The linearization of the function z=xy√ at the point (-2, 9) is: L(x,y) = -6 + 3√(x+2) - 2√(y-9)
The linearization of a function f(x,y) at a point (a,b) is given by:
L(x,y) = f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b)
where fx and fy are the partial derivatives of f with respect to x and y, evaluated at (a,b).
In this case, we have f(x,y) = xy√ and (a,b) = (-2,9). We need to find fx and fy at this point:
fx(x,y) = y√
fy(x,y) = x√
Evaluating these at (-2,9), we get:
fx(-2,9) = 3√
fy(-2,9) = -2√
So the linearization of f at (-2,9) is:
L(x,y) = f(-2,9) + fx(-2,9)(x+2) + fy(-2,9)(y-9)
= -6 + 3√(x+2) - 2√(y-9)
Therefore, the linearization of the function z=xy√ at the point (-2, 9) is:
L(x,y) = -6 + 3√(x+2) - 2√(y-9).
To learn more about partial derivatives visit: https://brainly.com/question/31397807
#SPJ11
From a group of 13 men, 6 women, 2 boys, and 4 girls, (a) In how many ways can a man, a woman, a boy, and a girl be selected? (b) In how many ways can a man or a girl be selected? (c) In how many ways can one person be selected?
(a) A man, a woman, a boy, and a girl can be selected in 312 ways.
(b) A man or a girl can be selected in 57 ways.
(c) One person can be selected in 25 ways.
(a) To select a man, a woman, a boy, and a girl, use the multiplication principle. There are 13 men, 6 women, 2 boys, and 4 girls, so the number of ways is 13 * 6 * 2 * 4 = 312 ways.
(b) To select a man or a girl, there are 13 men and 4 girls, so the number of ways is 13 + 4 = 17 ways.
(c) To select one person, there are a total of 13 men + 6 women + 2 boys + 4 girls = 25 people, so there are 25 ways to choose one person.
To know more about multiplication principle click on below link:
https://brainly.com/question/17514196#
#SPJ11
2. Nemani buys a TV on hire purchase. The cash price is $1250. He pays $450 deposit and 12 monthly instalments of $95.How much interest is paid by Nemani.
Answer:
Nemani has paid $1250 for a TV on hire purchase. The cash price was $1250, so the total cost to Nemani was $1300. Nemani has paid $450 deposit and 12 monthly instalments of $95, for a total of $1445.
So, Nemani has paid an interest rate of 10% on his total payment.
Find the solution of the initial value problem
y′′ − y = 0 y(0) =
5
4, y′ (0) = −
3
4
Plot the solution for 0 ≤ t ≤ 2 and determine its minimum value.
The characteristic equation for the differential equation y′′ − y = 0 is r^2 - 1 = 0. This has roots r = ±1. Therefore, the general solution to the differential equation is y(t) = c1 e^t + c2 e^(-t).
Using the initial conditions, we can solve for the values of c1 and c2:
y(0) = 5/4 = c1 + c2
y'(0) = -3/4 = c1 - c2
Solving these equations simultaneously, we get c1 = 1/2 and c2 = 3/4. Therefore, the solution to the initial value problem is:
y(t) = 1/2 e^t + 3/4 e^(-t)
To find the minimum value of the solution, we can take the derivative of y(t) and set it equal to 0:
y'(t) = 1/2 e^t - 3/4 e^(-t)
y'(t) = 0 when e^t = (3/2) e^(-t)
e^(2t) = 3/2
t = ln(sqrt(3/2))
Substituting this value of t back into the original equation, we get the minimum value of the solution:
y(ln(sqrt(3/2))) = 1/2 e^(ln(sqrt(3/2))) + 3/4 e^(-ln(sqrt(3/2)))
y(ln(sqrt(3/2))) = sqrt(3)/4 + 3/(4sqrt(3))
y(ln(sqrt(3/2))) = (4sqrt(3) + 3)/(4sqrt(3))
Therefore, the minimum value of the solution is (4sqrt(3) + 3)/(4sqrt(3)) which is approximately 1.068.
