Answer:
P is maximum at I = 2
Step-by-step explanation:
Here is the complete question
The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 100I/(I² + I + 4) where I is the light intensity (measured in thousands of foot candles). For what light intensity P is a maximum?
To find the value of I at which P is maximum, we differentiate P with respect to I and equate it to zero.
So, dP/dI = d[100I/(I² + I + 4)]/dI
= [(I² + I + 4)d(100I)/dI - 100Id(I² + I + 4)/dI]/(I² + I + 4)²
= [(I² + I + 4)100 - 100I(2I + 1)]/(I² + I + 4)²
= [100I² + 100I + 400 - 200I² - 100I]/(I² + I + 4)²
= [-100I² + 400]/(I² + I + 4)²
= -100[I² - 4]/(I² + I + 4)²
Since dP/dI = 0, -100[I² - 4]/(I² + I + 4)² = 0 ⇒ I² - 4 = 0 ⇒ I² = 4 ⇒ I = ±√4
I = ±2
Since I cannot be negative, we ignore the minus sign
To determine if this is a maximum point, we differentiate dP/dI. So,
d(dP/dI)/dI = d²P/dI² = d[-100[I² - 4]/(I² + I + 4)²]/dI
= [(I² + I + 4)²d(-100[I² - 4])/dI - (-100[I² - 4])d(I² + I + 4)²/dt]/[(I² + I + 4)²]²
= [(I² + I + 4)²(-200I) + 100[I² - 4]) × (2I + 1) × 2(I² + I + 4)]/(I² + I + 4)⁴
= [-200I(I² + I + 4)² + 200[I² - 4])(2I + 1)(I² + I + 4)]/(I² + I + 4)⁴
= [-200(I² + I + 4)[I(I² + I + 4) - [I² - 4])(2I + 1)]]/(I² + I + 4)⁴
= [-200(I² + I + 4)[I³ + I² + 4I - I² + 4])(2I + 1)]]/(I² + I + 4)⁴
= [-200(I² + I + 4)[I³ + 4I + 8])(2I + 1)]]/(I² + I + 4)⁴
Substituting I = 2 into d²P/dI², we have
= [-200(2² + 2 + 4)[2³ + 4(2) + 8])(2(2) + 1)]]/(2² + 2 + 4)⁴
= [-200(4 + 2 + 4)[8 + 8 + 8])(4 + 1)]]/(4 + 2 + 4)⁴
= [-200(10)[24](5)]]/(10)⁴
= -240000/10⁴
= -24
Since d²P/dI² = -24 < 0 at I = 2, this shows that it I = 2 is a maximum point.
So, P is maximum at I = 2
Due to employee safety negligence at a nuclear waste facility, 2000 tons of a radioactive element is spilled into the nearby pond. The half-life of the radioactive element is 36 days. In order to be declared safe for swimming, based on its size and the amount of water, there must be less than 100 tons of the material found in the pond. How long, to the nearest day, until it is safe to swim again?
How long, to the nearest day, until it is safe to swim again will be 156 days
Let x represent number of day until it is safe to swim again
First step
=2000 *1/2^x
100=2000 *0.5^x
0.05=0.5^x
Second step
Log 0.05=xLog 0.5
Log 0.05/L0g 0.5=x
x=36 days* Log 0.05/L0g 0.5
x=36 days*43.22
x=156 days
Inconclusion How long, to the nearest day, until it is safe to swim again will be 156 days
Learn more about radioactive element here:
https://brainly.com/question/13812761
An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions. The eastbound train travels 6 miles per hour faster than the westbound train. After 2 hours, they are 276 miles apart. At what speeds are the two trains traveling
Both? or just the westbound?
the range of the function y=secx-2 is all reals except
-1
1
-3
-2
Answer:
For a function y = f(x), the range is the set of all the possible values of y.
