answer this question on trigonometry

As we have proved that the matrix u can be written as a linear combination of the column vectors of a, which implies that u lies in the plane in ℝ3 spanned by the columns of a.

Let us consider the given vectors u=−16 13 20 and the matrix a=5 −7 −2 4 2 2. To determine whether u lies in the plane in ℝ3 spanned by the columns of a, we need to check whether u can be written as a linear combination of the column vectors of a.

We can express the matrix a as a linear combination of its column vectors as follows:

a = 5 4 −2 ⋅ [1 0 0] + (-7) 2 4 ⋅ [0 1 0] + (-2) 2 2 ⋅ [0 0 1]

Therefore, the column vectors of a span a plane in ℝ3.

Now, let us try to express u as a linear combination of the column vectors of a:

u = α[5 4 −2] + β[-7 2 4] + γ[-2 2 2]

where α, β, and γ are constants to be determined.

Setting up a system of linear equations, we get:

5α − 7β − 2γ = −16

4α + 2β + 2γ = 13

−2α + 4β + 2γ = 20

Solving this system of equations, we get α = −4, β = −1, and γ = 3.

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We have three points that represent the vertices of the triangle

- A( -1, 5 )

- B( 4, 5 )

- C( -1, 1 )

We need to calculate the distances between the points to calculate the perimeter

To calculate the distances we must use the next equation

Distance for AB:

Distance for BC:

Distance for AC:

Finally, the perimeter is

So, the answer is

Each of the three used up an equal fraction of pencils.

To find the fraction used by each of them,

 Fraction used = total used pencils/ total no.of pencils

Ramesh :

  Total no. of pencils = 20

  Total used pencils = 10

  Fraction used = 10/20

                          = 1/2

Sheelu :

  Total no. of pencils = 50

   Total used pencils = 25

  Fraction used = 50/25

                          = 1/2

Jamai :

 Total no. of pencils = 80

  Total used pencils = 40

  Fraction used = 40/80

                          = 1/2

We see that, all fractions on simplifying are equal .

∴Each of the three used up an equal fraction of pencils.

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The expression which ehi has a value of three-fourths is cos(x).

Expression in math is an equation, statement, or a combination of symbols and numbers that represent a mathematical operation or value. It is used to calculate or solve mathematical problems. Expressions can be simple or complex, and may involve constants, variables, operations, and functions.

This can be determined by rearranging the equation csc(x) = five-thirds.

This gives us cos(x) = three-fourths.

Therefore, the expression with a value of three-fourths is cos(x).

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The area of the floor which is not carpeted is 36 m².

The area of the room can be calculated by multiplying the length and width of the room. Since the room is a rectangle, the area of the room is:

Area of room = length × width

Area of room = 12.5 m × 8 m

Area of room = 100 m²

Similarly, the area of the square carpet can be calculated by multiplying the length of one side of the carpet by itself. The area of the square carpet is:

Area of carpet = side × side

Area of carpet = 8 m × 8 m

Area of carpet = 64 m²

To find the area of the floor that is not carpeted, we need to subtract the area of the carpet from the area of the room. The area of the floor which is not carpeted is:

Area of floor not carpeted = Area of room - Area of carpet

Area of floor not carpeted = 100 m² - 64 m²

Area of floor not carpeted = 36 m²

Therefore, the area of the floor which is not carpeted is 36 m².

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Answer:

I think it's the lightning bolts and moons

Step-by-step explanation:

Dennis and Christine scored 32 and 23, respectively, in the National Career Assessment Examination (NCAE).

The NCAE is an examination that assesses students' aptitude and career interests, providing insights into their strengths and potential career paths.

Dennis achieved a score of 32, indicating a higher performance level compared to Christine's score of 23. This suggests that Dennis may have demonstrated a better understanding of the assessed subjects or displayed stronger skills in the areas covered by the examination.

It is important to note that the NCAE score is just one measure of a student's abilities and does not solely determine their future success. Other factors such as personal motivation, study habits, and individual interests also contribute to one's overall academic and career development.

Dennis and Christine's scores in the NCAE can serve as valuable information for them to reflect upon their strengths and areas for improvement, helping them make informed decisions regarding their academic and career paths. It is essential for them to utilize their scores as a starting point for self-assessment and further exploration of their interests and aspirations.

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Answer:

he is using at least 1,237 minutes a month

Step-by-step explanation:

15+0.06m ≥ 89.22

m ≥ 1,237

the value of the triple integral ∫∫∫_E dV, where E is the region bounded by the spheres x^2 + y^2 + z^2 = 1 and x^2 + y^2 + z^2 = 9, using spherical coordinates, is (104π/3).

