A honeybee population starts with 100 bees and increases at arate of n' (t) bees per week. What does 100 + what does ∫ 15 0 r(t) dt represent?
Answers
The given statement shows that the honeybee population starts with 100 bees and increases at a rate of n'(t) bees per week. However, Adding the initial population (100 bees) to this total increase gives the total honeybee population after 15 weeks.
The population is a function of time, t, so it is denoted by P(t). Thus, the function P(t) represents the honeybee population, where P(0) = 100. What does 100 + what does ∫ 15 0 r(t) dt represent? The following are some definitions and formulas to help you understand the problem better. The rate of change of the population with respect to time is given by the differential equation: dP (t)/dt = n'(t). This equation can be solved using integration to obtain the function P(t). The solution to the differential equation is given by: P(t) = P(0) + ∫ n'(t) dt, where P(0) is the initial population at time t = 0, and n'(t) is the rate of change of the population at time t. The definite integral ∫ 15 0 r(t) dt represents the area under the curve of the function r(t) between the limits t = 0 and t = 15. This area can be interpreted as the total number of bees produced during the first 15 weeks. Therefore, 100 + ∫ 15 0 r(t) dt represents the total population of honeybees after 15 weeks, starting with an initial population of 100 bees.
The expression "100 + ∫ 15 0 r(t) dt" represents the total honeybee population after 15 weeks. The honeybee population starts with 100 bees, and it increases at a rate of n'(t) bees per week. The integral ∫ 15 0 r(t) dt calculates the total increase in the honeybee population over the 15 weeks. Adding the initial population (100 bees) to this total increase gives the total honeybee population after 15 weeks.
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Related Questions
Janice lost a total of 75 pounds over the course of 12 months. How many pounds on average did Janice lose each moth? Answer with a mixed number.
Answers
Answer:
The awnser is 6.25 pounds
Step-by-step explanation: 75/12 = 6.25 which means every month she lost a total of 6.25 pounds and on a 12 month average she lost 75 pounds
what is the equation for this line
Answers
Answer:
y=-1.5x+0.5 or y+1.5x-0.5=0
Who can help me? This is solving cube root equation help ?
Answers
Answer:
22: 2
23: -7
25: 6
26: 3
Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!
Step-by-step explanation:
For 22: 2 * 2 * 2 = 8, therefore, 2
For 23: -7 * -7 * -7 = -343. This results in a negative number because there is is an odd number of negative numbers (follows the odd-even negative rule).
For 25: Multiply both sides of the equation by -1/2 to get z^3 = 216. The cube root of 216 is 6
For 26: Add 11 to both sides to get 2h^3 = 54. Divide both sides by 2 to get h^3 = 27. Cube root of 27 is 3.
Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!
derive an equation that relates the initial release height hx of block x and the speed vs of the two-block system after the collision in terms of mx , my , and fundamental constants, as appropriate.
Answers
The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).
Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).
Combining everything, we get the following equation:
m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.
where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.
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help please! really appreciate it
Answers
Answer:
x=26
Step-by-step explanation:
exterior angles theorem meaning they're equal to each other.
5x+7=8x-71
add 71 to 7
5x+78=8x
subtract 5x from 8x
78=3x
divide 78 and 3
x=26
to check your work plug 26 into each equation:
5(26)+7= 137°
8(26)-71= 137°
because they're the same you know that x must equal 26
hope this helps!❤
Suppose that x
0
,x
1
,…,x
t
,x
t+1
,…, denote the (daily) share prices of a particular stock over time. Answer the following questions (you should add a bias term): 1. Write a linear model to predict x
t+1
using the share prices on the two preceeding days, i.e., x
t
and x
t−1
. (6 marks) 2. The more useful quantity to predict is Δ
t+1
:=x
t+1
−x
t
(the ':=' means 'is defined to be'), the change in share value. Write a linear model to predict Δ
t+1
using x
t
and x
t−1⋅
(6 marks ) 3. Write a linear model to predict Δ
t+1
using Δ
t
. (6 marks) 4. Write a linear model to predict Δ
t+1
using Δ
t
and x
t
. (6 marks) 5. Which of the above four models, if any, are equivalent? Justify your answer briefly. (6 marks)
Answers
(i) The linear model to predict xₜ₊₁ is given by,
xₜ₊₁ = a xₜ + b xₜ₋₁ + c, where a, b, c are constants and t ≥ 1.
