In a chemical reaction, 20 units of a compound are injected into a reaction chamber every 30 min. Within that 30 min, 50% of the compound is used up in the chemical process. Suppose that the reaction starts at t = 0 with 20 units of the chemical in the chamber.
a) Make a table of values showing the amount of the compound remaining for the first 5 h, in 30-min intervals, that the reaction has been occurring.
b) Write the amount of the chemical remaining after each 30-min interval as a sequence.
c) Determine a recursion formula for the sequence.
Answers
The compound will be completely used up in the reaction chamber after 60 minutes.
When will the compound be completely used up in the reaction chamber.In the given chemical reaction, 20 units of a compound are injected into the reaction chamber every 30 minutes. Within that 30-minute period, 50% of the compound is used up in the chemical process. This means that after 30 minutes, half of the compound has reacted and only 10 units remain in the chamber.
After another 30 minutes, another 20 units are injected, making a total of 30 units in the chamber. However, within this 30-minute period, 50% of the compound is again used up. This results in 15 units being consumed, leaving only 15 units in the chamber.
Following this pattern, we can see that after each 30-minute interval, the number of units remaining in the chamber is halved. Starting with 20 units, after the first 30 minutes, we have 10 units, and after the second 30 minutes, we have 5 units.
Therefore, it can be inferred that after 60 minutes (two 30-minute intervals), the compound will be completely used up in the reaction chamber. No units of the compound will be left.
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Related Questions
Which statement describes the graph of f(x) = –x4 + 3x3 + 10x2?
Answers
Answer:
The graph touches the x axis at x = 0 and crosses the x axis at x = 5 and x = -2.
Step-by-step explanation:
find the equation of a line that is perpendicular to the line 4x-5y-20=0
Answers
The equation of a line perpendicular to 4x - 5y - 20 = 0 is 5x + 4y + C = 0, where C is a constant.
To find the equation of a line perpendicular to 4x - 5y - 20 = 0, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
First, we rewrite the given line in slope-intercept form (y = mx + b) by solving for y:
4x - 5y - 20 = 0
-5y = -4x + 20
y = (4/5)x - 4
The slope of the given line is 4/5. The slope of a line perpendicular to it will be the negative reciprocal, which is -5/4.
Using the slope-intercept form, we have y = (-5/4)x + b. To find the equation, we need to determine the y-intercept (b). Since the line is perpendicular to the given line, it can have any y-intercept value.
Therefore, the equation of a line perpendicular to 4x - 5y - 20 = 0 is 5x + 4y + C = 0, where C is a constant representing the y-intercept.
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I need help on thid snf the first person who answer correctly gets BRANILIST
Answers
Answer:
D
Step-by-step explanation:
B and C is an increased dilation, but A and D are not. A is a decreased dilation of more than half, but D is only by 10% and so it would be D.
Show that if two n × n matrices A and B have a
common eigenvector x (but not necessarily a common
eigenvalue), then x will also be an eigenvector
of any matrix of the form C = αA + βB.
Answers
To show that if two n × n matrices A and B have a common eigenvector x, then x will also be an eigenvector of any matrix of the form C = αA + βB, we can use the definition of eigenvectors and some basic algebra.
First, let v be the common eigenvector of A and B, such that Av = λv and Bv = μv for some eigenvalues λ and μ. Then, consider the matrix C = αA + βB. We can rewrite this as C = αAv + βBv, and substitute in the expressions for Av and Bv in terms of v:
C = αλv + βμv = (αλ + βμ)v
Thus, we see that Cv = (αλ + βμ)v, which shows that x is an eigenvector of C with eigenvalue αλ + βμ. Therefore, any common eigenvector of A and B is also an eigenvector of any linear combination of A and B.
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Find the function, f, that satisfies the following conditions f"(x)=-sin x/2, f'(π) = 0, f(π/3)=-3
Answers
The function f(x) = -4*sin(x/2) - 1 is the solution that meets the specified conditions.
To find the function, f, that satisfies the given conditions f"(x) = -sin(x/2), f'(π) = 0, and f(π/3) = -3, we need to integrate the given second derivative twice and apply the boundary conditions. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x).
1. Integrate f"(x) = -sin(x/2) with respect to x to find f'(x):
f'(x) = ∫(-sin(x/2)) dx = -2*cos(x/2) + C1, where C1 is the integration constant
2. Apply the boundary condition f'(π) = 0:
0 = -2*cos(π/2) + C1
C1 = 0, since cos(π/2) = 0.
3. Now, f'(x) = -2*cos(x/2).
4. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x):
f(x) = ∫(-2*cos(x/2)) dx = -4*sin(x/2) + C2, where C2 is the integration constant.