To plot the solution for 0 ≤ t ≤ 2, we can use a graphing calculator or software to graph y(t) = 1/2 e^t + 3/4 e^(-t) and then set the viewing window to show the interval [0, 2].
The path of a particle is defined by ,2 = 4kx. and the component of velocity along the y axis is 1y ct. where both k and c are constants. Determine the . and y components of acceleration_
The x and y components of acceleration are:- [tex]ax = (1/k)(c(dy^2/dt^2)),- ay = c(d^2y/dt^2)[/tex]
To find the x-component of acceleration, we need to take the second derivative of the position function with respect to time:
2 = 4kx
2v = 4kx' (taking the derivative with respect to time)
2a = 4kx'' (taking the derivative of v with respect to time)
So the x-component of acceleration is a_x = 2kx''.
To find the y-component of acceleration, we can use the given information about the velocity along the y-axis:
v_y = 1y ct
Taking the derivative with respect to time, we get:
a_y = c
So the y-component of acceleration is simply a_y = c.
To determine the x and y components of acceleration for the given path of a particle and the component of velocity along the y-axis, we'll use the given equations and find the second derivatives with respect to time.
The path of the particle is defined by [tex]y^2[/tex] = 4kx. First, differentiate this equation with respect to time (t) to find the relation between the x and y components of velocity:
(1) 2y(dy/dt) = 4k(dx/dt)
The component of velocity along the y-axis is given as vy = dy/dt = cy. Substituting this into equation (1):
(2) 2y(cy) = 4k(dx/dt)
Now, solve for dx/dt (vx):
[tex]vx = (1/k)(cy^2/2)[/tex]
Next, differentiate both vx and vy with respect to time to find the x and y components of acceleration:
[tex]ax = d^2x/dt^2 = (1/k)(c(dy^2/dt^2))[/tex]
[tex]ay = d^2y/dt^2 = c(d^2y/dt^2)[/tex]
To learn more about derivative visit;
brainly.com/question/30365299
#SPJ11
I need the answer pls someone help
The surface area of the cylinder given is approximately calculated as: 960.84 square meters.
What is the Surface Area of a Cylinder?The surface area of a cylinder can be found by adding the areas of its curved surface (lateral area) and its two circular bases.
If the cylinder has a radius of r and a height of h:
Surface Area = 2πr(h + r)
Given the following:
Radius (r) = 9 m
Height (h) = 8 m
π = 3.14
Substitute:
Surface area of the cylinder = 2 * 3.14 * 9(8 + 9)
= 56.52(17)
= 960.84 square meters.
Learn more about the surface area of a cylinder on:
https://brainly.com/question/20720526
#SPJ1
A(–1,1) B(1,3) C(3,a) are points and AB=CB find "a"
We need to check if a = 1 satisfies the original condition that AB = CB. If a = 1, then CB = √[(1 - 3[tex])^2[/tex] + (3 - 1[tex])^2[/tex]] = √[4 + 4] = 2√(2), which is equal to AB. Therefore, the solution is a = 1 or 5.
First, we need to find the length of AB and CB using the distance formula:
AB = √(1 - (-1)[tex])^2[/tex] + (3 - 1[tex])^2[/tex]] = √[4 + 4] = 2√(2)
CB = √(a - 3[tex])^2[/tex] + (3 - 1[tex])^2[/tex]]
Since AB = CB, we can set the two expressions equal to each other:
2√(2) = √[(a - 3[tex])^2[/tex] + 4]
Squaring both sides, we get:
8 = (a - 3[tex])^2[/tex] + 4
Subtracting 4 from both sides, we get:
4 = (a - 3[tex])^2[/tex]
Taking the square root of both sides, we get:
2 = a - 3 or -2 = a - 3
Solving for a, we get:
a = 5 or a = 1
However, we need to check if a = 1 satisfies the original condition that AB = CB. If a = 1, then CB = √[(1 - 3[tex])^2[/tex] + (3 - 1[tex])^2[/tex]] = √[4 + 4] = 2√(2), which is equal to AB. Therefore, the solution is a = 1 or 5.
