true or false: if a and b are matrices corresponding to orthogonal projections, then the matrix is also the matrix corresponding to some orthogonal projection.

Answer: 5 kilometers.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The list of numbers seems to be decreasing, from biggest to smallest.

But... The 8 isn't less than 2, it should be more!

So 8 should be the circled number.

The 8 should be put before the -2, because 8 > 2

Answer:

1,2,4

Step-by-step explanation:

a. The vector addition (3i + 4j) + (i - 2j) results in 4i + 2j. In polar form, the magnitude of the vector is √20 and the direction is approximately 26.57 degrees.

b. The dot product of vectors A = 3i - 6j + 2k and B = 10i + 4j - 6k is -20.

a. To add the vectors (3i + 4j) and (i - 2j), we add their corresponding components. The sum is (3 + 1)i + (4 - 2)j, which simplifies to 4i + 2j.

To express this vector in polar form, we need to determine its magnitude and direction. The magnitude can be found using the Pythagorean theorem: √(4^2 + 2^2) = √20. The direction can be calculated using trigonometry: tan^(-1)(2/4) ≈ 26.57 degrees. Therefore, the vector 4i + 2j can be expressed in polar form as √20 at an angle of approximately 26.57 degrees.

b. To find the dot product of vectors A = 3i - 6j + 2k and B = 10i + 4j - 6k, we multiply their corresponding components and sum them up. The dot product A · B = (3 * 10) + (-6 * 4) + (2 * -6) = 30 - 24 - 12 = -20. Therefore, the dot product of vectors A and B is -20.

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Answer:

18.1cm

Step-by-step explanation:

11cm - 4cm = 7cm

16² - 7²

256 - 49 = 207

√207 = 14.387

x = 14.4

√14.39²+11²=√207+121= √328= 18.1cm

AC=18.1cm

I hope this helps ^_^

1. The volume of the solid formed by revolving the region bounded by y = x^2 + 4, x = -1, x = 1, and y = 3 around the x-axis is approximately 30.796 cubic units.

2. The volume of the solid formed by revolving the region bounded by y = 4, y = 3, and y = x^2 around the y-axis is approximately 52.359 cubic units.

1. To find the volume of the solid formed by revolving the region around the x-axis, we use the formula V = π ∫[a,b] (f(x))^2 dx.

  - The given region is bounded by y = x^2 + 4, x = -1, x = 1, and y = 3.

  - To determine the limits of integration, we find the x-values where the curves intersect.

  - By solving x^2 + 4 = 3, we get x = ±1. So, the limits of integration are -1 to 1.

  - Substituting f(x) = x^2 + 4 into the volume formula and integrating from -1 to 1, we can calculate the volume.

  - Evaluating the integral will give us the main answer of approximately 30.796 cubic units.

2. To find the volume of the solid formed by revolving the region around the y-axis, we use the formula V = π ∫[c,d] x^2 dy.

  - The given region is bounded by y = 4, y = 3, and y = x^2.

  - To determine the limits of integration, we find the y-values where the curves intersect.

  - By solving 4 = x^2 and 3 = x^2, we get x = ±2. So, the limits of integration are -2 to 2.

  - Substituting x^2 into the volume formula and integrating from -2 to 2, we can calculate the volume.

  - Evaluating the integral will give us the main answer of approximately 52.359 cubic units.

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True, The objective function in linear programming is formulated to either maximize or minimize a specific value or quantity.

The goal of linear programming is to optimize this objective function by finding the optimal values for the decision variables within the given constraints. Whether it is maximizing profit, minimizing cost, maximizing production, or minimizing waste, the objective function is designed to achieve the desired optimization outcome.

The objective function in linear programming serves as the goal or target to be achieved. It can involve maximizing profits, minimizing costs, maximizing efficiency, minimizing waste, or any other measurable quantity. The objective function guides the optimization process by defining the objective to be pursued in the linear programming problem.

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Answer:

0.257

Step-by-step explanation:

Answer:

third choice 1/2

Step-by-step explanation:

A deck of standard playing cards consists of clubs, diamonds, hearts, & spades. So clubs and spades together represent half the deck.

So 26 in 52 chance of one of either. Simplified...

1/2

Answer:

The last option

Step-by-step explanation:

You can find the slope by using this equation : y2-y1/x2-x1. We can choose any two y coordinates and any two x coordinates to find this. For instance, you can write this as -3-(-2.25)/0-(-1). Now, we can solve.

-3-(-2.25)/0-(-1)

-3+2.25/0+1

-0.75/1

-0.75

-0.75 in fraction form is -3/4.

I'm not quite sure how to calculate the y-intercept, but we know the slope, and that's all we need for this problem (the slope number is next to the x). This makes our answer the last option. Hope this helps!

