or, - 12= - 5x-5-15
or, - 12= - 5x-20
or, - 12+20= - 5x
or, 8= - 5x
or, x= 8÷-5
Also,
F(x)= - 5(x+1+3)
or, f(8÷-5)= - 5(8÷-5+1+3)
= - 5(8-5-15÷-5)
= - 5×-12÷-5
= - 12 #
The rate (In mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function 110I 12 +1+ 9 where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
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
Solve. Algebra 1
1-4p-2p=1-5p
Answer:
p = 0
Step-by-step explanation:
1 - 4p - 2p = 1 - 5p
-6p + 1 = -5p + 1
-p + 1 = 1
-p = 0
p = 0
the question is on the image
Answer:
(i) - rectangular prism
(Ii) - triangular prism
(iii) - square pyramid
Step-by-step explanation:
is my answers correct?
Answer:
Saleh is x years old. And 10 years ago he was 100 years old.
Suha is x years old. Saleh is 10 years younger than Suha. Saleh is 100 years old.
Solve for the questions (both of them) and label you answers for which question
What number could replace the box so that the system of equations has
infinitely many solutions?
A. -9
B. 3
C. 9
D. -3
Answer:
d || if its wrong cancel me lol <3
Step-by-step explanation:
Find the greatest common factor of the
following monomials:
12a^2, 32a^3
Answer:
4a^2
Step-by-step explanation:
GCF of 12 and 32 is 4.
GCF of a^3 and a^2 is a^2.
Therefore, the answer is 4a^2.
After simplification, the value of 1-2/1(1+2)-3/(1+2)(1+2+3)-4/(1+2+3)(1+2+3+4)-...-100/(1+2+...+99)(1+2+...+100)
is a proper fraction in its lowest form. Find the difference of its numerator and denominator.
Answer: no
Step-by-step explanationn. .......................................................w:eorkeok,feoferkeorkoe
determine if 5yx - 17xy are like terms
Step-by-step explanation:
yes they are because they have the same variables which are X& Y
Answer:
5yx-7xy
they are like terms, it's all multiplication just a different arrangement
5xy-7xy=-2xy
Step-by-step explanation:
hope this is helpful
Help please
What value of x will ensure that the shelves are parallel?
for the to be parallel both the angle must be equal
so 7x - 20 = 3x + 20 - > 4x = 40⁰
x = 10⁰
please help it’s easy i’ll give u brainilest <33
Answer:
for (a)
Step-by-step explanation:
15 and 25 are the numbers that come in A union to B
1. Students were surveyed and asked if they play lacrosse and/or football. The results are shown below.
What percent of football players also play lacrosse?
36%
Step-by-step explanation:
28 + 16 = 44 Football players
Of those, 16 are on the lacrosse team.
16 / 44 × 100 = 36.36% (We round to 36%)
To verify:
44 × 36.36% = 15.84 (Which we can round to 16)
Pardon me if it's wrong
Which ordered pair is the best estimate
for the solution of the system of
equations?
y= 3/2x +6
y=1/4x -2
Answer: -6.4, -3.6
Explanation: A souloution of the system of equations is, when two equations intercept (y= 3/2x +6, y=1/4x -2)
Can someone please help me. If you do thanks
Answer:
(B)
Step-by-step explanation:
Can't explain lol, but that's the answer
Arc AC is adjacent to arc CD. If arc AC measures 35 degrees and arc CD measures 45 degrees, what is the measure of arc AD according to the Arc Addition Postulate?
Answer:
80°Step-by-step explanation:
You just need to sum up the values according to arc addition postulate:
the measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcsm(arc AD) = m(arc AC) + m(arc CD)m(arc AD) = 35° + 45° = 80°Now we have to find,
The measure of arc AD according to the Arc Addition Postulate.
AD is the sum of the measures of the other two arcs. Then measure of AD is,
→ AC + CD
→ 35° + 45°
→ 80° (final answer)
Hence, the measure of arc AD is 80°.
Which is the graph of the equation y-1=- f (x-3)?
Solve: 4(x + 3) ≤ 44
x ≥ 16
x ≤ 16
x ≤ 8
x ≥ 8
Please help
Answer:
C
Step-by-step explanation:
[tex]4(x + 3) \leqslant 44 \\ \\ 4x + 12 \leqslant 44 \\ 4x \leqslant 44 - 12 \\ 4x \leqslant 32 \\ 4x \div 4 \leqslant 32 \div 4 \\ x \leqslant 8[/tex]
The scale on a map is 1cm = 250 km. What would be the distance on the map, if the actual distance between the two cities is 1,000km? *
Answer:
so if its actually 1000 and that map thing is 250
250 goes into 1000 4 times so
4cm
Hope This Helps!!!
A student answered 68 questions correctly in a test and received a grade
of 85%. How many problems were on the test, if all the problems carried
the same number of points?
Answer:
There are 80 questions on the test
Step-by-step explanation:
I think this is right, but don't quote me on this.
Write an equation that represents the line.
Answer:
y = 7/5x + 7
Step-by-step explanation:
cone is inscribed in a cylinder. A square pyramid is inscribed in a rectangular prism. The cone and the pyramid have the same volume. Part of the volume of the cylinder, 1 V 1 , is not taken up by the cone. Part of the volume of the rectangular prism, 2 V 2 , is not taken up by the square pyramid. What is the relationship of these two volumes, 1 V 1 and 2 V 2 ?