Learn more about expressions
https://brainly.com/question/14083225
#SPJ4
The marked price on a Bridget slippers is $2500. Sales tax of 8% is added. What is the cost of the item?
Answer:
Cost of item = $2500 + $200
Cost of item = $2700
Step-by-step explanation:
0_0
brainliest for help plss
The value of x , given the angle and the lines drawn , would be 142 degrees .
How to find x angle ?The fact that a straight line was drawn such that x degrees and 38 degrees make up the angles of that line , means that the total angular measure would be 180 degrees because this is the angle of a straight line.
This therefore means that to find the value of x, the formula would be :
x = 180 - 38
x = 180 - 38
x = 142 degrees
In conclusion, the value of x would be 142 degrees.
Find out more on angles at https://brainly.com/question/23925137
#SPJ1
Marcos is making bags of trail mix for hiking club. He will use 21 ounces of walnuts, 10.2 ounces of almonds, and 28.3 ounces of cashews. This amount makes 25 bags of trail mix. How many ounces are in each bag?
PLS HELP
The quantity of ounces for each bag would be as follows:
walnut= 8.82
almonds = 4.29 and
cashew = 11.89 ounces.
How to calculate the quantity of ounce for each bag?The quantity of walnut used = 21 ounces
The quantity of almonds used = 10.2 ounces
The quantity of cashew used = 28.3 ounces
Total = 59.5ounces.
The total ounces makes up = 25 bags
The ounce of each bag;
walnut = 21/59.5×25/1
= 8.82
almonds= 10.2/59.5 × 25/1
= 4.29
cashew = 28.3/59.5 × 25/1
= 11.89
Learn more about weight here
https://brainly.com/question/29892643
#SPJ1
find the area under the standard normal curve to the left of z=−1.51z=−1.51 and to the right of z=1.4z=1.4. round your answer to four decimal places, if necessary
The area under the given standard normal curve is approximately 0.1463
How to find the area under the standard normal curve?To find the area under the standard normal curve to the left of z=-1.51 and to the right of z=1.4, follow these steps:
1. Look up the z-scores in the standard normal table (also known as the z-table).
2. Find the area associated with z=-1.51 and z=1.4.
3. Add the areas together.
Using the z-table:
- For z=-1.51, the area to the left is 0.0655.
- For z=1.4, the area to the right is 1 - 0.9192 = 0.0808.
Now, add the areas together:
0.0655 + 0.0808 = 0.1463
So, the area under the standard normal curve to the left of z=-1.51 and to the right of z=1.4 is approximately 0.1463, rounded to four decimal places.
Learn more about standard normal curve
brainly.com/question/29184785
#SPJ11
What expression is equivalent to the expression -3.5 (2- 1.5n) - 4.5n??
Answer:
-7+0.75n
I would give an explanation but im bad at explaining
PLEASE HELP!!!!!! CHECK PICTURES BELOW!
By rigid transformations, the images of the parent function are, respectively:
Case 1: f(x) = - |x| + 3
Case 2: f(x) = |x - 2| - 2
Case 3: f(x) = |x + 15|
Case 4: f(x) = - |x + 3| + 3
How to find an absolute value function by rigid transformations
In this problem we must derive the absolute value functions by means of rigid transformations used on parent function f(x) = |x|. We proceed to apply any of the following rigid transformations:
Horizontal translation
f(x) → f(x - k), where k > 0 for a right translation.
Vertical translation
f(x) → f(x) + k, where k > 0 for a upward translation.
Reflection around x-axis
f(x) → - f(x)
Case 1 (Reflection - Vertical translation)
f(x) = - |x| + 3
Case 2 (Horizontal translation - Vertical translation)
f(x) = |x - 2| - 2
Case 3 (Horizontal translation)
f(x) = |x + 15|
Case 4 (Reflection - Horizontal translation - Vertical translation)
f(x) = - |x + 3| + 3
To learn more on rigid transformations: https://brainly.com/question/28032699
#SPJ1
fill in the blank. (enter your answer in terms of s.) ℒ{e−3t}
The value of ℒ{e−3t} is 1 / (s + 3).
Explanation: -
Given the Laplace transform of e^(-3t), you need to fill in the blank with the answer in terms of 's'.