(ii) The Δₜ₊₁ in terms of xₜ₋₁ and xₜ is given by, Δₜ₊₁ = (a - 1) xₜ + b xₜ₋₁ + c
Let x₁, x₂, x₃, ....., xₙ denotes the share prices.
(i) We know that linear model with x, y, z is given by,
z = ax + by + c, where a, b, c are constants.
Hence the predicted value of xₜ₊₁ is given by using linear model,
xₜ₊₁ = a xₜ + b xₜ₋₁ + c for t ≥ 1
(ii) The change in share value is defined by,
Δₜ₊₁ = xₜ₊₁ - xₜ = (a xₜ + b xₜ₋₁ + c) - xₜ = (a - 1) xₜ + b xₜ₋₁ + c
Hence, Δₜ₊₁ = (a - 1) xₜ + b xₜ₋₁ + c
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Let a function f be analytic everywhere in a domain D. Prove that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D.
Answers
By using the Cauchy-Riemann equations on a real-valued function, it can be proven that the function f(z) is constant in the domain D. This is important for understanding analytic functions in complex analysis.
To prove that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D, let a function f be analytic everywhere in a domain D. We know that a real-valued function is said to be a function whose values lie on the real line. In the case of the complex plane, a function whose values lie on the real line is real-valued.
The Cauchy-Riemann equations, which define the necessary conditions for a function f(z) to be analytic in a domain, say that the imaginary component of f(z) is determined by its real component.
To be more precise, if f(z) is real-valued for all z in D, then we can say that:u(x, y) = f(z),v(x, y) = 0
By definition, the Cauchy-Riemann equations can be stated as:
∂u/∂x = ∂v/∂y∂u/∂y = -∂v/∂x
Taking the first equation, we get:
∂u/∂x = ∂v/∂y => ∂v/∂y = 0
Since v is equal to 0 for all values of x and y, the above equation reduces to ∂u/∂x = 0, which implies u is constant with respect to x.
Similarly, taking the second equation, we get:
∂u/∂y = -∂v/∂x => ∂u/∂y = 0
Since u is equal to a constant for all values of x and y, the above equation reduces to ∂v/∂y = 0, which implies v is constant with respect to y. Since u and v are both constant with respect to their respective variables, u + iv = f(z) is a constant with respect to z throughout the domain D. Thus, we have proved that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D.
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Help please!!! Thank you
Answers
Answer:
2y+6x=180
Step-by-step explanation:
Because we know that side lengths BD, DC, and AD are all congruent, we can conclude that triangles BDA and CDA are congruent because they have at least two congruent sides. Since these triangles are both 45-45-90 triangles, angle C is equal to 45 degrees, or 3x. 45/3 is 15, so x=15. Angle B is equal to 45 degrees, or y, so y=45.
From there, we plug these numbers into the equation with 2(45) + 6(15), or 90+90 = 180.
Find the variance and standard deviation of the data. Round your answers to the
nearest hundredth.
78, 83, 85, 89, 92, 95
Answers
this week luiz made 80% of what he made last week if he made $72 this week how much did he make last week?
Answers
Answer: He made $90 last week.
Assumption :
Let, Luis made $X last week.
He made $72 this week which is 80% of $X that he made last week
⇒ X * 80% = 72
⇒ X * 80/100 = 72
⇒ X = (72 * 100)/80
⇒ X = 90
Therefore, he made $90 last week.
To remember :
While solving this type of problems, be careful to understand which one of last time and current time is not given; just assume that one and input other conditions, the problem will be solved.
What is the next number in the sequence? 9…. 16…. 24…. 33….
Answers
Therefore, the next number in the sequence is 43.
To find the next number in the sequence, let's examine the differences between consecutive numbers:
16 - 9 = 7
24 - 16 = 8
33 - 24 = 9
We can observe that the differences between consecutive numbers are increasing by 1 each time. Therefore, it suggests that the pattern in the sequence is adding consecutive integers to the previous number.
To continue the sequence, we add 10 to the last number in the sequence:
33 + 10 = 43
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The angle of elevation from a ship to the top of a cliff on the coastline is 4.5°. The cliff is 375 feet in height. How far is the ship from the base of the cliff? Round to the nearest tenth.