Answer:
The answer is "[tex]v_1 \ and\ v_2[/tex] are equal".
Step-by-step explanation:
Its volume could be defined both by cone as well as the cylinders
[tex]\to \text{(base area)} \times \text{(solid height)} \times (\frac{1}{3})\\\\[/tex]
We are planning to write this as [tex]V = \frac{Bh}{3}[/tex]
When we relate this formula to the cylindrical and prism volume formula, we can see that when we multiply the cone volume by 3, the cylinder size where it is registered comes in. The very same goes for the pyramid as well as the inscription of the rectangular prism. That both pyramid and the cone have the same volume V, hence it would have the same volume of a cell and rectangle prism. [tex]v_1 \ and\ v_2[/tex] are so similar.
17
Select the correct answer from each drop-down menu.
Consider this system of equations:
2x+ıy=3
(equation A)
fr-y=6
(equation B)
The expressions that give the value of y are
The solution for the given system is
and
Answer:
The expressions that give the value of y are A - 3B and (1/3)A - B
The solution is (27/13, -60/13)
Step-by-step explanation:
We can see both equation A and equation B.
Equation A: 2x + (1/4)y = 3
Equation B: (2/3)x - y = 6
To find the value of y, we have to solve both equations A and equation B simultaneously. This is done by multiplying equation B by 3 and subtracting from equation A (A - 3B) to get:
(13/4)y = -15
y = -60/13
you can also get y by dividing equation A by 3 and subtracting equation B (1/3A - B)
Put y = -60/13 in equation A to get x:
2x + (1/4)(-60/13) = 3
2x = 3 + 15/13
2x = 54/13
x = 27/13
The solution is (27/13, -60/13)
if two angles are supplementary, then what is the measurement of the missing angle, if one angle is 120?
Answer: 60°
Step-by-step explanation:
If two angles are supplementary, that means they add up to 180°.
Therefore, if one angle is 120°, the other missing angle can be calculated by:
180° - 120° = 60°
Evaluate the expression. 24.32
2^4×3^2 = 144
___________
Answer:
144 would be the answer.
Step-by-step explanation:
Question:- [tex]2^{4}[/tex] · [tex]3^{2}[/tex]
[tex]2^{4}[/tex] = 2 x 2 x 2 x 2
= 4 x 2 x 2
= 8 x 2
= 16
[tex]3^{2}[/tex] = 3 x 3
= 9
So, [tex]2^{4}[/tex] · [tex]3^{2}[/tex] = 16 x 19
= 144
What is the image of the point (8,4) after a rotation of 90° counterclockwise about the origin?
=========================================================
Explanation:
The 90 degree counterclockwise rotation rule we use is
[tex](x,y) \to (-y,x)[/tex]
the x and y coordinates swap places, and we change the sign of the first coordinate after the swap.
After using that rotation rule, we would go from (8,4) to (-4, 8) which is the final answer.
----------------
Extra info (optional section):
Define the following three points
A = (0,0)
B = (8,4)
C = (-4,8)
Use the slope formula to find that AB and AC have slopes of 1/2 and -2 in that order.
Those slopes multiply to -1, since (1/2)*(-2) = -1. This is a property of any two perpendicular lines as long as neither line is vertical and neither is horizontal. So this is sufficient to prove that the lines are perpendicular. This further means that a 90 degree rotation has taken place.
2. What is the area of the figure below. Simplify.
Answer:
x^2 - 9
Step-by-step explanation:
length = 2x - 6 = 2(x-3)
Area = [2(x-3) * (x + 3)]/2 = (x-3)(x+3) = x^2-9
Answer: x = 9
2x -6= x +3
2x -x= 3 +6
x= 9
what is the measure of 6 ?
Answer:
54°
Step-by-step explanation:
Here :-
13x + 9 + 5x + 9 = 1801 8x + 18= 180 18x = 162x = 9Measure of 6 :-
6 = 5x + 9 6 = 5*9 +9 6 = 45 + 9 6 = 54°Answer:
m<6 = m<2 = 54º
Step-by-step explanation:
13x + 9 + 5x + 9 = 180
18x + 18 = 180
18x = 180 - 18
18x = 162
x = 162 / 18
x = 9
13x + 9
13(9) + 9
126
180 - 126
54
m<6 = m<2 = 54º
Which is the equation of a line perpendicular to the line with the equation: y = −14x + 7
y = -4x - 7
y = 4x + 2
y = 14x − 12
y = −14x + 3
how do I solve this question (step by step)?
Answer:
see explanation
Step-by-step explanation:
Angles on the circumference subtended on the same arc are equal
Angle at the centre is twice the angle at the circumference subtended on the same arc.
Then
∠ BAC = ∠ BDC = 29°
∠ BOC = 2 × ∠ BDC = 2 × 29° = 58°
A tether ball is attached to the top of a 15-foot pole. Maddy holds the ball 3 feet off the ground and 4 feet from the pole. How long is the rope that the tether ball is attached to?
Answer:
15.52 ft
Step-by-step explanation:
the length of the rope can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
√15² + 4²
= √225 + 16
=√ 241
= 15.52 ft
Answer:
the answer is b the square root of 160
Step-by-step explanation:
i did it on the assignment