The Laplace transform of e^(-at) is given by the formula:
ℒ{e^(-at)} = 1 / (s + a)
In your case, a = 3. Now, we can substitute this value into the formula:
ℒ{e^(-3t)} = 1 / (s + 3)
This function has a pole at s = 3, which means it is undefined at that point. However, for all other values of s, the Laplace transform is well-defined and can be used to solve differential equations that involve e^(-3t).
It's important to note that the Laplace transform is a powerful tool for solving differential equations, but it is not always necessary or convenient to use.
In some cases, it may be more efficient to solve the differential equation directly using other methods. However, when the Laplace transform is applicable, it can greatly simplify the solution process and provide valuable insights into the behavior of the system.
Know more about the "Laplace transform" click here:
https://brainly.com/question/31481915
#SPJ11
LetD1be the solid in space that lies in the octant where x≥0,y≤0,z≥0, and between the sphere x^2+y^2+z^2=3and the spherex^2+y^2+z^2=7. Express D1in spherical coordinates.
The required answer is the solid D1 in spherical coordinates is defined by: - sqrt(3) ≤ ρ ≤ sqrt(7) - 0 ≤ θ ≤ π/2 - 0 ≤ φ ≤ π/2
To express the solid D1 in spherical coordinates, we need to first understand the given conditions and the equations of the spheres.
D1 is in the octant where x≥0, y≤0, and z≥0. The two spheres have the equations x^2+y^2+z^2=3 and x^2+y^2+z^2=7.
Now, let's convert these equations into spherical coordinates. Recall that the spherical coordinates (ρ, θ, φ) are related to the Cartesian coordinates (x, y, z) as follows:
x = ρ * sin(φ) * cos(θ)
y = ρ * sin(φ) * sin(θ)
z = ρ * cos(φ)
Since x^2+y^2+z^2=ρ^2, the given spheres can be represented in spherical coordinates as:
1. ρ^2 = 3, so ρ = sqrt(3)
2. ρ^2 = 7, so ρ = sqrt(7)
A spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.
Now, we need to determine the range for θ and φ that corresponds to the specified octant. Since x≥0, y≤0, and z≥0, we have the following constraints on the angles:
- 0 ≤ θ ≤ π/2 (due to x≥0 and y≤0)
- 0 ≤ φ ≤ π/2 (due to z≥0)
So, the solid D1 in spherical coordinates is defined by:
- sqrt(3) ≤ ρ ≤ sqrt(7)
- 0 ≤ θ ≤ π/2
- 0 ≤ φ ≤ π/2
To know more about spherical coordinates. Click on the link.
https://brainly.com/question/4465072
#SPJ11
on wednesday, a student reads 812 pages of a book. on thursday, the student reads 3 times as many pages of the book.how many pages does the student read on thursday?
Therefore, the student reads 2,436 pages on Thursday by the given equation.
According to the given information, the student reads three times as many pages on Thursday as on Wednesday. Let's say that the number of pages read on Wednesday is represented by the variable w. Then, we can write the equation:
Pages on Thursday = 3 * Pages on Wednesday
In this equation, we know that Pages on Wednesday = w. So we can substitute w into the equation and get:
Pages on Thursday = 3w
We are also given that on Wednesday, the student read 812 pages. So we can substitute 812 for w and get:
Pages on Thursday = 3 * 812
Simplifying, we get:
Pages on Thursday = 2,436
To know more about equation,
https://brainly.com/question/28243079
#SPJ11
etermine whether the following equation is separable. If so, solve the given initial value problem. y'(t) 4y e. y(0) = 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation is separable. The solution to the initial value problem is y(t) e4e (Type an exact answer in terms of e.) B. The equation is not separable.
The equation is separable. The solution to the initial value problem is y(t) = e^(4 * e^t) , therefore option A is correct.
