5. [-15 Points] DETAILS 0/2 Submissions Used Find the absolute maximum and absolute minimum values off on the given interval. f(x) = 6x4 - 8x3 - 24x2 + 1, 1-2, 3] absolute minimum value absolute maximum value

The incenter is where a triangle's angle bisectors meet. Since C is the incenter, segment BC should be the angle bisector. So, there is an error in line 3; segment AB and BC are congruent.

Any triangle with any 2 sides that are the same length is defined as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides.

If all three angles of the three triangles are acute, the circumcenter of an isosceles triangle sits inside the triangle. The circumcircle's chords are the sides of the triangle. In this case, the circumcenter is outside of the triangle since one of the angles is 90 degrees.

The circumcenter of a triangle ABC is the location where the perpendicular bisectors of its sides cross.

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The complete question is given below:

Answer:

it is 20 if I am not mistakin

Answer:

2, -1

Step-by-step explanation:

Edge2022

Answer:

2, -1

Step-by-step explanation:

That seems like what the midpoint is to the picture

Answer:

Great tip

READ THE TEXTBOOK

Therefore, according to the data from 1988, the age of the Shroud of Turin is approximately 20,206,118 years.

(a) To find the value of the constant k in the differential equation C' = (-kC), we can use the fact that carbon-14 has a half-life of 5557 years. The half-life is the time it takes for half of the initial amount of carbon-14 to decay.

Using the formula for exponential decay, we have:

C_(t) = C₀ × e^{-kt},

where C₀ is the initial amount of carbon-14 at time t = 0.

Since the half-life is 5557 years, we know that after 5557 years, the amount of carbon-14 is reduced to half. Therefore, we have:

C_(5557) = C₀ × (1/2) = C₀ × e^{(-k) × 5557}.

Dividing the equation by C₀, we get:

1/2 = e^{(-k) × 5557}.

To solve for k, we take the natural logarithm of both sides:

ln(1/2) = (-k) × 5557.

ln(1/2) is equal to (-ln(2)), so we have:

(-ln(2)) = (-k) × 5557.

Simplifying, we find:

k = ln(2) / 5557.

Therefore, the value of the constant k in the differential equation C' = (-kC) is approximately k ≈ 0.00012427.

(b) In 1988, the Shroud of Turin was found to contain about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material. We can use this information to determine the age of the Shroud of Turin in 1988.

Let's denote the amount of carbon-14 in the freshly made cloth as C₀ (initial amount), and the amount of carbon-14 in the Shroud of Turin in 1988 as C_(1988).

We know that C_(1988) is 91% of C₀. So we have:

C_(1988) = 0.91 × C₀.

Using the exponential decay formula, we have:

C_(t) = C₀ × e^{-kt}.

Substituting t = 1988 and C_(t) = C_(1988), we get:

C_(1988) = C₀ × e{(-k) × 1988).

Substituting C_(1988) = 0.91 × C₀, we have:

0.91 × C₀ = C₀ × e^{(-k) × 1988}.

Canceling out C₀ on both sides, we get:

0.91 = e^{(-k) × 1988}.

Taking the natural logarithm of both sides, we have:

ln(0.91) = (-k )× 1988.

Solving for k, we find:

k =( -ln(0.91)) / 1988.

Using the previously found value of k ≈ 0.00012427, we can calculate the age of the Shroud of Turin in 1988:

Age = 1988 / k.

Substituting the value of k, we have:

Age ≈ 1988 / (ln(0.91) / 1988).

Age ≈ 1988 × (1988 / ln(0.91)).

Calculating the approximate value, we find:

Age ≈ 1988 × (1988 / (-0.093169)) ≈ (-20,206,118) years.

Therefore, according to the data from 1988, the age of the Shroud of Turin is approximately 20,206,118 years.

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Answer:

I believe number 9 is the middle answer

Step-by-step explanation:

please correct me if I'm wrong

Answer:

y = 120

Step-by-step explanation:

If y = 32 when x = 8, then y is 4 times the number of x. If x = 30, then (4)30 = 120.

Answer:

C) Similar - SAS

For any m x n matrix A, AAT and ATA are symmetric matrices as  (AAT)^T = AAT and (ATA)^T = ATA.

To prove or disprove that for any m x n matrix A, AAT and ATA are symmetric, we can use the definition of a symmetric matrix and the properties of matrix transposes.
A matrix B is symmetric if B = B^T, where B^T is the transpose of B. So, we need to show that (AAT)^T = AAT and (ATA)^T = ATA.
Step 1: Find the transpose of AAT:
(AAT)^T = (AT)^T * A^T (by the reverse order property of transposes)
(AAT)^T = A * A^T (since (A^T)^T = A)
(AAT)^T = AAT
Step 2: Find the transpose of ATA:
(ATA)^T = A^T * (AT)^T (by the reverse order property of transposes)
(ATA)^T = A^T * A (since (A^T)^T = A)
(ATA)^T = ATA

Since (AAT)^T = AAT and (ATA)^T = ATA, we have proved that for any m x n matrix A, AAT and ATA are symmetric matrices.