5. Apply the boundary condition f(π/3) = -3:
-3 = -4*sin(π/6) + C2
-3 = -4*(1/2) + C2
C2 = -1.
So, the function f(x) that satisfies the given conditions is f(x) = -4*sin(x/2) - 1.
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the ratio of angles in a triangle is 11:6:7. find the largest angle
Answers
Answer:
Step-by-step explanation:
A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. Assume Newton's Law of Cooling: An object cools at a rate proportional to the difference between its temperature and the temperature of the surrounding air or other medium. (Round your answers below to the nearest whole number.) (a) If the temperature of the turkey is 150°F after half an hour, what is the temperature after 40 minutes? T(40) = °F (b) When will the turkey have cooled to 95°? t = min.
Answers
a) The temperature of the turkey after 40 minutes would be approximately 81°F.
b) It would take approximately 169 minutes for the turkey to cool down to 95°F.
(a) We are given that the initial temperature of the turkey is 185°F, and after half an hour (30 minutes), its temperature drops to 150°F. We need to find the temperature after 40 minutes (T(40)).
To solve this, we can use the general solution of Newton's Law of Cooling:
\(T(t) = T_s + (T_0 - T_s) * exp(-kt)\)
Where:
T(t) represents the temperature of the object at time t.
T_0 represents the initial temperature of the object.
To find the value of the proportionality constant k, we can use the information that the turkey's temperature drops to 150°F after 30 minutes. Let's substitute the given values into the equation and solve for k:
150 = 75 + (185 - 75) * exp(-30k)
Simplifying the equation:
75 = 110 * exp(-30k)
Divide both sides by 110:
0.6818 = exp(-30k)
To isolate k, take the natural logarithm (ln) of both sides:
ln(0.6818) = -30k
Now we can solve for k:
k ≈ -0.0231
Substituting the value of k back into the general solution equation, we can find the temperature after 40 minutes:
T(40) = 75 + (185 - 75) * exp(-0.0231 * 40)
Calculating this expression:
T(40) ≈ 81°F
Therefore, the temperature of the turkey after 40 minutes would be approximately 81°F.
(b) When will the turkey have cooled to 95°F?
To find the time it takes for the turkey to cool to 95°F (t), we can rearrange the general solution equation:
\(T(t) = T_s + (T_0 - T_s) * exp(-kt)\)
Substituting the given values:
95 = 75 + (185 - 75) * exp(-0.0231 * t)
Simplifying the equation:
20 = 110 * exp(-0.0231 * t)
Divide both sides by 110:
0.1818 = exp(-0.0231 * t)
Take the natural logarithm of both sides:
ln(0.1818) = -0.0231 * t
Solve for t:
t ≈ 169.23 minutes
Therefore, the turkey will have cooled to 95°F after approximately 169 minutes.
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Jam World Amusement Park sells special multi-day passes for guests who want to visit the park for more than one day. Their most popular passes are the 3-day pass, which costs $207, and the 7-day pass, which costs $364. How much more does the 3-day pass cost per day than the 7-day pass?
Answers
Answer: 17
Step-by-step explanation:
To find much each pass earns per day is to divide the two numbers. $207 divided by 3 is 69 and $364 divided by 7 is 52. Then you subtract 69 and 52 which is 17!
what is the equation for calculating the number of pairwise comparisons in a pairwise ranking matrix?
Answers
The equation for calculating the number of pairwise comparisons in a pairwise ranking matrix is: (n*(n-1))/2 where n is the number of items being compared in the matrix.
A pairwise ranking matrix is a tool that is used to rank items on the basis of pair-wise comparisons of the items. In order to find out the number of pairwise comparisons in such a matrix, one needs to use the following formula:(n*(n-1))/2where n is the number of items being compared in the matrix.
The formula works on the principle that every item in the matrix needs to be compared with every other item, but each comparison needs to be done only once. This is why the formula divides the total number of comparisons by two.
Therefore, the equation is: (n*(n-1))/2
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3.22*10^-4 in standard form
Answers
Answer:
that is standard form but r u looking for 0.000322
Step-by-step explanation:
find the slope of -2x + 3y = 21
Answers
Answer: ☁️ m = 2/3 ☁️
Hope it helps!~
Explanation: Have a nice day. ￣▽￣❤️
your answer is 7/3 its gonna be 7/3
The diagram shows a circle with centre O. A, Y and B lie on a straight line. C, Y and D lie on a straight line. Given that: AB = 6mm; BY = 2mm; and DY = 2.5mm; work out the length CD.