Answers
Solution:
The given information would be illustrated with the image below as;
We would apply the tangent ratio. Let x be the distance between the base of cliff and the ship. We have;
\(\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 4.5^o=\frac{375}{x} \\ \\ \end{gathered}\)Then, we have;
\(\begin{gathered} x=\frac{375}{\tan4.5^o} \\ x=4764.8ft \end{gathered}\)FINAL ANSWER:
\(4764.8\text{feet}\)
factor x^3+3x^2y - x + 3y
Answers
The factored form of the expression x^3 + 3x^2y - x + 3y is (x + 3y)(x + 1)(x - 1).
The given expression is x^3 + 3x^2y - x + 3y. In order to factor the given expression, we can apply factoring by grouping.
1: Separate the terms into two groups.
Group 1: x^3 + 3x^2y
Group 2: -x + 3y
2: Factor out the common factors within each group.
Group 1: x^2(x + 3y)
Group 2: -1(x - 3y)
Notice that we need to change the sign in Group 2 to make the expressions in the parenthesis the same.
3: Now, since both groups have a common factor of (x + 3y), we can factor that out.
(x + 3y)(x^2 - 1)
4: Further factor the difference of squares in the second term.
(x + 3y)(x + 1)(x - 1)
So the factored form of the expression is (x + 3y)(x + 1)(x - 1).
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Find the cube roots of unity in standard form (a+bi). Use exact values.
Answers
Every non-zero complex number has three cube roots. In general, any non-integer exponent, like
1
3
here, gives rise to multiple values. The way we find them is by multiplying
z
by 1 before exponentiating. We write
1
using Euler's Identity to the
2
k
power for integer
k
. That's
What is a mathematical expression in linear programming that maximizes or minimizes some quantity?.
Answers
The term "Objective Function" refers to a mathematical model in linear programming which maximizes as well as minimizes some quantity.
What is termed as the Objective Function?To solve optimization problems, the objective function is required. An objective function is a linear representation of a form Z = ax + by, for which a, b are constraints and x, y are variables that must be maximized or minimized. The decision variables are variables x and y. A few constraints govern an objective function, among them are x > 0, y > 0. Linear Programming (LP): The notion of linear programming is concerned with determining the optimal value of such a linear function, also known as an objective function. The term linear refers to all of the mathematical relationships applied to the problem, and the term program makes reference to the method used to determine a specific program or plan of action.Thus, in either a mathematical optimization problem, the objective function is the real-valued function for whom value must be minimized or maximized well over set of feasible alternatives.
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A square has a side length of 6 inches.it is enlarged and the new side length is 18. What is the scale factor
Answers
Answer:
2
Step-by-step explanation:
It's 2
5x+21-7x=-3+3+x-4x+6
Answers
"f(x) = In (x) at xo = 1" can be expanded given as In(x) = (x-1)/a + (x-1)/b + (x-1)/c. What is the bin above equation? (A) 6 (B) 4 (C)3 (D) 2 (E) None of (A) to (D)
Answers
The correct answer to the question is (D) 2, indicating that the expansion contains terms up to the second power of \((x - 1)\).
The expansion you have provided for \(f(x) = \ln(x)\) at \(x_0 = 1\) is incorrect. The correct expansion for \(\ln(x)\) using the Maclaurin series is:
\(\ln(x) = (x - 1) - \frac{(x - 1)^2}{2} + \frac{(x - 1)^3}{3} - \frac{(x - 1)^4}{4} + \dots\)
This expansion is obtained by substituting \(x - 1\) for \(x\) in the series expansion of \(\ln(x)\) around \(x_0 = 0\).
From the given expansion, we can see that there are terms involving powers of \((x - 1)\) up to the fourth power. Therefore, the correct answer to the question is (D) 2, indicating that the expansion contains terms up to the second power of \((x - 1)\).
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please help, i have to have this done by tonight.
Answers
Answer:
a. 2.5 miles an hour
b. yes, she will get there before 11 am since she could walk 5 miles in 2 hours if she wanted.
Step-by-step explanation:
what is 3x=75 solve for x
Answers
Answer:
x = 25
Step-by-step explanation:
you need x on its own, so just divide both sides by 3, and you get 25.
Can someone help me with number 13 I need the equation fast
Answers
The expression is given as
\((-2+7i)(-1-6i)(6+3i)\)Solve and simplify the expression by opening the brackets
\((2+12i-7i-42i^2)(6+3i)\)\((2+5i+42)(6+3i)=(5i+44)(6+3i)_{}\)\(30i+15i^2+264+132i\)\(162i+264-15=162i+249\)Hence the answer is
\(162i+249\)Find the best linear approximation, L(x), to f(x) = e' near x = 0. i.L(x) = x+1 ii. L(x) = x iii. LX) = c + 1
Answers
The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.
