At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was 0 mg.
A limit is a value that a function or sequence approaches as the input or index approaches a certain value. Limits are a fundamental concept in calculus, and they are used to define important ideas such as derivatives and integrals. They are also used in other areas of mathematics, such as real analysis and mathematical analysis.
The rate at which the drug is being eliminated is the derivative of the amount of drug present at time t. We can write this as:
r(t) = dA(t)/dt = 50(e^-0.1 t - e^-0.20 t) mg/hr
If we integrate both sides of this equation with respect to t, we get:
A(t) = ∫r(t) dt = ∫50(e^-0.1 t - e^-0.20 t) dt
This integral can be evaluated using integration by parts. Let u = e^-0.1 t and dv = e^-0.20 t. Then du = -0.1 e^-0.1 t and v = -1/(0.2) * e^-0.20 t = -5e^-0.20 t. We can then write:
A(t) = -5 ∫e^-0.1 t * e^-0.20 t dt + (1/0.2) ∫e^-0.1 t dt
The first integral on the right-hand side can be evaluated using the substitution y = -0.3t, which gives:
A(t) = -5 ∫e^y dy + (1/0.2) ∫e^-0.1 t dt
The first integral is simply -5e^y, and the second integral is -5e^-0.1 t. Substituting these results back into the expression for A(t) gives:
A(t) = -5(-5e^-0.3 t) + (1/0.2)(-5e^-0.1 t)
Combining constants and simplifying gives:
A(t) = 25e^-0.1 t - 25e^-0.3 t
We are told that all the drug is eventually eliminated, so A(t) approaches 0 as t approaches infinity. This means that the original dose A(0) must be equal to the limit of A(t) as t approaches 0.
Taking the limit as t approaches 0 gives:
A(0) = lim t → 0 [25e^-0.1 t - 25e^-0.3 t]
This limit is equal to 25 - 25 = 0, so the original dose was 0 mg.
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Solve the system of equations.
Y=2x+7
Y=-x-8
Please Help
There are several marbles of different colours in a bag in front of you. Your job is to select three marbles and record the colour of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles and 3 purple marbles. What are the chances of selecting one red marble, one yellow marble and a blue marble?
Assume that once each marble is chosen, it is not returned to the bag.
The probability is 2.54%.
What is probability?The formula of the favorable outcome over the total outcomes is used to describe probability.
given, There are several marbles of different colors in a bag in front of you. Your job is to select three marbles and record the color of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles, and 3 purple marbles.
The final probability if conditions are not dependent on each other is multiple possibilities of happening these events.
Probability of getting desired outcomes = (17 / 50) (8/49) ( 22/48)
Therefore the probability of selecting one red marble, one yellow marble, and a blue marble is 2.54%.
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1. A taxi service charges a $ 1.95 flat rate plus $ 0.55 per mile. Jason only has $ 12 to spend on a ride. Which graph best represents the number of miles Jason can afford to travel?
Answer:
B
Step-by-step explanation:
Subtract $1.95 from $12 to account for the flat rate that Jason must pay, then divide that by 0.55, or the per mile charge. The answer, or the highest amount of miles he can go with $12, is 18.27272727. The answer that best represents the number of miles he can go is B because he can go up to 18 miles, including 18 miles, hence the closed circle.
root of 63x to the power of 11 yz to the power of 10
The value of the equation is [tex]A = (\sqrt{63x}^{(11yz)^1^0}[/tex]
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
Root of 63x to the power of 11 yz to the power of 10
The value of root of 63x = [tex]\sqrt{63x}[/tex]
Now , the value of root of 63x to the power of 11 yz is
The value of root of 63x to the power of 11 yz = [tex](\sqrt{63x}^{(11yz)[/tex]
And ,
The value of root of 63x to the power of 11 yz to the power of 10 is
Value of root of 63x to the power of 11 yz to the power of 10 is [tex](\sqrt{63x}^{(11yz)^1^0}[/tex]
Therefore , the value of A is [tex](\sqrt{63x}^{(11yz)^1^0}[/tex]
Hence , The value of the equation is [tex]A = (\sqrt{63x}^{(11yz)^1^0}[/tex]
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Round 10.29 to the nearest tenth
Answer:
10.3
Step-by-step explanation:
10.29 rounded to the nearest tenth is 10.3.