In the question you wrote:
y = secx - 2
This can be interpreted as:
y = sec(x - 2)
or
y = sec(x) - 2
So let's see each case (these are kinda the same)
If the function is:
y = sec(x - 2)
Firs remember that:
sec(x) = 1/cos(x)
then we can rewrite:
y = 1/cos(x - 2)
notice that the function cos(x) has the range -1 ≤ y ≤ 1
Then for the two extremes we have:
y = 1/1 = 1
y = 1/-1 = -1
Notice that for:
y = 1/cos(x - 2)
y can never be in the range -1 < x < 1
As the denominator cant be larger, in absolute value, than 1.
Then we can conclude that the range is all reals except the interval:
-1 < y < 1
If instead the function was:
y = sec(x) - 2
y = 1/cos(x) - 2
Then with the same reasoning, the range will be the set of all real values except:
-1 - 2 < y < 1 - 2
-3 < y < -1
Can anyone do this dont mind the 15x because i done it wrong
Please help i'm really struggling with this unit
A primary trigonometric ratio of an angle is given : tan = 2√5 / 5 . The terminal arm falls in quadrant 3. Find the other 2 primary trigonometric ratios in exact form (no decimals). Rationalize if necessary.
I WILL GIVE BRAINLIEST
Answer:
sin(theta)=-2/3 and cos(theta)=-sqrt(5)/3
Step-by-step explanation:
First of all, as the theta is in 3rd quadrant, all the other ratios will be negative. Second tan(theta)=P/B. So, 2=P and B=sqrt(5), H=sqrt(P^2+H^2)=sqrt(4+5)=3. sin(theta) will be P/H=-2/3 and cos(theta) will be B/H=-sqrt(5)/3
What is 7 3/8 rounded to the nearest whole number?
Answer:
7
Step-by-step explanation:
4/8 = 1/2
3/8 is less than 1/2 so round down
7 3/8 rounds to 7
Answer:
7
Step-by-step explanation:
7 3/8 = 7.375
The closest whole number is 7
Answer from Gauthmath
∣x−18∣=5 absolute value
Answer
x = 13 or x = 23
Step-by-step explanation:
|x-18| = 5 means there are two possibilities.
x-18 can equal 5 or equal -5 because absolute value sign makes everything inside it positive.
so you can write two equations and solve
first is x-18 = 5
x-18 + 18 = 5 + 18
x = 23
the second is x - 18 = -5
x - 18 + 18 = -5 + 18
x = 13
The two solutions are 13 and 23.
Which steps can be used to solve
6
X
1 7
2 8
for x?
Answer:
2856
Step-by-step explanation:
This question is a little unclear. 6 times 17 times 28 is equal to 2856 if that is what you are trying to ask.
Find all solution(s) of the quadratic equation x2 – 100 = 0. Question 9 options: A) x = 10, –10 B) x = –10 C) x = 10 D) x = 100, –100
Answer:
x = - 10, x = 10
Step-by-step explanation:
Given
x² - 100 = 0 ( add 100 to both sides )
x² = 100 ( take the square root of both sides )
x = ± [tex]\sqrt{100}[/tex] = ± 10
solutions are x = - 10, x = 10
Help plz and thanks
Given 4,7,10,13. Calculate the 20th term.
Answer:
61
Step-by-step explanation:
to calculate the 20th term you use the formula
Tn=a+(n-1)d where a stands for the first term,n the number of terms and d the common difference.in this case the first term is 4 the common difference is 3 cause they were adding 3 to go to the next term.. therefore the solution will be:
Tn=4+(20-1)3
=4+19×3
=4+57
=61
the 20th term is 61
I hope this helps
Myles has calculated that 1/2 a box of tile will cover 1/6 of his kitchen floor. How many boxes of tile will he need to cover the entire kitchen?
Answer: He need 3 boxes.
Step-by-step explanation:
Every 1/6 of his floor needs 1/2 of the tile box.Split his floor into 6 parts, each part needing 1/2 of the tile box:
[tex]6*\frac{1}{2} =\frac{6}{2} =3[/tex]
Or you can add 1/2 six times for each 1/6 of the floor:
[tex]\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} =\frac{6}{2}=3[/tex]
Palwasha took a non-stop flight to visit her grandmother.
The 1200 km trip took three hours and 45 minutes.
