A diver needs to descend to a depth of 100 feet. She wants to do it in 5 equal descents. How far should she travel in each descent?

Given that matrix A is a 3x3 matrix with only two distinct eigenvalues, let's denote the smaller eigenvalue as λ1 and its algebraic multiplicity as m1, and the larger eigenvalue as λ2 with algebraic multiplicity m2.

We are given that the trace of matrix A is 1, which is the sum of its eigenvalues:

tr(A) = λ1 + λ2

Since A is a 3x3 matrix, the sum of its eigenvalues is equal to the sum of its diagonal elements:

tr(A) = a11 + a22 + a33

We are also given that the determinant of matrix A is -45:

det(A) = λ1 * λ2

det(A) = a11 * a22 * a33

Based on these conditions, we can deduce the following:

λ1 + λ2 = 1

λ1 * λ2 = -45

We can solve these equations to find the values of λ1 and λ2.

Using the quadratic formula to solve for λ1 and λ2, we have:

λ1 = (1 ± √(1^2 - 4*(-45))) / 2

    = (1 ± √(1 + 180)) / 2

    = (1 ± √181) / 2

Therefore, the eigenvalues of matrix A, λ1 and λ2, are given by:

λ1 = (1 + √181) / 2

λ2 = (1 - √181) / 2

To determine the algebraic multiplicities of these eigenvalues, we need additional information or further calculations. The given information does not provide the specific values of m1 and m2.

Therefore, the eigenvalues of matrix A are λ1 = (1 + √181) / 2 and λ2 = (1 - √181) / 2, but the algebraic multiplicities are unknown without additional information.

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Answer:

X = 6 , – 2

Step-by-step explanation:

| 4x +4| - 10 =3x

4x +4 - 10 = 3x

4x - 3x = 10 - 4

x = 6

_____o___o____

– (4x + 4) – 10 = 3x

– 4x – 4 – 10 = 3x

3x + 4x = – 4 – 10

7x = – 14

x = – 14/ 7

x = – 2

I hope I helped you^_^

Step-by-step explanation:

|4x + 4| - 10 = 3x

4x + 4 - 10 = 3x

4x - 6 = 3x

4x - 3x = 6

x = 6

\( \: \)

-4x + 4 - 10 = 3x

-4x + 3x = -4 - 10

-x = -14.

x = 14

If demand or annual usage increases by 10 percent, the Economic Order Quantity (EOQ) will increase. The EOQ model is used in inventory management to determine the optimal order quantity that minimizes total inventory costs.

The Economic Order Quantity (EOQ) is a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. It takes into account factors such as demand, holding costs, and ordering costs. When demand or annual usage increases by 10 percent, it means that more units are being consumed or sold within a given time period.

With an increase in demand, the EOQ will also increase. This is because the EOQ formula takes into consideration the trade-off between holding costs and ordering costs. Holding costs are the costs associated with holding inventory, such as warehousing and insurance, while ordering costs are the costs incurred when placing an order, such as administrative and transportation costs.

When demand increases, more units need to be ordered to meet the higher demand. This results in an increase in ordering costs, as more frequent orders will need to be placed. Consequently, the EOQ will increase to find the new optimal order quantity that balances the increased ordering costs with the holding costs.

In summary, if demand or annual usage increases by 10 percent, the EOQ will increase due to the need to order more frequently to meet the higher demand, resulting in increased ordering costs. This adjustment ensures that the inventory management system remains efficient and cost-effective.

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Answer:

100

I first made 45 a fraction = 45/1

Then i made 2 2/9 into an improper fraction

then make my equation

45/1 ×20/9=100

answer is 100 red apples

Step-by-step explanation:

Answer:

12 + 4x

Step-by-step explanation:

You take all of the ones which you can group together and so, you can take the 5+7 and make it 12 and the 2x + 2x = 4x. I hope this helps!

Answer:

2x^4+4x^2+2

Step-by-step explanation:

f(x) = x^2+1

g(x) = 2x^2

g(f(x))=

Replace x in the function g(x) with the function f(x)

         =2( x^2+1)^2

         = 2( x^2 +2x^2 +1)

         = 2x^4+4x^2+2

Answer:

8th term = 8748 , Sum of 5 terms = 484

Step-by-step explanation:

Formula for nth term in an exponential sequence = a r^ (n-1)

Here : n = 4 , ratio r = 3 ; And nth ie 4th number = 108

So,  a r^ (n-1) = nth item implies that → a 3 ^ (4-1) = 108

a 3^3 = 108 →  27 a = 108 → a = 108 / 27 → a = 4

8th term = a r^ (n-1) , at  n = 8.  So, = 4 3^(8-1) = 4 3^7 = 4 x 2187 = 8748

Sum of n terms = a [(r^n) -1 ] / [r - 1] → Sum 5 terms = 4 [ (3^5)- 1] / [3 - 1]

= 4 [ (243) - 1] / 2 ] = 2 x 242 = 484

Order of the operations: parentheses, exponentials, division and multiplication, addition and subtraction.