Select all the expressions that are equal to
2/3 to power of 2
4/9 , 4/3, 1/9 x 4 , 1/3 x 1/3, 2/3 x 2/3
Answer to the problem:
4/9, 1/3 x 1/3, 2/3 x 2/3
A random sample of 16 pharmacy customers showed the waiting times below (in minutes).
20 27 24 23 19 21 18 17
22 15 18 32 16 20 19 19
Find a 90 percent confidence interval for μ, assuming that the sample is from a normal population.
The 90% confidence interval for the population mean is given as follows:
(18.75, 22.51).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 16 - 1 = 15 df, is t = 1.7531.
From the sample given in this problem, the parameters are as follows:
[tex]\overline{x} = 20.63, s = 4.3, n = 16[/tex]
Then the lower bound of the interval is given as follows:
20.63 - 1.7531 x 4.3/4 = 18.75.
The upper bound of the interval is of:
20.63 + 1.7531 x 4.3/4 = 22.51.
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a norman window has the shape of a rectangle surmounted by a semicircle. (thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) a window with the shape of a rectangle surmounted by a semicircle. the diameter of the semicircle is equal to the width of the rectangle. the rectangle has width x. if the perimeter of the window is 32 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.
Answer:
The exact value of x so that the greatest possible amount of light is emitted is 8.96ft.
What is the perimeter of a semicircle?
The perimeter of a semicircle is half that of a circle, that is [tex]\pi r[/tex], where r is the radius of the circle.
Step-by-step explanation:
Given the width of the rectangle is x, let the height of the rectangle be y.
The radius of the semicircle is x/2.
The perimeter of the window is equal to [tex]2y+x+\pi \frac{x}{2} =32[/tex].
The area of the window is [tex]xy+\frac{1}{2}(\pi )(\frac{x}{2})^2=xy+\frac{\pi x^2}{8}[/tex].
We can insert into the formula for the area to obtain the area in terms of only x by solving the equation for the perimeter of y in terms of x.
[tex]2y=32-(1+\frac{\pi }{2} )x=32-(\frac{2+\pi }{2} )x\\y=16-(\frac{2+\pi }{4} )x[/tex].
Now the area of the window in terms of only x is:
Area=[tex]16x-(\frac{2+\pi }{4} )x^2+\frac{\pi x^2}{8}[/tex].
Since it is given in the question that maximum light should be admiitted, we will differentiate the Area and set it to 0.
[tex]16-2(\frac{2+\pi }{4} )x+\frac{\pi x}{4}=0\\ 16=x(1+\frac{\pi }{4})\\ x=\frac{16}{1+\frac{\pi }{4}} \\x=8.96ft[/tex].
Therefore the exact value of x is 8.96ft.
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Find the value of x and y .
x°=__
y°=___
In triangle PQR , the value of x and y is equal to 90° and 85° respectively.
As given in the question,
In the given triangle PQR,
Measure of ∠R = 5°
From the diagram,
PQ ≅ QR
⇒ ∠P ≅ ∠R
⇒m ∠P = m ∠R
⇒m ∠P = 5°
In ΔPQR,
∠P + ∠Q + ∠R = 180°
⇒ 5° + ∠Q + 5° = 180°
⇒ ∠Q = 170°
From the diagram,
y° = (1/2) ( ∠Q)
= 170°/2
= 85°
∠P + y° + x° = 180°
⇒ 5° + 85° + x° = 180°
⇒ x° = 180° - 90°
⇒ x° = 90°
Therefore, in triangle PQR the measure of x° and y° is equal to 90° and 85° respectively.