Answers
The value for the length of CD is equal to 3.9 mm using the intersecting secant theorem
What is the intersecting secant theoremThe intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
DY × CY = BY × AY
{AY = 2 mm + 6 mm}
2.5 × CY = 2 mm × 8 mm
2.5 × CY = 16 mm
CY = 16mm/2.5 {divide through by 2.5}
CY = 6.4
{CD = CY - DY}
CD = 6.4 - 2.5
CD = 3.9
Therefore, the value for the length of CD is equal to 3.9 mm using the intersecting secant theorem.
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help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The point of maxima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
Given that,
Initial height of the launching pad is 4 feet,
Initial velocity of rocket is 48 feet/sec,
Height of the rocket as a function of time, h(t) = -16t² + 48t + 3
In order to find the time for maximum height equate h'(t) = 0 as follows,
-32t + 48 = 0
⇒ t = 48 / 32
⇒ t = 3 / 2
⇒ t = 1.5
To find the maximum height find h(t) for t = 1.5 as follows,
h(1.5) = -16 × 1.5² + 48 × 1.5 + 3
= -36 + 60 + 3
= -36 + 63
= 27
Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.
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Factorise fully
x2 - 42^2
Answers
Step-by-step explanation:
(x_42)(x+42)...
....
Given the triangle below:
4
20
Which is the length of the missing side?
A.24
B. square root 384
C. square root 416
D. 416
Answers
For this question we can use the pythagorean theorem: 20^2 + 4^2 = c^2
c^2 = 416
c = \(\sqrt{416}\)
3x - x^{2} + 2 < 0
solve this quadratic inequality graphically
Answers
(−∞,−3) (2,+∞)
Explanation:
graph the parabola
y=−x2−x+6
and consider which parts are less than zero, that is below the x-axis finding the x and y intercepts
let x = 0, in the equation for y-intercept
let y = 0, in the equation for x-intercepts
x=0→ y=6←
y-intercept
y=0→ −x2−x+6=0
multiply through by - 1
⇒ x2+x−6=0
the factors which multiply to give - 6 and sum to + 1 are + 3 and - 2
⇒(x+3)(x−2)=0
⇒x=−3 or x=2←
x-intercepts
obtaining the shape of the parabola
if a>0
then minimum if a < 0
then maximum for y =−x2−x+6xa<0
we can now graph the parabola
graph{-x^2-x+6 [-10, 10, -5, 5]}
x<−3 or x>2
are the parts below the x-axis
in interval notation
(−∞,−3)∪(2,+∞)
10. find the volume of the solid of intersection of the 2 right circular cylinders of radius r whose axes meet at right angles
Answers
The volume of the solid of intersection is V = (2/3) × 2πr³ = V = (4/3)πr³.
To find the volume of the solid of intersection of the two right circular cylinders of radius r whose axes meet at right angles, we can use the formula:
V = (2/3)πr³
where r is the radius of the cylinders.
First, we need to find the height of the intersection. Since the axes of the cylinders meet at right angles, the height of the intersection will be equal to the diameter of each cylinder. So, the height of the intersection will be 2r.
Now, we can find the volume of the solid of intersection by multiplying the area of the base (which is a circle of radius r) by the height of the intersection (2r):
V = πr²(2r)
Simplifying this equation, we get:
V = 2πr³
So, the volume of the solid of intersection of the two right circular cylinders of radius r whose axes meet at right angles is 2/3 of the total volume of a cylinder with radius r and height 2r, which is 2πr³.
Therefore, the volume of the solid of intersection is:
V = (2/3) × 2πr³
V = (4/3)πr³
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The volume of a sphere is 3,052.08 . To the nearest meter , what is the radius of the sphere? Use 3.14 for .
Answers
Answer:
9 cm
Step-by-step explanation:
v = 4/3 π r³
3052.08 = 4/3 × 3.142 × r³
3052.08 = 4.19 × r³
3052.08/4.19 = r³
728.42 = r³
change the position to solve it easier
r³ = 728.42
r = cubic root 728.42
r = 8.998 cm
round it
r = 9 cm
What is the value of (f+g)(5)if f(x)=7x-2 and g(x)=9x-4?
Answers
Answer:
74
Step-by-step explanation:
All you have to do it first add f(x)+ g(x) and then plug in x=5.
(f+g) = f(x) + g(x)
= (7x- 2) + (9x-4)
= 7x - 2 + 9x - 4
= 16x - 6
(f + g)(5) = 16(5) - 6
= 80 - 6
= 74
Time left: 0:48:24
Question 11 of 50
What are the roots of the quadratic equation
x2+3x+2?
Answers
Answer:
-1 & -2
Step-by-step explanation:
x²+3x+2
x²+2x+x+2
(x²+2x)+(x+2)
x(x+2)+1(x+2)
(x+1)(x+2)
As monte carlo simulation is essentially statistical sampling, the larger the number of trials used, the more precise is the result.
a. True
b. False
Answers
True, Monte Carlo simulation is used for statistical sampling where larger number of trials are used for the precise result.