Because of the bad weather, the return trip took four hours and 45 minutes. What was her average speed for the round trip in km/h?
Answer:
282.35km/hr
Step-by-step explanation:
1200km+1200km=2400km
time taken=3hr 45min+4hr 45min=8hr 30min
average speed=2400km/8hr 30min
What is the decimal eqivalent for a meter?
Answer:
One meter = 10 decimeters = 100 centimeters = 0.001 kilometers = 3.2808399 feet = 1.0936133 yard = 0.000621371192 mile = 39.3700787 inches
Step-by-step explanation:
PLZ HELP!!!
Find the range of the following piecewise function.
Answer:
B
Step-by-step explanation:
the answer is B because, our range starts at 2 but does not include 2 and continues to infinity (x>8) does not have a boundary.
Which of these is NOT an integer
A) 3 raised to the power of -5
B) -3 raised to the power of 5
C) (1/3) raised to the power of -5
Hi there!
»»————- ★ ————-««
I believe your answer is:
Option A
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}[/tex]
⸻⸻⸻⸻
[tex]\text{Option \textbf{A} does not simplify into an integer.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Find the surface area of the composite figure
Answer:
470
Step-by-step explanation:
2(7×2+2×2+2×7)+2(12×7+7×7+12×7)-2(7×2)
= 64+434-28
= 470 cm²
evaluate without multiplying directly 998³ x 103³
Answer correctly I will mark them as brainlist
Answer:
1,086,183,741,982,184
Step-by-step explanation:
998^3
= (1,000)^3 - (2)^3 - 3 · 1,000 · 2 (1000 - 2)
= 1,000,000,000 - 8 - 6,000 (998)
= 999,999,992 - 5,988,000
= 994,011,992
103^3
= (100 + 3)^3
= (100)^3 + (3)^3 + 3(100) (3) + (100+3)
= 1,000,000 + 27 + 900(103)
= 1,000,027 + 92,700
= 1,092,727
994,011,992 · 1,092,727
= 994,011,992 · (1,000,000 + 90,000 + 2,000 + 700 + 20 + 7)
= (994,011,992 · 1,000,000) + (994,011,992 · 90,000) + (994,011,992 · 2,000) + (994,011,992 · 700) + (994,011,992 · 20) + (994,011,992 · 7)
= 994,011,992,000,000 + 89,461,079,280,000 + 1,988,023,984,000 + 695,808,394,400 + 19,880,239,840 + 6,958,083,944
= 1,086,183,741,982,184
Function expressed by the formula y=-0.5x. Is there a value of x for which
y=-150? If there is such a value, compute it.
Answer:
x=300
Step-by-step explanation:
STEPS FOR SOLVING LINEAR EQUATION
−150=−0.5x
Divide both sides by −0.5.
−0.5
−150
=x
Expand
−0.5
−150
by multiplying both numerator and the denominator by 10.
−5
−1500
=x
Divide −1500 by −5 to get 300.
300=x
Swap sides so that all variable terms are on the left hand side.
x=300
Hope this helped!
if g(x) is x-3 then what is g(3x)
Work Shown:
g(x) = x-3
g(3x) = 3x-3
We simply replaced every x with 3x. There isn't much else to show in terms of work. I suppose you could factor out the GCF to say g(3x) = 3(x-1), but that isn't much of a simplification in my opinion.
Answer:
Step-by-step explanation:
The meaning of g(x) = x - 3 is that whatever you put in the x on the left, you will put in the x on the right.
g(3x) = 3x - 3 is the correct answer.
need help with this!!
Concrete is made by mixing screenings cement and sand in the ratio 3:1:15. How much sand would be needed
to make 125 tonnes of concrete?
Answer:
98.7 tonnes of sand.
Step-by-step explanation:
First find the total :
3 + 1 + 15 = 19
if 19 = 125 tonnes,
what about 15 = ?
(cross multiply)
[tex] \frac{15}{19} \times 125[/tex]
= 1875 ÷ 19
= 98.68
(rounded off to 1 decimal place)
= 98.7 tonnes of sand.