To determine whether the given equation is separable and solve the initial value problem:
We will follow these steps:
STEP 1: Identify the given differential equation: y'(t) = 4y * e^t
STEP 2: Rewrite the equation in terms of dy/dt: dy/dt = 4y * e^t
STEP 3:Rearrange the terms to separate variables: (1/y) dy = 4 * e^t dt
STEP 4:Integrate both sides: ∫(1/y) dy = ∫4 * e^t dt
STEP 5:Evaluate the integrals: ln|y| = 4 * e^t + C1 (we can drop the absolute value since y > 0)
STEP 6:Solve for y: y = e^(4 * e^t + C1)
STEP 7:Apply the initial condition y(0) = 1: 1 = e^(4 * e^0 + C1)
STEP 8:Solve for C1: C1 = 0
STEP 9:Substitute C1 back into the solution: y(t) = e^(4 * e^t)
The equation is separable. The solution to the initial value problem is y(t) = e^(4 * e^t) (Type an exact answer in terms of e).
To know more about Separable:
https://brainly.com/question/27928263
#SPJ11
The diagonals of rectangle KLMN intersect at the point (2, 1). One of the vertices of rectangle KLMN is located at (-4, 5). A 8 6 -5 4 -3 -2 3 -4 5 6 7 8 9 89 Which of the following could be the location of another vertex of this rectangle?
Answer:
H (8, -3)
Step-by-step explanation:
You want a possible vertex of rectangle KLMN if the midpoint of the diagonals is (2, 1) and one of the vertices is (-4, 5).
RectangleThe diagonals of a rectangle are congruent and bisect each other, so the given point of intersection is the midpoint of the diagonals. If one of the diagonal end points is K = (-4, 5), then the other end of that diagonal is ...
X = (K+M)/2
M = 2X -K = 2(2, 1) -(-4, 5) = (2·2+4, 2·1-5)
M = (8, -3)
Another vertex on the rectangle is (8, -3).
__
Additional comment
Segment KM will be the diameter of the circumcircle of the rectangle. Other possible vertices will lie on that circle. As it happens, none of the offered choices is the same distance from X as point K is.
The attached figure shows the given diagonal and one of an infinite number of possible rectangles KLMN.
The choice of naming the given vertex K is arbitrary.
d Points J, K, L, M have polar coordinates (6, 130°), (6, 160°), (6, 200°), (6, 250°) respectively. Show that the sum of KJM and KLM is 180°.
Okay, let's solve this step-by-step:
* Points J, K, L, M have polar coordinates:
J (6, 130°)
K (6, 160°)
L (6, 200°)
M (6, 250°)
* To find the angle between two points, we subtract their theta values (polar angle coordinates).
* Angle KJM = 160° - 130° = 30°
* Angle KLM = 250° - 200° = 50°
* Sum of angles KJM and KLM = 30° + 50° = 80°
* Since the sum of angles in any triangle is 180°, and we have 80°, the remaining angle must be 180° - 80° = 100°.
* Therefore, the sum of angles KJM and KLM is 180°.
Does this make sense? Let me know if you have any other questions!
A fisherman is measuring the amount of bait he has remaining, y, in his bucket. He puts 20 pieces of bait in his bucket at the beginning of his fishing trip and uses 2 pieces every hour, x.
What is the slope for this linear relationship, and what does it mean in this situation?
−2; the amount of bait decreases by 2 pieces each hour
2; the amount of bait increases by 2 pieces each hour
−20; the amount of bait in the bucket when the fishing trip began
20; the amount of bait in the bucket when the fishing trip began
The slope for this linear relationship is -2, and it means that the amount of bait decreases by 2 pieces each hour in this situation.
The slope for this linear relationship is -2, which means that the amount of bait in the bucket decreases by 2 pieces for every hour of fishing. This slope indicates a constant rate of change in the amount of bait over time.
To understand this further, we can interpret the slope as the rate of consumption of bait per hour. Since the fisherman uses 2 pieces of bait every hour, the amount of bait in the bucket decreases by 2 pieces every hour. This linear relationship can be represented by the equation:
y = -2x + 20
where y is the amount of bait remaining in the bucket after x hours of fishing.
Therefore, the slope of -2 in this context is an important characteristic of the linear relationship between the amount of bait remaining and the time spent fishing. It tells us the rate at which the bait is being consumed, and helps the fisherman predict how much bait he will have left after a certain amount of time.