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Substitute 3 for x in new equation. Do you get a ture statement explain
Q is the average of A,B and C whrite a formula for calculating Q and then to solve A
The formula for calculating Q which is the bis
(A + B + C) / 3
To solve for A, the formula is
A = 3Q - (B + C)
What is average?In mathematics, the middle value which is determined by dividing the sum of all the values by the total number of values is the average value in a set of numbers.
If we want to calculate the average for a set of data, we add up all the values and divide this sum by the total number of values.
For the given problem the sum of the data is
= A + B + C
they are 3 hence we divide by 3
average, Q = (A + B + C) / 3
To solve for A we make A the subject
Q = (A + B + C) / 3
3Q = (A + B + C)
A = 3Q - (B + C)
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suppose that there are 5 children in a gymnastics class. one day, they count the number of steps each persontakes while walking on their hands until they lose balance and come down. the results are: ashley (20),brittany (8), carol (22), darla (26), and erica (24).the mean number of steps these children took whilewalking on their hands is 20 steps.
The population is the number of children in gymnastic class = 5.
A parameter is the mean number of steps taken by the 5 children.
What is a parameter?
Four parameters, referred to as hybrid or h Parameters, can be used to assess any linear circuit with input and output terminals. These parameters are one measured in ohm, one in mho, and two dimensionless. Hybrid is short for "mixed." These parameters are referred to as hybrid parameters since they have dual dimensions
Here, we have
Given that,
Suppose that there are 5 children in a gymnastics class.
One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down.
The mean number of steps these children took while walking on their hands is 20 steps.
We have to find the population and parameters.
The area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class make up the population.
Population = number of children in gymnastic class = 5.
Parameter = mean number of steps taken by the 5 children.
Hence, Population is the number of children in gymnastic class = 5.
A parameter is the mean number of steps taken by the 5 children.
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the accompanying data file shows the average monthly debt payments (debt in $) for residents of 26 metropolitan areas.
Let X and Y be IID Unif(0, 1). the distance between X and Y.Expected value: 0 and Standard deviation: [tex]$\sqrt{\frac{1}{3}}$[/tex]
Expected value:
E(X-Y)
= E(X) - E(Y) = 0 - 0 = 0
Standard deviation:
Var(X-Y) = Var(X) + Var(Y) = 1 + 1 = 2
SD(X-Y) = [tex]$\sqrt{2}$ \\[/tex] [tex]= $\sqrt{\frac{1}{3}}$[/tex]
The expected value of X-Y is the difference of the expected values of X and Y, which are both 0 since they are both IID Unif(0, 1). The variance of X-Y is the sum of the variances of X and Y, which are both 1. Since the standard deviation is the square root of the variance, the standard deviation of X-Y is the square root of 2
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if the correlation coefficient is .4, the percentage of variation in the dependent variable explained by the estimated regression equation is .
If the correlation coefficient is 4, the percentage of variation in the dependent variable explained by the estimated regression equation is 16%.
The correlation coefficient is a measure of linear association between two variables, usually denoted by r. A correlation coefficient of 4 indicates a strong positive linear relationship between the two variables.
A correlation coefficient of 4 does not give any indication as to the percentage of variation in the dependent variable explained by the estimated regression equation. To find this percentage, we must use the coefficient of determination, denoted by r2.
The coefficient of determination is the square of the correlation coefficient and can be interpreted as the percentage of the variance in the dependent variable that is explained by the estimated regression equation.
Hence, in this case, r2 would be 16, indicating that the estimated regression equation explains 16% of the variance in the dependent variable.
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Dwight Donovan, the president of Munoz Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of four years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $106,000 and for Project B are $47,000. The annual expected cash inflows are $40,947 for Project A and $16,131 for Project B. Both investments are expected to provide cash flow benefits for the next four years. Munoz Enterprises’ desired rate of return is 6 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.) Required Compute the net present value of each project. Which project should be adopted based on the net present value approach? Compute the approximate internal rate of return of each project. Which one should be adopted based on the internal rate of return approach?