1. Solve operations in parentheses:

2. Solve exponentials:

3. Solve division:

4. Solve multiplication:

5. Solve subtraction:

Answer: Answer is 20( please make me brainliest i just did this all in my head)

Step-by-step explanation: soo (14-2) =12  12divided by 3=4 so (2*3)= 6 so 4x6=24 24-2*2 =20 (2*2)=4 so 24-4=20 well this is confusing but i tried my best so hope my answer wasn't toooo confusing lol :)

The McNemar's Test can be thought of as the chi-square type equivalent to the paired t-test.

The McNemar's Test is a non-parametric statistical method used to analyze the differences between paired or matched categorical data, such as repeated measurements on a single group. Like the paired t-test, which is used to compare continuous data, the McNemar's Test evaluates the changes in the proportions of success or failure between the paired observations.

This test is particularly useful when dealing with small sample sizes or when the assumptions of normality and homogeneity of variances required for the paired t-test are not met. By using the chi-square distribution, McNemar's Test provides a way to determine the significance of the differences between paired categorical data, while accounting for the dependency between the observations.

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Answer:

f(4)=14

Step-by-step explanation:

f(x)=3x+2

f(4)=3x+2

f(4)=3*4+2

f(4)=12+2

f(4)=14

Hope this helps!

Hello!

To solve for the y-values in the table:

 \(\hookrightarrow \text{ Must plug in the corresponding x's value into the equation}\)

             \(y = 2(-2) + 3 = -4 + 3 = -1\)

             \(y = 2(0) + 3 =3\)

            \(y = 2(1) +3=5\)

           \(y = 2(3) + 3=6 + 3=9\)

Hope that helps!

The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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Answer:

−11y^3+7y2^+7y

Step-by-step explanation:

Answer:

what are the answer choices

Step-by-step explanation:

Answer:

That's like 20 feet probably

Step-by-step explanation:

Okay so the distance between Tom and Jaime is the height of the triangle (South is directly down) (A=15 yards)

The distance between Tom and Ladonna is the base of the triangle (since Ladonna is west of Tom) (B is unknown)

The hypotenuse is the distance between Jaime and LaDonna (C=25 yards)

1. So 15^2 plus b^2 equals 25^2

2. 225 plus b^2 equals 625

3. Subtract 225 from both sides (b^2=400)

4. Find the square root of both sides.

5. B= 20 yards

Answer:

do the pemdas

p=()

e=X^x

md= multiply then devide

as= add then subtract

Step-by-step explanation:

y=3x^2+9x-18

y=9x+9x-18

18x-18=y

Answer:

a.) 0 feet.

b.) 36 feet.

c.) 60 feet.

d.) 1 second.

Step-by-step explanation:

a. The initial height of the golf ball is given by the height at time t=0, which we see is h(0) = -16(0)^2 + 64(0) = 0 feet.

b. The height of the ball after 1.5 seconds is h(1.5) = -16(1.5)^2 + 64(1.5) = 36 feet.

c. The maximum height of the golf ball is given by the vertex of the parabola, which we can find by completing the square. Completing the square, we get h(t) = -16(t-1)^2 + 64. The vertex is at t=1, so the maximum height is h(1) = -16(1-1)^2 + 64 = 60 feet.

d. It takes 1 second for the golf ball to reach its maximum height.

Here is a graph of the height of the golf ball over time:

                       y

                        |

                        |

                        |

                        |

                        |

                        |

                        |

                        |

                        |

   --------------------------|------------> x

                       0        1.5       2.5

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Step-by-step explanation:

For a RIGHT triangle   Sin = opposite LEG / Hypotenuse

           sin x = 45/ 83

                 x = arcsin (45/83)  = use calculator = 32.8 degrees

Answer:

1232 m^3 to nearest whole number.

Step-by-step explanation:

The volume of a cone = 1/3 π r^2 h     where r = radius of base and h = height.

The radius of the base = 1/2 * 14 = 7m.

The height can be found by using the Pythagoras theorem:

25^2 = h^2 + 7^2

h^2 = 625 - 49 = 576

h = √576 =  24m

So the volume = 1/3 π *  7^2 * 24

=  1231.504 m^3.

Answer:

$1,500

Step-by-step explanation:

Divide 126 by 8.4% (.084)

Your answer is 1500

Answer: Add 7 to n to make it a positive number and easier to work with

Step-by-step explanation:

first all 7 then divide by divide by 3

Answer:

Less

Step-by-step explanation:

Because every negative number is smaller than any positive number

The rule of the perimeter of the square is

L is the length of its side

Since the perimeter is 11 times the length decrease by 35

Then multiply L by 11, then subtract 25 from the product

Substitute the value of P in the rule above

Add 35 to both sides

Now, subtract 4L from both sides

Divide both sides by 7

The length of the side of the square is 5 units

The area of the triangle is 24 square units, the correct option is D.

Remember that for any triangle of base B and height H, the area is given by:

A = H*B/2

In this case, the base is the distance between (-3, -3) and (3, 3)

Then the base is:

B = √( (3 + 3)² + (3 + 3)²) = 6*√2

And the height is:

H = √( (-4)² + 4²) = 4*√2

Then the area is:

A = (6*√2)*(4*√2)/2

A = 24

The correct option is D.

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The probability that all adjacent points differ in colour is \(\frac{1}{5}\).

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given ,

We have first three colour Green that is g1 , g2 and g3

And We have next three colour red that is r1 , r2 and r3

The probability that all adjacent points differ in colour = 3! * \(^{4}C_{3}\) 3! / 6!

=> \(\frac{ 3! * 4! *3!}{6!}\)

=> \(\frac{1}{5}\)

The probability that all adjacent points differ in colour is \(\frac{1}{5}\).

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To determine the total grade we mutiply each one by the percentage it represents of the overall grade in decimal form and add them, that is:

Therefore, the overall grade is 69

The approximate numbers of cell sites for the years 1998, 2008, and 2015 based on the given model.

To find the number of cell sites in the years 1998, 2008, and 2015 using the given model equation:

y = 336.01/(1 + 29.39e^(-0.256))

We substitute the respective years into the equation and calculate the value of y.

For the year 1998:

Substituting t = 1998 into the equation:

y = 336.01/(1 + 29.39e^(-0.256*1998))

For the year 2008:

Substituting t = 2008 into the equation:

y = 336.01/(1 + 29.39e^(-0.256*2008))

For the year 2015:

Substituting t = 2015 into the equation:

y = 336.01/(1 + 29.39e^(-0.256*2015))

To find the actual numerical values, we need to evaluate these expressions using a calculator or a computer program that can handle exponentiation and arithmetic calculations.

Please note that it is important to follow the correct order of operations when evaluating the exponent term, particularly the negative sign and the multiplication. The exponent term should be calculated first, and then the result should be multiplied by -0.256.

By substituting the respective years into the equation and evaluating the expression, you will obtain the approximate numbers of cell sites for the years 1998, 2008, and 2015 based on the given model.

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9514 1404 393

Answer:

Step-by-step explanation:

A tangent makes a right angle with the radius to the point of tangency. Hence ∠PAO is 90°. The ratio of the short side (OA) of the right triangle OAP to the hypotenuse (OP) is 5 : 10 = 1 : 2. These are the ratios found in a 30°-60°-90° triangle, so we know that ∠APO = 30°.

OP is a bisector of angle APB, so that angle is 60°. Angle AOB is the supplement to angle APB, so ∠AOB = 120°.

__

As we said above, triangle OAP is a 30°-60°-90° triangle, so its side lengths have the ratios 1 : √3 : 2. This means PA = PB = 5√3 ≈ 8.7.

The result of convolving \(\(x(t) = u(t+2)\)\) and \(\(h(t) = e^{-4(t-3)}u(t-3)\)\) using the convolution integral is \(\(y(t) = \frac{e^{4t}}{4} - \frac{e^{-8}}{4}\)\).

To compute the convolution \(\(y(t) = x(t) * h(t)\)\), where\(\(x(t) = u(t+2)\)\) and \(\(h(t) = e^{-4(t-3)}u(t-3)\)\), we can use the convolution integral:

\(\[y(t) = \int_{-\infty}^{\infty} x(\tau)h(t-\tau) d\tau\]\)

Substituting the given functions:

\(\[y(t) = \int_{-\infty}^{\infty} u(\tau+2)e^{-4(t-\tau-3)}u(t-\tau-3) d\tau\]\)

Now we need to split the integral based on the range of the step functions. Since \(\(u(t+2)\)\) is nonzero for\(\(\tau \geq -2\)\)  and \(\(u(t-\tau-3)\)\) is nonzero for\(\(\tau \leq t-3\)\), the integral can be written as:

\(\[y(t) = \int_{-2}^{t-3} e^{-4(t-\tau-3)} d\tau\]\)

To solve this integral, we can simplify the expression inside the integral:

\(\[e^{-4(t-\tau-3)} = e^{-4t}e^{4\tau}e^{12}\]\)

Now the integral becomes:

\(\[y(t) = e^{12} \int_{-2}^{t-3} e^{4\tau} d\tau\]\)

Integrating\(\(e^{4\tau}\)\)gives us:

\(\[y(t) = e^{12} \left[\frac{1}{4}e^{4\tau}\right]_{-2}^{t-3}\]\)

Simplifying further:

\(\[y(t) = \frac{e^{12}}{4} \left(e^{4(t-3)} - e^{-8}\right)\]\)

Therefore, the expression for \(\(y(t)\)\) is:

\(\[y(t) = \frac{e^{4t}}{4} - \frac{e^{-8}}{4}\]\)

This is the result of convolving\(\(x(t)\) and \(h(t)\)\) using the convolution integral.

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