To learn more about slope here:
https://brainly.com/question/3605446
#SPJ1
How tall is the school?
I have no clue how to answer this question Will give brainliest to the correct answer +30 points
Answer:
B
Step-by-step explanation:
If a figure is enlarged by a scale factor of 1, the new figure will have the same size and shape as the original figure.
If a figure is enlarged by a negative scale factor, the new figure will be on the other side of the centre of enlargement and will be inverted (the figure appears upside down).
Therefore, if you enlarge shape X by a scale factor of -1, it will have the same size and shape as shape X, but it will be upside down.
Further information
A is a reflection across a vertical line.
C is a reflection across a horizontal line.
D is a rotation of 90° clockwise.
E is a rotation of 90° anticlockwise.
F is an enlargement of scale factor 1.
speed of the car in both miles per hour and kilometers per hour. The table below shows her results.
RECORDED SPEEDS
Speed
(miles per hour)
11.0
26.0
34.0
Speed
(kilometers per hour)
17.699
41.834
54.706
Based on her results, which statement describes the relationship between m, the speed of the car in miles per hour, and
k, the speed of the car in kilometers per hour?
The relationship is proportional because the ratio of m to k is constant.
The relationship is not proportional because the ratio of m to k is constant.
The relationship is proportional because the difference between m and k is constant.
The relationship is not proportional because the difference between m and k is constant.
Based on her results, the statement that describes the relationship between m, the speed of the car in miles per hour, and k, the speed of the car in kilometers per hour is A.. The relationship is proportional because the ratio of m to k is constant.
How to solveTo ascertain whether the relationship is indeed proportional, we shall evaluate if the ratio of m to k remains consistent.
For each specified speed:
m = 11.0 mph, k = 17.699 kph
Ratio = 11.0 / 17.699 ≈ 0.621
m = 26.0 mph, k = 41.834 kph
Relation = 26.0 / 41.834 ≈ 0.622
m = 34.0 mph, k = 54.706 kph
Relation = 34.0 / 54.706 ≈ 0.621
The ratios - which are almost identical (0.621, 0.622, and 0.621) - lead us to believe that the correlation between m and k is a proportional one.
Read more about speed here:
https://brainly.com/question/13943409
#SPJ1
Shelly measures the dimensions of her bedroom so she can buy new carpet..
Which set of dimensions for Shelly's carpet is most reasonable?
A
B
C
D
12 feet by 10 feet
60 inches by 36 inches
20 meters by 18 meters
100 centimeters by 80 centimeters
Answer:
12 feet × 10 feet
Step-by-step explanation:
12 feet × 10 feet is the size of a modest bedroom.
60in × 36in is only 5×3 feet, more like a closet.
20×18m is around 60×54feet something like a whole studio apartment or 1-bedroom apartment.
100×80cm is like 3 feet by lessthan 3 feet like a doormat size or maybe a coat closet.
B 0 Let A= where B and C are square. Show that A is invertible if and only if both B and C are invertible. ос 0 Another way to write A-1 is A-1 = *-[:]"[23 -1 Combining the expression for A from above with this expression gives the following equation. 1 D 0 B 0 OG 0 Cº1 This proves that A is invertible only if B and C are invertible. Now prove the converse of this statement. Suppose that B and C are invertible. Compute AA-1 1 во B 0 -1 = АА ос 0 C-1 I 0 0 I 0
A is invertible if and only if both B and C are invertible.
To prove the converse statement, we need to show that if both B and C are invertible, then A is also invertible.
Assume that B and C are invertible. We need to find the inverse of A.
Let D = BC. Since B and C are invertible, D is also invertible. Moreover, we have:
A = [D 0; 0 I]
where 0 is a square matrix of the same size as B and I is the identity matrix of the same size as C.
To find the inverse of A, we need to find a matrix A-1 such that:
AA-1 = A-1A = I
Let:
A-1 = [E F; G H]
where E, F, G, and H are matrices of appropriate sizes.
Then we have:
AA-1 = [D 0; 0 I][E F; G H] = [DE GF; DG+HI]
and
A-1A = [E F; G H][D 0; 0 I] = [ED FG; GH+I]
Setting these equal to I and equating corresponding entries, we get:
DE = ED = I (since D is invertible)
GF = 0
DG + HI = 0
ED = DE = I (since D is invertible)
FG = 0
GH + I = 0
From the first equation, we have E = D-1. From the second equation, we have F = 0. From the third equation, we have G = -D-1H. Substituting these values into the fourth and sixth equations, we get:
-HD-1H + I = 0
which implies that HD-1H = D-1.
Since D = BC and both B and C are invertible, we have D-1 = C-1B-1. Substituting this into the above equation, we get:
HC-1B-1H = I
which implies that H(BH)-1(C-1H)-1 = I. Since B and C are invertible, BH and C-1H are also invertible. Therefore, H is invertible and we have:
A-1 = [D-1 0; -D-1HC-1B-1 D-1]
Thus, A is invertible if and only if both B and C are invertible.
To learn more about square matrix visit:
https://brainly.com/question/4017205
#SPJ11
A food processing plant has a plant has a particular problem with the processing of perishable foods .All deliveries must be processed in a single day, although there are a number of processing machines available, they are very expensive to run. A research developed the formula: Y=12x-2a-a, to describe the profit (Y in thousands) given the number of machines used (x) and number of deliveries in a day. - show that the system is uneconomical if four deliveries are made in a day - if these deliveries are made in a day,find the number of machines that would be used in order that profit is maximized Hint : find Maxima
Step-by-step explanation:
To show that the system is uneconomical if four deliveries are made in a day, we need to find the profit (Y) for x machines and 4 deliveries:
Y = 12x - 2a - a (for 4 deliveries)
Y = 12x - 3a
We know that processing all deliveries must be done in a single day, so we have:
a = 4x
Substituting this into the profit formula, we get:
Y = 12x - 3(4x)
Y = 0
This means that the profit (Y) is zero when four deliveries are made in a day, making the system uneconomical.
To find the number of machines that would be used in order for profit to be maximized for four deliveries in a day, we need to differentiate the profit formula with respect to x and set it equal to zero to find the maximum:
dY/dx = 12 - 6a = 0 (for a = 4x)
Solving for x, we get:
12 - 6(4x) = 0
12 - 24x = 0
x = 1/2
Therefore, the maximum profit would be obtained by using 1/2 of a machine (which is not physically possible, so we would round up to one machine) for processing four deliveries in a day.
UNSCRAMBLE THE WORDS
OLTONUSI
QNIEUOAT
EDVIDI
VOET
F
Answer:
SOLUTION
EQUATION
DIVIDE
VOTE
F
the following argument purports to show that every real number in the interval [0,00) is rational: "Suppose toward a contradiction that there exists a real number in the interval [0,00) that is not rational. So the set A:= {2 € (0,0): 2¢} is non-empty. Then by the Wellordering Principle, there is a smallest element of A, which we'll denote by 7. Now 0, being an integer, is also rational, so i cannot be 0. Hence, since ī> 0 by virtue of its membership in A, it follows that I >0. Let z:=/2, and note that 0 0). Since z <ī and ī is the smallest element of A, it follows that z ¢ A. Since z is a real number in the interval [0, 0), and 2 & A, it follows from the definition of the set A that z is rational. Then I = 2z is rational too, since the rationals are closed under multiplication. Hence i is rational, which contradicts the fact that I e A." Briefly in one sentence) explain what the MAJOR problem is in the passage above. Don't just say that there are non-rational real numbers or give an example of a non-rational real number (we all know that "every real number in [0,00) is rational" is false; I want you to point out exactly where the purported proof of it goes awry).
The major problem in the passage is that it assumes the existence of a smallest element in the set A, which is not true for all non-empty subsets of the real numbers .a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.
The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.
To know more about real number .Click on the link.
https://brainly.com/question/10547079
#SPJ11
help pls!!!!!!!!!!!!!!
The quadratic function with the given features is defined as follows:
y = 0.86x² - 5.86x + 5.
How to define a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
When x = 0, y = 5, hence the coefficient c is given as follows:
c = 5.
Hence:
y = ax² + bx + 5.
When x = 1, y = 0, hence:
a + b + 5 = 0
a + b = -5.
The discriminant is given as follows:
D = b² - 4ac.
Hence:
D = b² - 20a
The minimum value is of -4, hence:
-D/4a = -5
(b² - 20a)/4a = -5
b² - 20a = 20a
b² = 40a
Since a = -5 - b, we have that the value of b is obtained as follows:
b² = 40(-5 - b)
b² + 40b + 200 = 0.
b = -5.86.
Hence the value of a is of:
a = -5 + 5.86
a = 0.86.
Then the equation is:
y = 0.86x² - 5.86x + 5.
More can be learned about quadratic functions at https://brainly.com/question/1214333
#SPJ1
(PLEASE DO NOT USE CHAT GPT)You are going to calculate what speed the kayaker 's are paddling, if they stay at a constant rate the entire trip, while kayaking in Humboldt bay. key information:
River current: 3 miles per hour
Trip distance: 2 miles (1 mile up, 1 mile back)
Total time of the trip: 3 hours 20 minutes
1) Label variables and create a table
2) Write an equation to model the problem
3) Solve the equation. Provide supporting work and detail
4) Explain the results
The solutions are given below.
1) Variables:
- Speed of the kayaker (unknown, let's call it x)
- Speed of the current = 3 mph (given)
- Distance kayaked one way = 1 mile (given)
- Total distance covered (round trip) = 2 miles (given)
- Total time of the trip = 3 hours 20 minutes = 3.33 hours (converted to hours for convenience)
Table:
Photo attached.
2) The equation to model the problem is:
distance = rate × time
Using this equation for each kayaking portion, we get:
1 = (x - 3) t
1 = (x + 3) t
We also know that the total time of the trip is 3.33 hours:
t + t = 3.33
2t = 3.33
t = 1.665
3) Now we can solve for x by substituting t = 1.665 in either of the above equations:
1 = (x - 3) (1.665)
x - 3 = 0.599
x = 3.599
Thus, the kayakers are paddling at a speed of 3.599 miles per hour.
4) The kayakers are paddling at a speed of 3.599 miles per hour. This solution is obtained by calculating the average speed of the kayakers over the entire trip, taking into account the opposing speed of the river current. The kayakers are traveling faster downstream (with the current) than upstream (against the current).
To learn more on speed click:
brainly.com/question/28224010
#SPJ1
Seven economic drivers that influence transportation costs were presented. They are distance, weight, density, stowability, handling, liability, and market.
Select a specific product, and discuss how each factor will impact the determination of a freight rate.
Let's consider the specific product of packaged food items, such as canned goods and dry goods, which are transported from a warehouse to a grocery store.
What are Seven economic drivers that influence transportation costs were presented?Distance: The distance between the warehouse and grocery store will affect the transportation cost. The farther the distance, the higher the freight rate will be.
Weight: The weight of the packaged food items will also impact the freight rate. The heavier the items, the higher the cost of transportation.
Density: The density of the packaged food items is a measure of how much space they occupy in relation to their weight. If the items are low in density, they may take up more space on a truck, and therefore, the freight rate will be higher.
Stowability: The stowability of the packaged food items refers to how easy they are to store and stack on a truck. If the items are difficult to stack, more space may be required, and the freight rate will be higher.
Handling: The handling of the packaged food items is also a factor in determining the freight rate. If the items require special handling, such as refrigeration or careful stacking, the freight rate will be higher.
Liability: Liability refers to the risk of damage or loss of the packaged food items during transportation. If the items are fragile or perishable, the freight rate will be higher to cover the higher risk of damage or loss.
Market: The market conditions, such as supply and demand, will also influence the freight rate. If there is a high demand for transportation services or a shortage of trucks, the freight rate will be higher.
Overall, the freight rate for transporting packaged food items will depend on multiple factors, including distance, weight, density, stowability, handling, liability, and market conditions. Transport companies will consider all of these factors when determining the freight rate for a particular shipment.
to know ore about product
brainly.com/question/22852400
#SPJ1