The given function is f(x) = e^x near x = 0.
To find the best linear approximation, L(x), we use the formula:
L(x) = f(a) + f'(a)(x-a),
where a is the point near which we are approximating.
Let a = 0, so that a is near the point x = 0.
f(a) = f(0) = e^0 = 1
f'(x) = d/dx (e^x) = e^x;
so f'(a) = f'(0) = e^0 = 1
Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1
Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.
For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.
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what is the reciprocal of -0.06
Answers
Answer:
-16.666
Step-by-step explanation:
You can find the reciprocal by turning the intended fraction upside down.
\(\frac{-0.06}{1}\) ⤭ \(\frac{1}{-0.06}\) = \(\frac{100}{-6}\) = \(\frac{50}{-3}\) = -16.6666666667
how to fry AN EGG with 34 meter of plastic
Answers
Answer:
Step-by-step explanation:
amama
Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems. 1. 2. 3. maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0. maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0. maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.
Answers
The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.
1. Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems.
maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
Now, To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 3/4), (0, 0), and (3, 0).
z = x₁ + 2x₂ = (0) + 2(3/4)
= 1.5z = x₁ + 2x₂ = (0) + 2(0) = 0
z = x₁ + 2x₂ = (3) + 2(0) = 3
The maximum value of the objective function z is 3, and it occurs at the point (3, 0).
Hence, the optimal solution is (3, 0), and the optimal value of the objective function is 3.2.
maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
To find the optimal solution and the optimal value of the objective function,
evaluate the objective function at each corner of the feasible region:
(0, 0), (3, 0), and (2, 5).
z = x₁ + x₂ = (0) + 0 = 0
z = x₁ + x₂ = (3) + 0 = 3
z = x₁ + x₂ = (2) + 5 = 7
The maximum value of the objective function z is 7, and it occurs at the point (2, 5).
Hence, the optimal solution is (2, 5), and the optimal value of the objective function is 7.3.
maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 1), (2, 0), and (5, 1).
z = 3x₁ + 4x₂ = 3(0) + 4(1) = 4
z = 3x₁ + 4x₂ = 3(2) + 4(0) = 6
z = 3x₁ + 4x₂ = 3(5) + 4(1) = 19
The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.
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50 points!! pls answer
Draw a diagram to show the given information.
Given: M is the midpoint of segment RX. Line JK is the perpendicular bisector of segment RX.
Answers
Answer:
liar it only 25 points but its ok i like to help the answer is m is the midpoint of the segment RX uw u welcome
Step-by-step explanation:
Answer:
The midpoint is M
Step-by-step explanation:
Because if the midpoint is m for RX it has to be the same for JK.
Perform the indicated operation, and write the answer in lowest terms.
−16/5 ⋅ (−15/56)
Answers
Answer:
6/7
Step-by-step explanation:
First, cancel out 16 and 56 by a common factor of 8. The resulting expression is -2/5*-15/7. Then, simply 5 and 15 by a common factor of 5. Then, you will get: -2*(-3/7). The negatives cancel out, so the answer is 6/7.
assume there are juniors, seniors, and graduate students in your class and we want to know if their average gpa differ. what is the proper statistical test?
Answers
If the average GPA of juniors, seniors, and graduate students in your class differ, you should use a one-way ANOVA test. This is the proper statistical test used to compare the average GPAs of different groups.
ANOVA is used to test whether there are any significant differences between the means of three or more independent groups. In this case, we have three independent groups (juniors, seniors, and graduate students) and we want to determine whether their average GPAs differ significantly by proper statistical test.
If the ANOVA test indicates that there are significant differences between the means, we can use post-hoc tests (such as Tukey's test or Bonferroni's test) to determine which specific group means differ significantly.
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Pls help ASAP pls pls pls i will give brainliest if 2 people reply whichever gives best explanation will get brainliset
Answers
Answer:
3 1/3 miles The answer is D
Step-by-step explanation:
The first trip to school is 5/6 miles. Multiply that by 2 because she also walked home and you get 10/6. Then add the distance she she walked to the library- which simplifies to 5/6 and you get 20/6. That simplifies to 3 1/3.
Answer:
3 1/3
Step-by-step explanation:
What is The length of CD?
Answers
Answer:
5 units
Step-by-step explanation:
just count the boxes from c to d