The net present value of a project is the sum of the present values of all the expected cash inflows and outflows for the project, discounted at the desired rate of return. The net present value is used to evaluate the profitability of a project by taking into account the time value of money, which is the idea that a dollar received today is worth more than a dollar received in the future.
To calculate the net present value of Project A, we need to find the present value of each expected cash inflow and outflow, and then sum them together. The initial cash expenditure for Project A is $106,000, and the annual expected cash inflows are $40,947. Using the present value of $1 table, we can find the present value of each cash inflow and outflow by multiplying the amount by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:
Initial expenditure: $106,000 * 0.943 = $99,858
Annual inflows: $40,947 * 0.943 * 0.943 * 0.943 * 0.943 = $136,046
The net present value of Project A is the sum of the present values of all the cash inflows and outflows, which is $136,046 - $99,858 = $36,188.
To calculate the net present value of Project B, we can use the same approach. The initial cash expenditure for Project B is $47,000, and the annual expected cash inflows are $16,131. Using the present value of $1 table, we can find the present value of each cash inflow and outflow by multiplying the amount by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:
Initial expenditure: $47,000 * 0.943 = $44,441
Annual inflows: $16,131 * 0.943 * 0.943 * 0.943 * 0.943 = $52,210
The net present value of Project B is the sum of the present values of all the cash inflows and outflows, which is $52,210 - $44,441 = $7,769.
Based on the net present value approach, the best project to invest in is the one with the highest net present value. In this case, Project A has a higher net present value than Project B, so it would be the better choice.
The internal rate of return of a project is the discount rate that makes the net present value of the project equal to 0. In other words, it is the rate of return that an investor would expect to earn from the project if all the expected cash flows were realized.
To calculate the internal rate of return of Project A, we can use the present value of an annuity of $1 table. The initial cash expenditure for Project A is $106,000, and the annual expected cash inflows are $40,947. We can use the present value of an annuity of $1 table to find the present value of the cash inflows by multiplying the annual cash inflow by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:
Annual inflows: $40,947 * 4.597 = $187,340
We can then use the present value annuity formula to find the internal rate of return of Project A, which is the rate that makes the net present value of the project equal to 0:
0 = $106,000 + $187,340 / (1 + r)^4
Solving for r, we find that the internal rate of return of Project A is approximately 10.35 percent.
To calculate the internal rate of return of Project B, we can use the same approach. The initial cash expenditure for Project B is $47,000, and the annual expected cash inflows are $16,131. We can use the present value of an annuity of $1 table to find the present value of the cash inflows by multiplying the annual cash inflow by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:
Annual inflows: $16,131 * 4.597 = $73,711
We can then use the present value annuity formula to find the internal rate of return of Project B, which is the rate that makes the net present value of the project equal to 0:
0 = $47,000 + $73,711 / (1 + r)^4
Solving for r, we find that the internal rate of return of Project B is approximately 10.09 percent.
Based on the internal rate of return approach, the best project to invest in is the one with the highest internal rate of return. In this case, Project A has a higher internal rate of return than Project B, so it would be the better choice.
Overall, both the net present value approach and the internal rate of return approach suggest that Project A is the better investment option for Munoz Enterprises. Project A has a higher net present value and a higher internal rate of return than Project B, indicating that it is likely to be more profitable and provide a higher rate of return on the investment.
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 3sin^2(t), y = 3cos^2(t), 0 = t = 5p
Find the length of the curve.
By The length of the curve can be found using the formula for the arc length of a parametric curve, the distance traveled by the particle is 30π.