To evaluate the triple integral using spherical coordinates, we need to express the region bounded by the spheres in terms of spherical coordinates and determine the appropriate limits of integration.

In spherical coordinates, the conversion from Cartesian coordinates is given by:

x = ρsinφcosθ

y = ρsinφsinθ

z = ρcosφ

The region bounded by the spheres x^2 + y^2 + z^2 = 1 and x^2 + y^2 + z^2 = 9 corresponds to the region where the radius ρ varies from 1 to 3 (since ρ represents the distance from the origin).

Let's set up the triple integral using spherical coordinates:

∫∫∫_E dV = ∫∫∫_E ρ²sinφ dρ dφ dθ

The limits of integration are as follows:

1 ≤ ρ ≤ 3

0 ≤ φ ≤ π (for the upper hemisphere)

0 ≤ θ ≤ 2π (full rotation around the z-axis)

Now, let's evaluate the triple integral:

∫∫∫_E dV = ∫[0,2π] ∫[0,π] ∫[1,3] ρ²sinφ dρ dφ dθ

Integrating with respect to ρ:

∫[1,3] ρ²sinφ dρ = (1/3)ρ³sinφ ∣ ∣ [1,3] = (1/3)(3³sinφ - 1³sinφ)

                                           = (1/3)(27sinφ - sinφ)

                                           = (1/3)(26sinφ)

Now, we integrate with respect to φ:

∫[0,π] (1/3)(26sinφ) dφ = (1/3)(26)(-cosφ) ∣ ∣ [0,π]

                                   = (1/3)(26)(-cosπ - (-cos0))

                                   = (1/3)(26)(-(-1) - (-1))

                                   = (1/3)(26)(2)

                                   = (52/3)

Finally, we integrate with respect to θ:

∫[0,2π] (52/3) dθ = (52/3)θ ∣ ∣ [0,2π]

                          = (52/3)(2π - 0)

                          = (104π/3)

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Answer:

the answer is 9.

Step-by-step explanation:

The total stimulations in which all three elevators are working is 12(option d) by the concept of data representation.

Data Representation: A method for analyzing numerical data is data representation. Data representation is used to create a diagram that shows the connections between facts, ideas, information, and concepts. It is a fundamental learning technique that is clear-cut and uncomplicated. The data type in a particular domain is always what determines it. There are many various styles and sizes of graphical representations.

According to the given data:

A building has 3 elevators.

The following set of random numbers represents 20 stimulations of the elevators, with 0, 1 representing the broken elevator and 2,3,4,5,6,7,8and 9 representing a working elevator.

Stimulation data:

931 188 763 841 559 144 652 277 653 673 404 396 011 843 599 797 414 761 273 844

Now, as we observe from the given data, the stimulation in which all three elevators are working are-

763,559,652,277,653,673,396,843,599,797,273,844a total of 12 stimulations.

Thus, the total stimulations in which all three elevators are working is 12

Hence, option d is correct.

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This can be calculated by dividing the initial reserves of 300 million tonsThe year when the cumulative extraction reaches or exceeds 300 million tons will be the time when the mineral reserves are exhausted.

a) If the extraction of minerals is kept constant at 50 million tons per year, the reserves will be exhausted in 6 years. This can be calculated by dividing the initial reserves of 300 million tons by the annual extraction rate of 50 million tons.

b) If the extraction of minerals declines by 15 percent each year due to increasing extraction costs, we need to determine how long the mineral reserves will last.

To do this, we can calculate the cumulative extraction each year until it reaches or exceeds the initial reserves of 300 million tons. Assuming the extraction declines by 15 percent each year, we can calculate the extraction in each subsequent year and add it to the cumulative extraction from previous years. The year when the cumulative extraction reaches or exceeds 300 million tons will be the time when the mineral reserves are exhausted.

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Answer:

P = \(\frac{40}{V}\)

Step-by-step explanation:

given P is inversely proportional to V then the equation relating them is

P = \(\frac{k}{V}\)

to find k use the condition when V = 8 , P = 5 , then

5 = \(\frac{k}{8}\) ( multiply both sides by 8 to clear the fraction )

40 = k

P = \(\frac{40}{V}\) ← equation of proportion

Answer:

P = 40/V.

Step-by-step explanation:

P = k/V where k is a constant

Substituting the given values:

5 = k/8

k = 5*8 = 40.

So the formula is:

P = 40/V

Answer:

D be because 2 +4 -5

Step-by-step explanation:

Based on the information, we can infer that the area of the figure is 120 in².

To find the area of a quadrilateral figure we must know the length of its sides and its base. In this case it is a rectangle with a base of 15 in. and sides of 8 in.