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Answer:

1/2

Step-by-step explanation:

1 L -1/4=3/4

3/4×2/3=1/2

(9/11)÷(5/6)

= 9/11×6/5

= 54/55

Answer:

Julio's number is 40

Step-by-step explanation:

"If you subtract 17 from my number and multiply the difference by negative 4​, the result is negative 92​.

n= number

(n-17)*(-4) = -92

distribute

-4 *n - 17*(-4) = -92

-4n +68 = -92

subtract 68 from each side

-4n +68-68 = -92 -68

-4n = -160

divide each side by -4

-4n/-4 = -160/-4

n = 40

correct answer is estimated useful life of the machine is 7 years.

To determine the estimated useful life of the machine, we will use the given information and apply the straight-line depreciation formula:

Depreciation Expense = (Cost - Residual Value) / Useful Life

We know the following:

Cost = $17,500
Depreciation Expense = $2,000 per year
Residual Value = 20% of Cost = 0.20 x $17,500 = $3,500

Now, we will plug these values into the formula and solve for Useful Life:

$2,000 = ($17,500 - $3,500) / Useful Life

Simplifying the equation:

$2,000 = $14,000 / Useful Life

Now, divide both sides by $14,000:

Useful Life = $14,000 / $2,000

Useful Life = 7 years

So, the estimated useful life of the machine is 7 years.

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Answer:

  24.1 billion

Step-by-step explanation:

One way to write the logistic function is ...

  P(t) = AB/(A +(B-A)e^(-kt))

where A is initial value (P(0)), and B is the carrying capacity (P(∞)). We are told to use relative population growth in the 1990s as the value for k.

In billions, we have ...

  A = 5.3

  B = 100

  k = 0.02/5.3 ≈ 0.003774 . . . . . relative growth rate at 20 M per year

  t = 2450 -1990 = 460

  \(P(t)=\dfrac{530}{5.3+94.7e^{-0.003774t}}\\\\P(460)=\dfrac{530}{5.3+94.7e^{-1.73604}}\approx \boxed{24.1\quad\text{billion}}\)

The expected value E(X) of a random variable X is -1.04

The expected value of a random variable is a measure of its central tendency. It represents the average value that would be obtained if the experiment or process that generates the variable is repeated many times.

To find the expected value of a discrete random variable X with probability distribution P(X), we multiply each possible value of X by its corresponding probability and then sum these products. Symbolically, this can be written as:

E(X) = Σ[x * P(X)]

In words, this formula says that we take each possible value of X, multiply it by its probability, and then add up these products to get the expected value.

In the given problem, we are given the probability distribution of X and asked to find its expected value. We can use the formula above to do this, by plugging in the values of x and P(X):

E(X) = (-9 * 0.16) + (-7 * 0.11) + (-5 * 0.14) + (-3 * 0.17) + (-1 * 0.10) + (1 * 0.32)

E(X) = -1.04

Therefore, the expected value of X is -1.04.

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Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:(7,6)

Equation Form: x=7, y=6

2x+y=20

6x-5y=12

First get y by its self

2x+y=20

y= -2x+20

Now plug into second equation for y

6x-5(-2x+20)=12

6x+10x-100

16x-100=12

16x=112

x=7

now plug in x value into first equation and solve for y

2(7)+y=20

14+y=20

y= 6

Now check by plugging x and y values back into equation

2(7)+6=20

6(7)-5(6)=12

They both work so x=7 and y =6

Answer:

D. 29

Step-by-step explanation:

just did the test and got it correct. Edmentum, Plato.

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer:

the length of the side opposite = 20.6 feet

Step-by-step explanation:

using SOHCAHTOA

Sin 40 = opp / hyp

Sin 40 = opp / 35

opp = sin 40 x 35

opp = 20.6 feet

Answer:

i thinkis D 11 because 8+3=11

Answer:

the answer is D

Step-by-step explanation:

hope this helps

The greatest common divisor (gcd) of 144 and 89 can be expressed as a linear combination of 144 and 89 as follows: gcd(144, 89) = 1 = (-21) * 144 + 34 * 89.

To express the gcd (144, 89) as a linear combination of 144 and 89, we can use the extended Euclidean algorithm. This algorithm finds the gcd of two numbers and also provides coefficients that represent the linear combination.

We start with the given numbers: a = 144 and b = 89.