The length of the curve can be found using the formula for the arc length of a parametric curve:
L = ∫0→5p √(dx/dt)2 + (dy/dt)2 dt
We can calculate dx/dt and dy/dt as follows:
dx/dt = 6sin(t)cos(t)
dy/dt = -6sin(t)cos(t)
Substituting these values into the formula for the arc length gives us:
L = ∫0→5p √[(6sin(t)cos(t))2 + (-6sin(t)cos(t))2] dt
= ∫0→5p 6√(sin2(t)cos2(t)) dt
= 6∫0→5p |sin(t)cos(t)| dt
= 6∫0→5p sin(t)cos(t) dt
= 6[(1/2)sin2(t) + (1/2)cos2(t)]5p
= 6[(1/2)(1) + (1/2)(1)]5p
= 6(1)5p
= 30π
Therefore, the distance traveled by the particle is 30π.
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Traffic flow is defined as the rale at which traffic flow at particular cars pass through an intersection , measured in cars intersection is modeled by the function F defined per minute. The Fl) = 82 4sin for 0 < [ < 30, where F) is measured in cars per minute and IS measured in minutes_ To the nearest whole number; how many cars pass through the intersection Is the traffic flow increasing Or decreasing at over the 30-minute period? 7 ? Give Whal is the reason for your answer: average value Of the traffic now Whal = over the time interval 10 < Is the < 15 average rale of change of Indicate units of measure. measure . the traffic flow over the time interval 10 < <15 Indieate units
The average rate of change of the traffic flow over the time interval 10 < t < 15 is 0.1085 cars per minute. Since this value is positive, the traffic flow is increasing over this time interval.
The traffic flow at the intersection is modeled by the function F(t) = 82 - 4sin(t) for 0 < t < 30, where F(t) is measured in cars per minute and t is measured in minutes.
To find the total number of cars that pass through the intersection over the 30-minute period, we can integrate the function over the time interval from 0 to 30 minutes. The integral of the function is given by:
∫F(t)dt = ∫(82 - 4sin(t))dt
= 82t - 4cos(t) + C
Evaluating this integral at t = 0 and t = 30, we get:
82(0) - 4cos(0) + C = 0
82(30) - 4cos(30) + C = 2184
Solving for C, we get C = -246.
Substituting this value back into the integral equation, we get:
∫F(t)dt = 82t - 4cos(t) - 246
Plugging in t = 30, we get:
∫F(t)dt = 82(30) - 4cos(30) - 246 = 2184 - 246 = 1939
Therefore, the total number of cars that pass through the intersection over the 30-minute period is 1939 cars.
To determine whether the traffic flow is increasing or decreasing over the time interval 10 < t < 15, we can find the average rate of change of the traffic flow over this time interval. The average rate of change is given by:
(F(t2) - F(t1))/(t2 - t1)
Plugging in t1 = 10 and t2 = 15, we get:
(F(15) - F(10))/(15 - 10)
= (82 - 4sin(15) - (82 - 4sin(10)))/(5)
= (-4sin(15) + 4sin(10))/5
= (-4(√(6)/4) + 4(1/2))/5
= (-√(6) + 2)/5
= (-1.4575 + 2)/5
= 0.5425/5
= 0.1085
The units of measure for the average rate of change are cars per minute.
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What information do you need to know to write the equation of a line?
the slope of the line in quadrant 2
the location of two ordered pairs that lie along the line
the slope of the line and the location of the origin
the location of 1 ordered pair the lies along the line
The location of two ordered pairs that lie along the line. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
To write the equation of a line we need two at least two ordered pairs that lie along the line
By using two ordered pairs, we can find slope of a line
The formula to find the slope of a line is (y2-y1)/(x2-x1)
Using the slope and one ordered pair we can find y-intercept
By substituting slope(m) and y-intercept(c) in y=mx+c, we get equation of line.
Therefore, option B is the correct answer.