PLEASEEEE HELLLLP MEEEE
Answer:
c. 20/21
Step-by-step explanation:
You just multiply straight
3×7 = 21
4×5 =20
21/20 <---- and it can't be reduced farther than this.
Answer:
C. ²¹⁄₂₀
Step-by-step explanation:
OKOKOK DON'T WORRY I'M HERE :)))
--
When multiplying fractions, you multiply the numerators together and then multiply the denominators together.
The numerators here are 3 and 7. Multiply those and you get 21 (7 x 3 = 21).
The denominators here are 4 and 5. Multiply those and you get 20 (4 x 5 = 20).
Then you put the newly-multiplied numerator over the newly-multiplied denominator and you get ²¹⁄₂₀.
Hope this helped!!
What is the probability that you roll at least one 3 in your dice? Convert your answer to
decimal form, then round to 3 decimal places,
Answer:
0.167
Step-by-step explanation:
1 dice has 6 faces, 2 dice will have a total of 12 faces
1 dice has 1 face with a 3 on it, so 2 dices will have 2 total 3s on them.
2 /12 = 1/6 = 0.16666666666
Rounded to 3 d.p = 0.16666
= 0.167
Answered by Gauthmath
Graph the line for y+1 = - 3(2x - 4) on the coordinate plane.
Lila uses craft sticks to make stars for an art project. She uses 5 craft sticks for each star,and she has 19 craft sticks. Lila makes as many stars as she can how many stars does Lila make?
Answer:
3
Step-by-step explanation:
5×3=15 she would have 4 left but can't make a full star
if R=[2 3 4] what is the number of element in
2 4 5
the matrix R?
Answer:
5
Step-by-step explanation:
May be correct than follow me please
TIME REMAINING
53:07
Solve for w.
5w + 9z = 2z + 3w
w = w equals negative StartFraction 7 Over 2 EndFraction z.z
w = w equals negative StartFraction 2 Over 7 EndFraction z.z
w = –2z
w = –7z
Answer:
w=-7/2z
Step-by-step explanation:
to solve for w you firstly have to group the like terms
5w-3w=2z-9z
2w=-7z
then you have to divide both sides by 2 inorder to remain with w on one side.
2w/2=-7/2
w=-7/2
I hope this helps
Answer:
A. w = (-7/2)z or w equals negative StartFraction 7 Over 2 EndFraction zStep-by-step explanation:
5w + 9z = 2z + 3w5w - 3w = 2z - 9z2w = - 7zw = (-7/2)zCorrect choice is A
If < A and < B are vertical angles, and < A = 2x - 11 degrees, and < B = x + 7 degrees, find x.
Answer:
x=18
Step-by-step explanation:
Vertical angles are congruent. This means that they are equal to each other. So, to solve set them equal to each other and isolate x. First, set up the equation. Then, subtract x from both sides. Finally, add 11 to both sides and simplify.
1) [tex]2x-11=x+7[/tex]
2) [tex]x-11=7[/tex]
3)[tex]x=18[/tex]
Luis dispone de una cantidad de dinero de 25,000 RD$ para ponerlos en el banco a plazo fijo con un interés de un 1.7% al cabo de 8 meses, ¿Cuánto dinero posee Luis si no ha gastado nada? *
Answer:
Luis's balance = $25,283.33
Step-by-step explanation:
Given the following data;
Principal = $25,000Interest rate, R = 1.7 %Time = 8 monthsTo find how much money Luis will have;
First of all, we would have to convert the value of time in months to a year.
Conversion:
12 months = 1 year
8 months = X year
Cross-multiplying, we have;
12 * X = 8
X = 8/12
X = 2/3 years
To find the simple interest, we would use the formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is the simple interest.P is the principal.R is the interest rate.T is the time measured in years.Substituting the values into the formula, we have;
[tex] S.I = \frac {25,000 * 1.7 * \frac {2}{3}}{100} [/tex]
[tex] S.I = \frac {28333.33}{100} [/tex]
S.I = $283.33
Luis's balance = S.I + Principal
Luis's balance = 283.33 + 25000
Luis's balance = $25,283.33