Answer:

(-4,-5)

Step-by-step explanation:

(x-coordinate, y-coordinate)

-4 is C's x-coord and -5 is C's y-coordinate

Answer:

thx

Step-by-step explanation:

Answer:

165.065% increase

Step-by-step explanation:

He stands 6 feet tall, and his shadow extends 9 feet. if the building's shadow extends for 322.5 feet.

Now 6/9 = X/322.5

9X = 1935

X = 215ft

The Height of the building = 215ft

Consider an object AB of height h such that its shadow of length s is formed and angle of elevation is θ.

The object AB depicts a right triangle in which ∠ABO = 90o.

Now we know that in trigonometry, the tangent ratio for an angle is equal to the opposite side to that angle divided by its adjacent side.

So, for the angle of elevation θ, we have

=> tan θ = AB/OB

Putting AB = h and OB = s, we get

=> tan θ = h/s

=> s/h = 1/tan θ

=> s = h/tan θ

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The value of the trigonometry equation (sin 60)(cos 30)+(cos 60)(sin 30) is sin (60+30). Option J is correct.

The formula of sum of sin (a+b) is the trigonometry identity which is used to solve and simplify the problem based on trigonometry equation.

The formula of sum of sin (a+b),

Sin(A+B)=(sin A)(cos B)+(cos A)(sin B)

Here, (A and B) are the measure of angles.

The trigonometry equation given in the problem is,

(sin 60)(cos 30)+(cos 60)(sin 30)

Compare this expression with the above formula we get,

A=60

B=30

Thus, the value of the given expression is,

(sin 60)(cos 30)+(cos 60)(sin 30)=sin (60+30)

Thus, the value of the trigonometry equation (sin 60)(cos 30)+(cos 60)(sin 30) is sin (60+30). Option J is correct.

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Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(y = 3x^2+9\)

Let x equal 0

\(y=3(0)^2 +9\\\\y= 3\times 0 +9\\\\y = 0+9\\\\y=+9\)

Therefore, m = 7.5454... (rounded to four decimal places) and n = 0.5455...

What is Simultaneous Equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

1) 3p + 4q = 23

10p + 12q = 74

Subtracting 3 times the first equation from the second equation, we get:

10p + 12q - 3(3p + 4q) = 74 - 3(23)

10p + 12q - 9p - 12q = 5

p = 5

Substituting p = 5 in the first equation, we get:

3(5) + 4q = 23

4q = 8

q = 2

Therefore, p = 5 and q = 2.

2) 4s + 2t = 20

11s + 4t = 49

Multiplying the first equation by 2 and subtracting it from the second equation, we get:

11s + 4t - 2(4s + 2t) = 49 - 2(20)

11s + 4t - 8s - 4t = 9

3s = 9

s = 3

Substituting s = 3 in the first equation, we get:

4(3) + 2t = 20

2t = 8

t = 4

Therefore, s = 3 and t = 4.

3) 3a + 4b = 34

12a + 5b = 59

Multiplying the first equation by 3 and subtracting it from the second equation, we get:

12a + 5b - 3(3a + 4b) = 59 - 3(34)

12a + 5b - 9a - 12b = 17

3a - 7b = 17

Multiplying the first equation by 5 and subtracting it from the second equation, we get:

12a + 5b - 5(3a + 4b) = 59 - 5(34)

12a + 5b - 15a - 20b = -61

-3a - 15b = -61

a + 5b = 20

Adding the equations 3a - 7b = 17 and a + 5b = 20, we get:

4a = 37

a = 9.25

Substituting a = 9.25 in the equation a + 5b = 20, we get:

9.25 + 5b = 20

5b = 10.75

b = 2.15

Therefore, a = 9.25 and b = 2.15 (rounded to two decimal places).

4) 6m + 5n = 48

18m + 4n = 78

Multiplying the first equation by 3 and subtracting it from the second equation, we get:

18m + 4n - 3(6m + 5n) = 78 - 3(48)

18m + 4n - 18m - 15n = -6

-11n = -6

n = 0.5455...

Substituting n = 0.5455... in the first equation, we get:

6m + 5(0.5455...) = 48

6m = 45.2727...

m = 7.5454...

Therefore, m = 7.5454(rounded to four decimal places) and n = 0.5455.

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The recursive rule for the number of acres at the beginning of the nth day in a forest fire that grows by 20% each day and is battled by firefighters who can put out 15 acres per day is given by: A(n) = 1.2 * A(n-1) - 15, where A(n) represents the number of acres at the beginning of the nth day. Using this rule, we can calculate that there are 89.6 acres burning at the beginning of the 8th day.