Apply the Euclidean algorithm to find the gcd:

Divide 144 by 89: 144 = 1 * 89 + 55

Divide 89 by 55: 89 = 1 * 55 + 34

Divide 55 by 34: 55 = 1 * 34 + 21

Divide 34 by 21: 34 = 1 * 21 + 13

Divide 21 by 13: 21 = 1 * 13 + 8

Divide 13 by 8: 13 = 1 * 8 + 5

Divide 8 by 5: 8 = 1 * 5 + 3

Divide 5 by 3: 5 = 1 * 3 + 2

Divide 3 by 2: 3 = 1 * 2 + 1

Divide 2 by 1: 2 = 2 * 1 + 0

The last non-zero remainder obtained is 1, which means the gcd is 1.

Now, we work backwards through the algorithm to find the coefficients:

From 3 = 1 * 2 + 1, we can express 1 as a linear combination of 2 and 3: 1 = 3 - 1 * 2

Substitute 2 = 5 - 1 * 3 from the previous step: 1 = 3 - 1 * (5 - 1 * 3) = 2 * 3 - 1 * 5

Continue substituting until we reach the original numbers:

1 = 2 * 3 - 1 * 5 = 2 * (5 - 1 * 3) - 1 * 5 = 2 * 5 - 3 * 5 = 2 * 5 - 3 * (8 - 1 * 5)

Repeat until we get the desired linear combination:

1 = 2 * 5 - 3 * (8 - 1 * 5) = 2 * 5 - 3 * 8 + 3 * 5 = (-3) * 8 + 5 * 5 - 3 * 8 = 5 * 5 - 6 * 8

Substitute 8 = 13 - 1 * 5: 1 = 5 * 5 - 6 * (13 - 1 * 5) = 11 * 5 - 6 * 13

Repeat the process until we reach the original numbers:

1 = 11 * 5 - 6 * 13 = 11 * (13 - 1 * 8) - 6 * 13 = 11 * 13 - 11 * 8 - 6 * 13 = (-17) * 8 + 11 * 13

Substitute 13 = 21

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Prove of the eigenvectors corresponding to distinct real eigenvalues of a symmetric matrix are orthogonal, given below -

The study of matrices is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.

a collection of integers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix, are the integers. In addition to several mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

Suppose  λ  and  μ  are 2 distinct values of matrix  A.

For the matrix to be Symmetric,

(Ax , y) = (x , Ay)  condition needs to be satisfied. Here, ( x,y)  is dot product between vectors  x  and  y

λ(u,v)=(λu,v) , where  u,v  are eigen vectors for eigen values  λ  and  μ

⟹λ(u,v)=(Au,v)

⟹λ(u,v)=(u,Av)

⟹λ(u,v)=μ(u,v)

⟹λ(u,v)=μ(u,v)

but  λ ≠ μ

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To determine if the yearbook photo is a dilation of the original photo, we need to compare the dimensions and check if there is a consistent scaling factor between the two.

Original photo dimensions: 4 inches by 6 inches.

Yearbook photo dimensions: 6 2/3 inches by 10 inches.

To check if it's a dilation, we can compare the ratios of corresponding sides:

Ratio of width:

Yearbook photo width / Original photo width = (6 2/3) / 4 = (20/3) / (12/3) = 20/12 = 5/3

Ratio of height:

Yearbook photo height / Original photo height = 10 / 6 = 5/3

The ratios of the corresponding sides are equal, with both being 5/3. This indicates that there is a consistent scaling factor of 5/3 between the original photo and the yearbook photo.

Therefore, the yearbook photo is indeed a dilation of the original photo, and the scale factor is 5/3. This means that each dimension of the yearbook photo is 5/3 times the corresponding dimension of the original photo.

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Answer:

Step-by-step explanation:

1.) C

2.) x - 2y = 6 ⇒ -2x + 4y = -12

-2x+4y = -12

2x+5y = -3

------------------

 9y = -15

y = -5/3

x = 2y+6 = 8/3

(x,y) = (8/3, -5/3)

can you send the answer more clear in the comments so I can help better

The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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An irregular quadrilateral, also known as an arbitrary quadrilateral, is a polygon with four sides that are not equal in length or congruent in any way.

Unlike regular quadrilaterals such as squares or rectangles, which possess congruent sides and angles, an irregular quadrilateral lacks these symmetries. Consequently, its shape can vary greatly, allowing for a wide range of possibilities. Examples of irregular quadrilaterals include trapezoids, parallelograms, and kites.

These quadrilaterals possess different combinations of side lengths and angles, resulting in unique shapes and characteristics. Due to their lack of regularity, irregular quadrilaterals do not conform to specific formulas or properties like regular polygons. Their diverse nature makes them a fascinating subject of study in geometry, as they exhibit a rich variety of properties and behaviors.

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