What is the equation of the line shown in the graph below. Please I really need help.

If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

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Answer:

-18

Step-by-step explanation:

Hope This Helps :)

Answer:

5 2/5 ÷ 3/2 = 3.6

I hope this is right

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer:

y"-6y'+18y=0

Second order

Step-by-step explanation:

Since there are 2 constants, the order of the differential equation will be 2. This means we will need to differentiate twice.

y = e^(3x) (acos3x +bsin3x)​

y'=3e^(3x) (acos3x+bsin3x)

+e^(3x) (-3asin3x+3bcos3x)

Simplifying a bit by reordering and regrouping:

y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)

y"=

3e^(3x) cos3x (3a+3b)+-3e^(3x) sin(3x) (3a+3b)

+3e^(3x) sin3x (3b-3a)+3e^(3x) cos(3x) (3b-3a)

Simplifying a bit by reordering and regrouping:

y"=

e^(3x) cos3x (9a+9b+9b-9a)

+e^(3x) sin3x (-9a-9b+9b-9a)

Combining like terms:

y"=

e^(3x) cos3x (18b)

+e^(3x) sin3x (-18a)

Let's reorder y like we did y' and y".

y = e^(3x) (acos3x +bsin3x)

y=e^(3x) cos3x (a) + e^(3x) sin3x (b)

Objective is to find a way to combine or combine constant multiples of y, y', and y" so that a and b are not appearing.

Let's start with the highest order derivative and work down

y"=

e^(3x) cos3x (18b)

+e^(3x) sin3x (-18a)

We need to get rid of the 18b and 18a.

This is what we had for y':

y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)

Multiplying this by -6 would get rid of the 18b and 18a in y" if we add them.

So we have y"-6y'=

e^(3x) cos3x (-18a)+e^(3x) sin3x (-18b)

Now multiplying

y=e^(3x) cos3x (a) + e^(3x) sin3x (b)

by 18 and then adding that result to the y"-6y' will eliminate the -18a and -18b

y"-6y'+18y=0

Also the characteristic equation is:

r^2-6r+18=0

This can be solved with completing square or quadratic formula.

I will do completing the square:

r^2-6r+18=0

Subtract 9 on both sides:

r^2-6r+9=-9

Factor left side:

(r-3)^2=-9

Take square root of both sides:

r-3=-3i or r-3=3i

Add 3 on both sides for each:

r=3-3i or r=3+3i

This confirms our solution.

Another way to think about the problem:

Any differential equation whose solution winds up in the form y=e^(px) (acos(qx)+bsin(qx)) will be second order and you can go to trying to figure out the quadratic to solve that leads to solution r=p +/- qi

Note: +/- means plus or minus

So we would be looking for a quadratic equation whose solution was r=3 ×/- 3i

Subtracting 3 on both sides gives:

r-3= +/- 3i

Squaring both sides gives:

(r-3)^2=-9

Applying the exponent on the binomial gives:

r^2-6r+9=-9

Adding 9 on both sides gives:

r^2-6r+18=0

Answer:

The value is \(P(8 < X < 10 ) = 0.8186\)

Step-by-step explanation:

From the question we are told that

    The mean is  \(\mu = 10 .0\)

     The standard deviation is  \(\sigma = 1\)

Generally the probability that a single reading is between 8 and 10 is mathematically represented as

      \(P(8 < X < 10 ) = P( \frac{8 - 10 }{ 1} < \frac{X - \mu }{ \sigma } < \frac{10 - 10 }{1} )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

=>    \(P(8 < X < 10 ) = P( -2 < Z< 1 )\)

=>   \(P(8 < X < 10 ) = P( Z< 1 ) - P( Z < -2 )\)

From the z table  the area under the normal curve to the left corresponding to  1 and  -2  is  

       \(P( Z< 1 ) = 0.84134\)

and

     \(P( Z < -2 ) = 0.02275\)

=>   \(P(8 < X < 10 ) = 0.84134 - 0.02275\)

=>   \(P(8 < X < 10 ) = 0.8186\)

Answer:  about 79 ft, its 78.8 ft

Step-by-step explanation:

\(sin\)θ\(=\frac{opp}{hyp}\)

\(sin52=\frac{h}{100 ft}\)

\(100sin52=h\)

\(100(0.7880)=h\)

\(78.80 ft=h\)

Answer:

is it multiple choice?? and id say the 1st one

Step-by-step explanation:

Answer:

the sum of two whole numbers is always greater than either number because even if one of the numbers to be added is 0, the answer will, well, not be greater, but at least equal to it.

Step-by-step explanation:

plz mark as brainliest

The least number of mice that he has to take out of his hat would be 23.

We have the following details to solve this problem

x = 14

t = 8

u = 6

n1 = x + t + 1

= 14 + 8 + 1 = 23

​

n2 = t + u + 1

= 8 + 6 + 1 = 15

​

n3 = x + u + 1

= =14+6+1=21

From here the

max n (n1, n2, n3) = 23, 15, 21

Hence the least number that has to be taken out would be 23.

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Answer:

$780

Step-by-step explanation:

12,000X6.5=78,000

78,000/100=780

Answer:

\(P(HH\ u\ C) = \frac{13}{16}\)

Step-by-step explanation:

Given

The Venn diagram

Required

\(P(HH\ u\ C)\)

This is calculated as:

\(P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}\)

Where:

\(n(U) = 16\) --- count of students

\(n(HH\ u\ C) =13\)

So, we have:

\(P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}\)

\(P(HH\ u\ C) = \frac{13}{16}\)

Answer:

The answer is the 4th one

Answer: This is the right answer

Step-by-step explanation:

The dimensions of the Norman window that admit the greatest possible amount of light are approximately:

Width (w) ≈ 11.72 ft

Height (h) ≈ 2.91 ft

To find the dimensions of the Norman window that admit the greatest possible amount of light, we need to maximize the area of the window. The window consists of a rectangle and a semicircle, so the area is the sum of the areas of both shapes.

Let's assume the width of the rectangle is "w" and the radius of the semicircle is "r".

Since the diameter of the semicircle is equal to the width of the rectangle, the radius "r" is half of "w".

Area of the rectangle = w * h, where h is the height of the rectangle.

Area of the semicircle = (1/2) * π * r²

The perimeter of the window is given as 30 ft, which can be written as:

Perimeter = 2 * (w + h) + π * r + w

Since r = w/2, we can rewrite the perimeter equation as:

Perimeter = 2 * (w + h) + (π/2) * w + w

Perimeter = 2w + 2h + (π/2 + 1) * w

Given that the perimeter is 30 ft, we have:

30 = 2w + 2h + (π/2 + 1) * w

Now, we can express "h" in terms of "w" using the perimeter equation:

h = (30 - 2w - (π/2 + 1) * w) / 2

Next, let's express the area "A" of the window in terms of "w" using the formulas for the area of the rectangle and the semicircle:

Area (A) = Area of rectangle + Area of semicircle

A = w * h + (1/2) * π * r²

A = w * ((30 - 2w - (π/2 + 1) * w) / 2) + (1/2) * π * (w/2)²

A = w * ((30 - 2w - (π/2 + 1) * w) / 2) + (1/2) * π * (w² / 4)

Now, we want to maximize the area "A."

To find the maximum value, we take the derivative of "A" with respect to "w" and set it equal to zero:

dA/dw = (30 - 2w - (π/2 + 1) * w) / 2 + (π/4) * w = 0

Solving for "w":

(30 - 2w - (π/2 + 1) * w) / 2 + (π/4) * w = 0

(30 - 2w - (π/2 + 1) * w) + (π/2) * w = 0

(30 - (2 + π/2) * w) + (π/2) * w = 0

30 - (2 + π/2) * w + (π/2) * w = 0

(30 - 2w) + (π/2 - π/4) * w = 0

30 - 2w + (π/4) * w = 0

(π/4) * w - 2w = -30

w ((π/4) - 2) = -30

w = -30 / ((π/4) - 2)

w ≈ 11.72 ft

Now that we have the value of "w," we can find the value of "h" using the perimeter equation:

Perimeter = 2w + 2h + (π/2 + 1) * w

30 = 2(11.72) + 2h + (π/2 + 1) * (11.72)

30 = 23.44 + 2h + (π/2 + 1) * 11.72

2h = 30 - 23.44 - (π/2 + 1) * 11.72

2h = 6.56 - (π/2 + 1) * 11.72

h = (6.56 - (π/2 + 1) * 11.72) / 2

h ≈ 2.91 ft

So, the dimensions of the Norman window that admit the greatest possible amount of light are approximately:

Width (w) ≈ 11.72 ft

Height (h) ≈ 2.91 ft.

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The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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Answer:

This is not a right triangle

Step-by-step explanation:

the bottom and side would have to be equal

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

21

Step-by-step explanation:

Divide 26.2 by 1 1/4

The number of water stations needed for this marathon will be 20.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

A marathon is 26.2 miles long. There is a water station every 1 1/4 miles along the race route.

Convert the mixed fraction number into a decimal number. Then we have

1 1/4 miles = 1 + 1/4

1 1/4 miles = 1 + 0.25

1 1/4 miles = 1.25 miles

The number of water stations needed for this marathon will be

Let x be the number of water stations. Then the inequality is given as,

x < 26.2 / 1.25

x < 20.96

The number of water stations needed for this marathon will be 20.

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Answer:

\(x=-4\)

\(y=3\)

\(z=-5\)

Step-by-step explanation:

Given:

\(x+y+z=-6\)

\(x-6y-7z=-29\)

\(-7y-5z=4\)

Solve for \(x\) in the 1st equation:

\(x+y+z=-6\)

\(x+y=-z-6\)

\(x=-y-z-6\)

Substitute the value of \(x\) into the 2nd equation and solve for \(z\):

\(x-6y-7z=-29\)

\((-y-z-6)-6y-7=-29\)

\(-7y-z-13=-29\)

\(-7y-z=-16\)

\(-z=-16+7y\)

\(z=16-7y\)

Substitute the value of \(z\) into the 3rd equation and solve for \(y\):

\(-7y-5z=4\)

\(-7y-5(16-7y)=4\)

\(-7y-80+35y=4\)

\(28y-80=4\)

\(28y=84\)

\(y=3\)

Plug \(y=3\) into the solved expression for \(z\) and evaluate to solve for \(z\):

\(z=16-7(3)\)

\(z=16-21\)

\(z=-5\)

Plug \(z=-5\) into the solved expression for \(x\) and evaluate to solve for \(x\):

\(x=-(3)-(-5)-6\)

\(x=-3+5-6\)

\(x=2-6\)

\(x=-4\)

Therefore:

\(x=-4\)

\(y=3\)

\(z=-5\)

Step-by-step explanation: i d0nt kn00w

Least number of packages of plates Shaniya needs to buy=24

Based on the given problem above, it is mentioned that in one pack of cups has 6 and one pack of plates has 8. Therefore, the least number of packages of plates that Shaniya needs to buy is 3 packages and for the cups, it would be 4 packages. 4 x 6 is 24 cups, and 3 x 8 would be 24 plates.

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Final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.

Let's break down the steps to determine the final speed:

Step 1: Convert the speed from miles per minute to miles per hour.

Since you're driving one and a half miles per minute, we need to convert it to miles per hour. There are 60 minutes in an hour, so we multiply 1.5 by 60 to get 90 miles per hour.

Step 2: Slow down by 15 miles per hour.

Subtract 15 from the initial speed of 90 miles per hour, resulting in 75 miles per hour.

Step 3: Reduce the speed by one third.

To find one third of 75 miles per hour, we divide it by 3, which gives us 25 miles per hour.

Therefore, the final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.

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Answer:

I am god at this.

Step-by-step explanation:

Answer:

from the graph we can see that

for 2 gallones - it can travell 70 miles

4 gallones - 140 miles

we will take the first case

2 gallones - 70 miles

17 gallones - ? miles

cross multiply

\( \frac{17 \times 70}{2} \)

= 595 miles

We have two values:

Old = $49.60

New = $38.10

Then, if we need to find if the change is increasing or decreasing, we have to use the following expression:

We have that the subtraction in the numerator is negative (the new value is smaller than the old value). Then, we finally have a decrease in change.

If we round the result to the nearest integer, we have that we have a decrease of -23%.

Answer:

c.

Step-by-step explanation:

Answer:

(x-5)²+(y+2)²=289

Step-by-step explanation:

To do this recall that when writing the center we have the opposite sing

for example in the equation (x+b)²+(y+c)² the center would be (-b,-c)

so we can write (x-5)²+(y+2)²

To find the radius we take the square root of what's on the other side of the equation. So the inverse is 17² or 289

so the final answer is

(x-5)²+(y+2)²=289