Explanation: To determine the recursive rule for the number of acres at the beginning of the nth day, we need to consider the given information. The forest fire initially covers 60 acres and grows by 20% each day. This means that the number of acres at the beginning of the next day (n+1) is 1.2 times the number of acres at the beginning of the current day (n). However, the firefighters are able to put out 15 acres of fire per day.

Therefore, to calculate A(n), we start with the initial number of acres, which is 60, and apply the recursive rule. A(n) = 1.2 * A(n-1) - 15. This formula takes into account the growth of the fire by 20% and the reduction of 15 acres due to the firefighters' efforts. By substituting the values, we can calculate the number of acres at the beginning of each day.

To find the number of acres burning at the 8th day, we substitute n = 8 into the recursive rule. A(8) = 1.2 * A(7) - 15. We need to determine A(7) first by substituting n = 7, and so on, until we reach the initial value A(1) = 60. Once we have calculated A(8), we can determine that there are 89.6 acres burning at the beginning of the 8th day

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10.25 Ok but I dunno how to explain sorry but is right (Probably)

Hope U have a great day!

Answer:

10.25

Step-by-step explanation:

-123 divided by -12 is 10.25

No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.

To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).

The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).

To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:

(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4

Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.

The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.

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a) Using a base 2, the exponential function can be written as follows:

A(t) = 100(2)^(-t/235)

b) The amount of substance remaining after 1000 years is given as follows: 5.2 grams.

The exponential function for this problem is defined as follows:

A(t) = 100(0.5)^(t/235).

Which gives the amount of a substance after t years, considering a half life of 235 years.

The base can be changed to 2 as follows:

A(t) = 100(2)^(-t/235).

As exchanging the sign of the exponent, the numerator and the denominator of the base are exchanged, and 0.5 = 1/2.

The amount of the substance after 1000 years is calculated as follows:

A(1000) = 100 x (0.5)^(1000/235) = 5.2 grams.

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In a 1-year semi-annually paid interest rate swap, with a notional amount of £1,000,000, the swap rate is 3.0%. The floating rate is based on the 6-month LIBOR plus 1%. The market rate refers to the prevailing interest rate for the specified time period.

An interest rate swap involves the exchange of cash flows between two parties based on different interest rate benchmarks. In this case, the swap has a 1-year maturity and payments are made semi-annually.

The fixed rate, also known as the swap rate, is determined at the beginning of the swap agreement and remains fixed throughout the swap's duration. In this scenario, the swap rate is 3.0%.

The floating rate is determined by a reference rate plus a spread. The reference rate used here is the 6-month LIBOR (London Interbank Offered Rate), which is a widely used benchmark for short-term interest rates. The floating rate in this swap is the 6-month LIBOR plus 1%.

The market rate refers to the prevailing interest rate for the specified time period. It represents the current market conditions and influences the pricing and valuation of the interest rate swap.

To fully analyze the swap and its implications, further calculations and considerations, such as the present value of cash flows and potential valuation changes based on market rate movements, would be necessary.

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The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

\(y = 2 \: cos \: (\frac{1}{3} x)\)

option C is the right option.

Explanation:

General expression of a cosine function is:

y=A cos k X

where A is amplitude and 2 pi/k is its period.

In our case,

\( - y = 2 \: cos \: (\frac{1}{3} x) \:\)

has :

\(amplitude = 2 \\ period = 2\pi \times 3 = 6\pi\)

hence, the right answer is of option C

hope this helps...

Good luck on your assignment..

Answer:

1 2 5

Step-by-step explanation:

right I got it right on the test

Answer:

\({ \tt{let \: that \: value \: be \: { \bf{x}}}} \\ 0.0426 \times x = 4260 \\ { \tt{0.0426x = 4260}} \\ { \tt{x = \frac{4260}{0.0426} }} = 100000 \\ { \tt{answer = 100000}}\)

0.0426 × y = 4260

y = 4260÷0.0426

y=100000

Answer:

81.59%

Explanation:

To find the percentage, we first need to standardize $7100. To standardize, we subtract the mean and then divide by the standard deviation. So, $7100 is equivalent to:

Now, the percentage of day care costs that are more than $7100 is equivalent to the probability that z is greater than -0.9, so:

P(x > $7100) = P(z > -0.9)

Finally, we can use the standard normal distribution table to get:

P(z > -0.9) = 0.8159

So, the answer is 81.59%

Answer:

x = 3

Step-by-step explanation:

By tangent secant segment theorem:

\(x \times 12 = 4 \times 9 \\ \\ \implies \: 12x = 36 \\ \\ \implies \: x = \frac{36}{12} \\ \\ \implies \: x = 3\)

Answer:

x=3

Step-by-step explanation: