex]
So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.
What is the value of the expression (14 ÷ 2) + 6 x 3 − 12?
please help
Answer:
13Steps:
(14 ÷ 2) + 6 x 3 − 12
7 + 6 x 3 - 12
7 + 18 - 12
25 - 12
13
For what values of x is the expression below defined?
Answer:
x > 0
Step-by-step explanation:
Given :-
√[3x²] ÷ √[4x ]And we need to find the value of x for which the expression is defined . The expression is ,
[tex]:\implies[/tex] √[3x²] ÷ √[4x]
As we can see that x is inside the squareroot. So for defining the expression the value of x should be Greater than 0 . As negative inside the squareroot will give rise to imaginary numbers.
Solution :-
[tex]:\implies[/tex] x > 0
In interval notation :-
[tex]:\implies\bf x \in ( 0 , \infty) [/tex]
Therefore x should be Greater than 0 .
A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the high-
quality version is 4.2 MB. Yesterday, there were 1110 downloads of the song, for a total download size of 4077 MB. How many
downloads of the high-quality version were there?
Number of high-quality version downloads: 0
Х
?
Answer:
100
Step-by-step explanation:
i gueesss sheeeesh dherh
Please help me (NO LINKS)
Answer:
[tex]0.25( \frac{1}{4} ) \\ 0.50( \frac{2}{4}) \\ 1.25(1 \frac{1}{4} )[/tex]
hope it's what u want
if f(x) = 5 + 4( x - 4)^2
then what is f(7)
Answer:
41
Step-by-step explanation:
f(7) = 5 + 4(7-4)²
= 5 + 4(3²)
= 5 + 4(9)
= 5 + 36
Answer:
f(7)=39
Step-by-step explanation:
f(7)=5+4((7)-4)^2
=5+4(3)^2
=5+4(9)
=5+36
=39
In an isosceles triangle, the base angles measure 65°. Which of the following expressions is a way to calculate the measure of the third angle?
Answer:
its A
Step-by-step explanation:
its A ️ ♀️ ️ ♂️ ️
x > -3 For each statement list three numbers that would make a solution to the inequality true.
Answer:
x = -2
x = -1
x = 0
Step-by-step explanation:
Find three numbers to the left of -3 on the number line
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
a)Solve for x:
y = 130 − 4x
b) What is the value of x when y = 120
Answer:
[tex]x = \frac{5}{2}[/tex]
Step-by-step explanation:
y = 130 - 4x
======================
120 = 130 - 4x
-10 = -4x
x = [tex]\frac{-10}{-4} =\frac{5}{2}[/tex]
what is the area of the triangle?
An equation represents a math expression of equality.
Group of answer choices
True or False
The volume of this sphere is 904.32 cubic inches. What is the surface area of this sphere?
Use a 3.14 and round your answer to the nearest hundredth.
Answer:
A = 4 pi R^2 V = 4/3 pi R^3
A / V = 3 / R
Also, R = (3 * V / 4 * pi)^1/3 = (3 * 904.32 / (4 * pi))^1/3 = 6 in
So A = 3 / 6 * V = 1/2 * 904.32 = 452.16 in^2
The surface area of the sphere is S = 452.39 inches²
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the volume of the sphere be V = 904.32 inches³
Let the surface area of the sphere be S
And , Volume of a Sphere = ( 4/3 ) πr³
In this case, we are given that the volume of the sphere is 904.32 cubic inches, so we can set up an equation:
904.32 = (4/3)πr³
Solving for r:
r³ = (3/4) x (904.32 / π)
r ≈ 6.0 inches (rounded to one decimal place)
Now that we know the radius, we can use the formula for the surface area of a sphere:
A = 4πr²
Plugging in the value of r:
A = 4 x 3.14 x 6.0²
A ≈ 452.39 inches² (rounded to two decimal places)
Hence , the surface area of the sphere is approximately 452.39 square inches.
To learn more about sphere click :
https://brainly.com/question/27933834
#SPJ2
6) WILL MAKE BRAINLIEST
write the slope-interception form of the equation of each line.
i will give Brainiest if your right
Answer:
J. 2*3*5^3
Step-by-step explanation:
What is the missing length?
6 mi
t
area =
60 mi2
Answer:
10 mi
Step-by-step explanation:
6mi x t = 60mi^2
this is basically
6 x t = 60
divide 6 to both sides
t = 10
3 2/5 es una fracción propia impropia o mixta
Answer:
es una fracción mixta
Step-by-step explanation:
3 2/5
prove sec^2x/tanx=secxcscx
Answer:
Is this even a questions?
Drag numbers to fill in the table to organize the information in this problem.
The average daily iron intake for 12-year-olds is 15.1 milligrams. Fernando typically consumes 11.8 milligrams of iron in his breakfast cereal and 3.6 milligrams of iron from a protein bar. If he eats a bowl of cereal and two protein bars today, how many milligrams over the average daily intake for iron will Fernando's intake be?
Answer:
3.9 milligrams more than the normal or whatever it said
Step-by-step explanation:
you multiply 3.6 by 2 and you get 7.2 then you add 11.8 to that 7.2 which give you 19, then subtract 15.1 from 19 which would give you 3.9 milligrams
Guys help me with this quick pls
Answer:
[tex]117 = 66 + \beta \\ \beta = 51[/tex]
Question and Answers below in photo!! Please answer! Will mark BRAINLIEST! ⬇⬇⬇⬇⬇⬇⬇
Please answer ALL questions in order for BRAINLIEST! NO links or else you will be reported and maybe even get banned.
-----------------------------------------------------------------------------------------------------------
Find the volume of the triangular prism:
-27yd^3
-72yd^3
-240yd^3
-360yd^3
Answer: 72
Step-by-step explanation:
[tex]V=\frac{1}{2}(3)(8)(6)=\boxed{72}[/tex]
HELP ME PLISSSS NO LINK I SWEAR IM SO MAD RN YOU KEEP TAKING POINTS FROM ME WITH THESE LINK STOP!!!!!!!!!!!!!!!!!!!!!!!!!!!!! JUST ANSWER THE DAMB QUESTION
50*36*2=3600
(48*14/2)2=672
Now time to add
3600+672=4272
4272 square inches
Find value of x for both
Answer:
19??????????????????
Which values are solutions to x<16?
Answer:
Option D.
x can take values from 15downwards. It can't be 16 because the expression clearly states that x is less than 16. So x can take value from any number below 16.
8,546.54 to nearest 1,000.00
Given the equation of the circle centered at the origin and passing through the point (0,-10)
Answer:
x^2 + y^2 = 100
Step-by-step explanation:
(i) Challenge: Thembi received 8% discount on an item which cost
R6 plus x cents. The price she paid was R6 minus x cents.
Determine the value of x.
Answer:
[tex]x = 0.25[/tex]
Step-by-step explanation:
Given
[tex]Cost\ Price = 6 + x[/tex]
[tex]Discount =8\%[/tex]
[tex]Amount\ Paid = R6 - x[/tex]
Required
Find x
First, we calculate the amount paid in terms of the cost price.
This is calculated using:
[tex]Amount\ Paid = Cost\ Price * (100\% - Discount)[/tex]
[tex]Amount\ Paid = (6 + x) * (100\% - 8\%)[/tex]
[tex]Amount\ Paid = (6 + x) * 92\%[/tex]
Express as decimal
[tex]Amount\ Paid = (6 + x) * 0.92[/tex]
Open bracket
[tex]Amount\ Paid = 5.52 + 0.92x[/tex]
So, we have:
[tex]Amount\ Paid = 5.52 + 0.92x[/tex] and
[tex]Amount\ Paid = R6 - x[/tex] ---- given
Equate both
[tex]6 - x = 5.52 + 0.92x[/tex]
Collect like terms
[tex]- x -0.92x= 5.52-6[/tex]
[tex]-1.92x= -0.48[/tex]
[tex]1.92x= 0.48[/tex]
Solve for x
[tex]x = \frac{0.48}{1.92}[/tex]
[tex]x = 0.25[/tex]
14. A cone has twice the base diameter and
three-fourths the height of a cylinder. Can
you tell what the relationship between the
volume of the cone and the volume of the
cylinder is? Explain your reasoning.
Answer:
1+1 is cannot be
Step-by-step explanation:
jajauajhwhahwwhhahwhauwu
If you use the amount of flour that was used on Day 4, how many
cups of flour will you use?
5. Zhao purchased a used car for $11,500. This make and model used car
straight line depreciates to zero after 9 years. (a) Identify the coordinates
of the x and y intercepts. *
Answer:
(9, 0)
(0, 11200)
Step-by-step explanation:
The x - intercept is the value of x when y = 0 ; similarly, the y - intercept is the value of y, when x = 0
From the given relation :
y = price, x = number of years
Price after 9 years of usage, the price of car is depreciated to 0
Hence,
x = 9, y = 0
(9, 0)
At purchase, the value of car is 11,200 ;
At this price, the number of years of usage of car is 0
Hence ;
x = 0 ; y = 11200
(0, 11200)
6x-9y+45 in slope intercept form
PLEASE HELP!!!!!!!!!!
Answer:
The line graph
Step-by-step explanation:
Why the line graph is more professional and simple to see and understand. And is the preferred graph for numbers, unlike the box graphs its preferred for comparing.
Answer: the second one
Step-by-step explanation:
the second one is easier to read and understand how many people attended. For me, it is clearer to figure out and shows the difference better.
sorry if this is the wrong answer but this is what I would have put if this was my question.