Step by Step Explanation:
Monte Carlo simulation is a mathematical technique or statistical sampling which is used to predict all possible outcomes of any uncertain event.The larger the number of trials more is the accuracy as it is based on the past data to predict the future outcomes.example : For the prediction of first month sale of any new launch product you can revise more number of old data.It help to calculate probability more accurately.Therefore, it is true to have more number of trials in Monte Carlo simulation statistical sampling for precise result.
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What can you conclude about the paths of the skaters? There is no chance that the skaters will hit each other. The skaters' paths cross each other at two different points on the rink. The skaters are traveling on the same path, but possibly in different directions.
Answers
Answer:
C: The skaters are traveling on the same path, but possibly in different directions.
Step-by-step explanation:
edge 2021-2022
Answer:
The skaters are traveling on the same path, but possibly in different directions.
Step-by-step explanation:
can Someone help me
Answers
Answer:
B
Step-by-step explanation:
anyone know collage level algebra 2? I need help
Evaluate the series: image Question 1 options: A) 392 B) 249 C) 420 D) 406
Answers
Answer:
The required sum is 392
Step-by-step explanation:
Given the sum as shown;
\(\sum \left \77} \atop {a=1}} \right. (3a^2-4)\)
When n = 1
f(1) = 3(1)²-4
f(1) = 3 - 4
f(1) = - 1
When n = 2
f(2) = 3(2)²-4
f(2) = 12 - 4
f(2) = 8
When n = 3
f(3) = 3(3)²-4
f(3) = 27 - 4
f(3) = 23
When n = 4
f(4) = 3(4)²-4
f(4) = 48 - 4
f(4) = 44
When n = 5
f(5) = 3(5)²-4
f(5) = 75 - 4
f(5) = 71
When n = 6
f(6) = 3(6)²-4
f(6) = 108 - 4
f(6) = 104
When n = 7
f(7) = 3(7)²-4
f(7) = 147 - 4
f(7) = 143
Taking their sum
Sum = f(1)+f(2)+(3)+f(4)+f(5)+f(6)+f(7)
Sum = -1 + 8 + 23 + 44 + 71 + 104 + 143
Sum = 392
Hence the required sum is 392
Simplify the given expression using the order of operations and exponent rules. Write the answer without negative exponents
2w^5z(6w²z^5)
Answers
Answer:
\(12w^7 z^6\)
Step-by-step explanation:
\(2w^5 z(6w^2 z^5)=(2)(6)w^5 w^2 z^5 z=12w^7 z^6\)
the price of sugar increase from shs 1000 to shs 1200.In what percentage did the price increase
Answers
Answer:
20%
Step-by-step explanation:
1000×120%=1200
120-100=20
7/8 x 1/3 x 2/3 in fractions
Answers
Answer:
14/72
Step-by-step explanation:
Just line them all up and multiply numerators with numerators and denominators with denominators. You have your answer.
Hope it helps
(2x2-3x -1) + (2x2 + x-4)
A. 4x2 -2x-5
B. 4x4 -4x3 -13x2 + 11x + 4
C. -3
D. 4x + 3
Answers
Answer:the answer is x= -3
Step-by-step explanation:
Find the Cartesian equation of the curve with parametric equations x = 2 sec(t) and y = 3 tan(t) for t ∈ π/2 , 3π/2, and describe the curve.
Answers
Answer:
4y^2 - 9x^2 = -36
Step-by-step explanation:
x = 2 sec t
y = 3 tan t
x^2 = 4 sec^2 t
y^2 = 9 tan^2 t
Now sec^2t = 1 + tan^2 t so we have:
4(1 + tan^2 t) + 9 tan^2 t = x^2 + y^2
4 + 13 tan^2 t = x^2 + y^2
13 tan^2 t = x^2 + y^2/ - 4
tan^2 t = x^2/13 + y^2/13 - 4/13
But , from the second equation tan t = y/3 so tan^2 t = y^2/9, so:
y^2/9 = x^2/13 + y^2/13 - 4/13
LCM of 9 and 13 is 117 so multiply thru by 117:
13y^2 = 9y^2 + 9x^2- 36
4y^2 - 9x^2 = -36
what is 1/8 divided by 2 3/4?A 1/32B 2 1/3C 1/22D 2 1/2
Answers
Answer: It is letter C. 1/22
Step-by-step explanation:
Change 2 3/4 to an improper fraction to get 11/4, then multiply 1/8 by the reciprocal of 11/4 which is 4/11.
1/8 x 4/11= 4/88
4/88 simplified = 1/22