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Consider a particle in a rigid box of length L. For each of the states n = 1, n = 2 and n = 3:
a. Sketch graphs of ǀ (x) ǀ2. Label the points x = 0 and x = L.
b. Where, in terms of L, are the positions at which the particle is most likely to be found?
c. Where, in terms of L, are the positions at which the particle is least likely to be found?
d. Determine, by examining your ǀ (x) ǀ2 graphs, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than 1 3. Explain your reasoning.
e. Calculate the probability that the particle will be found in the left one-third of the box.
For states, n = 1, 2, and 3 the probability of finding the particle at left 1/3rd of the box is P₁ = (3/4) * (2/L)² P₂ = (1/4) * (2/L)² and P₃ = (1/3) * (2/L)² respectively
a.
The wave function for the particle in a rigid box of length L for the state
n = 1, is given by:
|ψ₁(x)|² = (2/L)² * sin²(πx/L)
the wave function for the state n = 2, is given by:
|ψ₂(x)|² = (2/L)² * sin²(2πx/L)
And the wave function for the state n = 3, is given by:
|ψ₃(x)|² = (2/L)² * sin²(3πx/L)
The graphs of |ψ₁(x)|², |ψ₂(x)|², and |ψ₃(x)|² is attached.
b.
The points of maximum probability density, which occur at x = 0 and x = L for all three states are the positions at which the particle is most likely to be found.
c.
The points of minimum probability density, occur at x = L/2 for the state
n = 1, and at x = L/4 and x = 3L/4 for the state n = 2. For the state n = 3, the points of minimum probability density occur at x = L/3, x = 2L/3, and
x = L are the positions at which the particle is least likely to be found.
d.
Since the probability density is highest at x = 0, which is in the left one-third of the box for the state n = 1 the probability of finding the particle in the left one-third of the box is greater than 1/3.
Since the probability density is highest at x = 0 and x = L, which are both outside the left one-third of the box for the state n = 2, the probability of finding the particle in the left one-third of the box is less than 1/3.
Since the probability density is highest at x = 0, which is in the left one-third of the box for the state n = 3, the probability of finding the particle in the left one-third of the box is equal to 1/3.
e.
We need to integrate the probability density over the region of interest to calculate the probability that the particle will be found in the left one-third of the box for each of the states n = 1, n = 2, and n = 3.
the probability for the state n = 1, is given by:
P₁ = ∫ |ψ₁(x)|² dx = (2/L)² * ∫ sin²(πx/L) dx
The probability for the state n = 2, is given by:
P₂ = ∫ |ψ_2(x)|² dx = (2/L)² * ∫ sin²(2πx/L) dx
The probability for the state n = 3, is given by:
P₃ = ∫ |ψ₃(x)|² dx = (2/L)² * ∫sin²(3πx/L) dx
Here all integrals have limits 0 and L/3
Solving these integrals gives:
P₁ = (3/4) * (2/L)²
P₂ = (1/4) * (2/L)²
P₃ = (1/3) * (2/L)²
Thus, the probabilities that the particle will be found in the left one-third of the box are:
P₁ = (3/4) * (2/L)²
P₂ = (1/4) * (2/L)²
P₃ = (1/3) * (2/L)²
for the states n = 1, n = 2, and n = 3, respectively.
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Consider the leaking bucket example from the lecture notes. The derivation for the governing equation assumed proportional relationship between the fluid exit velocity and the height of the water (i.e , Qout Kh(t)) . Another cOmmon assumption of this relationship (called the Toricelli model) assumes the relationship to be Qout Kvhc) Using built-in MATLAB solver; solve both differential equations below and plot the height of the water for 120 seconds where . 30 in" . K = 1.4.and h(O) 10 cm antor nro (t) dhpror Khpropt (t) = 0 What t0 turn in: a) A printout of each of your function files b) Publish your script file in which You use your functions
function dhdt = propt(t,h) %propt calculates the rate of change of the height of the liquid in the bucket given , %Define the initial condition h0 = 10; %Define the time span tspan = 0:120 with height of the water.
Function file 1:
function dhdt = propt(t,h) %propt calculates the rate of change of the height of the liquid in the bucket given by dhdt = -1.4h %Inputs: %t = time %h = height of the liquid in the bucket %Output: %dhdt = rate of change of the height of the liquid in the bucket dhdt = -1.4*h; end
Function file 2:
function dhdt = toricelli(t,h) %toricelli calculates the rate of change of the height of the liquid in the bucket given by dhdt = -K*sqrt(h) %Inputs: %t = time %h = height of the liquid in the bucket %Output: %dhdt = rate of change of the height of the liquid in the bucket K = 1.4; dhdt = -K*sqrt(h); end
Script file:
clear; close all; clc; %Define the initial condition h0 = 10; %Define the time span tspan = 0:120;
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Find all the real and complex eigenvalues of the following real matrices. Then, diagonalize them over C
, if possible. A=[0 2;-2 0]; B= [0-1 0; 1 0 0;0 0 1]
The eigenvalues of A are the complex numbers +2i and -2i.The diagonalized form of the matrix B is [1 0 0; 0 1 0; 0 0 -1]
A. A matrix A can be written in the form of
A = [a b; c d]
The eigenvalues λ of A can be calculated using the following formula:
λ = (a+d ± √(a+d)^2 -4(ad-bc))/2
Substituting the values of A gives
λ = (0 + 0 ± √(0)^2 - 4(-2))/2
λ = 2i and -2i
Since the eigenvalues are complex, the matrix cannot be diagonalized over C.
B. The eigenvalues of B can be calculated using the same formula as above
λ = (a+d ± √(a+d)^2 -4(ad-bc))/2
Substituting the values of B gives
λ = (0 + 1 ± √(1)^2 - 4(0))/2
λ = 1, 0, -1
To diagonalize the matrix, we must find the eigenvectors associated with each eigenvalue. The eigenvectors of B can be calculated using the following formula:
v = (a - λI)x
Substituting the values of B and the eigenvalues gives:
v1 = (0 - 1I)x
v2 = (0 - 0I)x
v3 = (0 - (-1I))x
The eigenvectors are
v1 = [1 0 0]
v2 = [1 0 0]
v3 = [0 1 0]
The diagonalized form of the matrix B is
[1 0 0; 0 1 0; 0 0 -1]
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Given: AB AC and DA bisects /BAC.
Prove: ZDBC ZDCB.
Step
Statement
AB AC
DA bisects BAC
AD AD
ZBAD ZDAC
A
Reason.
Given
Reflexive Property
Select a Resison
B
Solve for proof
Use photo to understand better PLEASE HELP
The correct option is C ie 3.
D is the midpoint of BC.
What is Congruence of triangles?
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
What are the congruency properties of a triangle?
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
RHS (Right angle-Hypotenuse-Side)
In triangles BAD and CAD,
(i) AD=AD (common)
(ii)∠DAB=∠CAD (Given, AD bisects ∠BAC)
(iii)AB = AC (given)
Thus, by SAS property both the triangles BAD and CAD are congruent .
By cpct , ∠ADB=∠ADC = x (let)
Since ∠ADB and ∠ADC lies in a straight line
So by the property of straight lines the sum is 180°.
Now ∠ADB+∠ADC= 180°
⇒x+x= 180°
⇒2x= 180°
⇒x=90°
∴AD ⊥ BC
By cpct ,BD=DC
So D is the midpoint of BC.
Hence option C that is 3 is the right answer.
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help i suck at math!!!!
Answer:
146
Step-by-step explanation:
the sides of a triangle always equal 180, so just subtract those numbers from 180
Gabe is practicing for his upcoming track meet. One lap around the track is 1/4 of a mile. Gabe sets a goal to
run more than 2 miles today. How many laps should Gabe run to meet his goal?
Answer:
20=-7
Step-by-step explanation:
j
Answer:
8 Laps
Step-by-step explanation:
This is because one lap is 1/4 so it would take 4 laps to make it a whole, which would be a mile.
We could now times this by two, since 1 mile is half of 2 miles.
4 x 2 = 8
Which would make it 8
What do I do now cause I’m stuck in the middle of the equation and not sure what else I may need to do besides make the x alone but I’m not sure how.
2x + 8 = 10
Answer:
x = 1
Step-by-step explanation:
2x + 8 = 10 Subtract 8 from both sides
2x + 8 - 8 = 10 - 8
2x = 2 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{2}{2}[/tex]
x = 1
Check:
2x + 8 = 10
2(1) + 8 = 10
2 + 8 = 10
10 = 10 checks.
To test if an observed frequency distribution with five classes is normally distributed, we need to find _____.a. The t-statisticb. The expected, normally distributed class frequenciesc. The class marksd. The class relative frequencies
Finding the t statistic is necessary to check the normality of a five-class observed frequency distribution.
what the T statistic means?The t-value gauges the magnitude of the difference in relation to the range of your sample's data. Or to put it another way, T is just the calculated difference shown in units of standard error. The evidence is stronger against the null hypothesis the larger the value of T.
Which T statistic value is optimal?In general, t-values that are more than +2 or less than -2 are acceptable. We are more confident in the coefficient's ability to predict outcomes the higher the t-value. Low t-values are a sign of the predictability of that coefficient's coefficient being unreliable.
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Give two ways to write K-6 in algebbraic expression
What is K in algebraic?
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra.
What does K mean in mathematics?
K is derived from the Greek word kilo, which signifies 1,000. The Greeks similarly referred to a million as M, which stands for Mega. Therefore, if we adhere to the Greek abbreviations, billion would be represented by the letter G. (Giga).
Give some examples of what algebraic expressions are.
image outcome
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). A good example of an algebraic expression is 3x2 2xy + c.
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PLEASE ANSWER FAST THIS IS TIMED
The graph of the linear inequation [tex]y \leq \frac{1}{2}x -5[/tex] has been described below
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by
[tex]> , < , \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
The given linear inequation is
[tex]y \leq \frac{1}{2}x -5[/tex]
Here equality is maintained. So the line is a solid line
Now, (0, 0) does not satisfy the inequality.
So the solution is below the line
When graphing the inequality above, we will draw a solid line and the solution lies below the line
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The sketch shows a curve with equation y = ab* where a and b are constants and b>0 The curve passes through the points (0,5) and (2,45) Calculate the value of a and b.
NEED PROPER ANSWER AND WORKING OUT
WILL MARK BRAINLIEST
q1 signaling when education is productive i 6 points grading comment: a single worker incurs a cost of obtaining education of amount ee given by: c(e)=3⋅e 2 The worker's wage is based on how much education he obtains. If he receives education less than a threshold amount e, then he receives a wage that is proportional to his level of education: w(e)=5⋅e And if he receives education greater than or equal to the threshold eˉ, then his wage is proportional to the threshold: w(e)=12⋅ e ˉ So the utility that he receives when he chooses a level of education e is a piecewise function: u(e)={ 5⋅e−3⋅e 2 12⋅ e ˉ −3⋅e 2 e< eˉ e⩾ eˉ Answer the following. Round all numeric answers to at least three decimal places. Suppose that
eˉ=0.5
The worker's marginal cost of education when e=0.5 is 6.00. the derivative of the cost function with respect to the amount of education obtained.
The worker's marginal cost of education is the rate of change in the cost of obtaining education with respect to the amount of education obtained. In this case, the worker's cost of obtaining education is given by the equation c(e)=3e². At e=0.5, we can calculate the marginal cost of education by taking the derivative of the cost function with respect to the amount of education obtained. This gives us the equation c'(e)=6. Thus, the worker's marginal cost of education when e=0.5 is 6.00.
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