According to the above, we must apply the following formula to find the area:

So, the area of this figure is 120 in². Additionally, we can conclude that the side length and base length of this rectangle is regular.

Note: This question is incomplete. Here is the complete information:

Find the rectangle's area:

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To solve for angle A and angle B in the given triangle, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

In this case, we have side a with length 2 and side c with length 9. Let's denote angle A as angle opposite side a and angle B as angle opposite side b (which is unknown).

Using the Law of Sines, we have:

sin(A) / a = sin(B) / b

Plugging in the known values, we get:

sin(A) / 2 = sin(B) / 9

To find angle A, we can use the arcsine function:

A = arcsin((sin(B) / 9) * 2)

To find angle B, we can rearrange the equation:

sin(B) = (sin(A) / 2) * 9

B = arcsin((sin(A) / 2) * 9)

Now we can calculate the angles using a calculator:

A ≈ 19.5 degrees (rounded to one decimal place)

B ≈ 84.1 degrees (rounded to one decimal place)

Therefore, angle A is approximately 19.5 degrees and angle B is approximately 84.1 degrees.

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To evaluate the surface integral of f(x,y,z) dS over the given surface, the first step is to set up the surface integral as a double integral over a region R in the xy-plane. To do this, we can express f(x,y,z) in terms of two parameters, u and v, as f(u,v). Then, the surface integral is expressed as follows:
Integral f(u,v) dS = Integral Integral f(u,v) dA,
where A is the area of the region R in the xy-plane.

For the given surface, we can express the equation of the cone as z2 = (x2 +y2), for 0≤z≤8. To parameterize this equation, we can set u = x and v = y, and express x and y in terms of z as follows:
x = rcosθ and y = rsinθ.
Therefore, the double integral of f(u,v) dA can be expressed as:
Integral Integral f(u,v) dA = Integral Integral f(r cosθ,r sinθ) rdrdθ,
where 0≤r≤5 and 0≤θ≤2π.
Finally, substituting f(x,y,z) with 4x and evaluating the integral, we obtain the surface area of the given cone as A = 80π.
In conclusion, the surface integral of f(x,y,z) dS over the given cone is 80π.

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For a moving particle with velocity at time t is v(t) = t² -t - 6 (m/s), the displacement and distance of particle during the time period 1≤t≤4, are equal to -4.5 m and 1.16 m respectively.

We have a particle moves along a line. Velocity of particle at time t, v(t) = t² - t - 6, We have to calculate the displacement of the particle during the time period 1≤t≤4 and along with it calculate distance traveled during this time period. Using integration for determining the displacement, d\(= \int_{1}^{4} v(t)dt\)

\(= \int_{1}^{4} ( t² - t -6)dt\)

\(=[\frac{t³}{3} - \frac{t²}{2} - 6t]_{1}^{4}\)

\(= [ \frac{4³}{3} - \frac{4²}{2} - 6×4 - \frac{1³}{3} + \frac{1²}{2} + 6×1]\)

\(= 21 - 18 - \frac{15}{2}\)

= -4.5

Thus, the displacement of this object is -4.5 units of distance. Now, To determine the distance traveled, we need to consider all of the movement to be positive. So, v(t) = t² - t - 6

= t² + 2t - 3t - 6

= t( t + 2) - 3( t + 2)

= ( t + 2) (t -3)

so, v(t) > 0 for t [ 3, 4] and v(t) < 0 , [ 1, 3] so, distance \(= \int_{1}^{4} v(t)dt\)

\(= \int_{1}^{3} - ( t² - t -6)dt + \int_{3}^{4} ( t² - t -6)dt \)

\(=[-\frac{t³}{3} + \frac{t²}{2} + 6t]_{1}^{3} + [\frac{t³}{3} -\frac{t²}{2} - 6t]_{3}^{4}\)

\(=[-\frac{3³}{3} + \frac{3²}{2} + 18 +\frac{1³}{3} - \frac{1²}{2} - 6 ] + [\frac{4³}{3} -\frac{4²}{2} - 24 - \frac{3³}{3} +\frac{3²}{2} + 18]\)

\(=[\frac{11}{3} + 6 + \frac{1}{2} ]\)

= 1.166 m

Hence, required value is 1.16m.

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Answer:

B

Step-by-step explanation:

4 x 5 = 20, and that is the total number of squares in the grid.

10% of 20 is 2.

Therefore 10% of the graph is B.

Answer:

u = -2/3w + 4/3

Step-by-step explanation:

-12u + 13 = 8w-3

-12u = 8w - 16

u = -2/3w + 4/3

Answer:

-7

Step-by-step explanation:

To find this out we just place -3 where x is

f(-3)=4(-3)+5

f(-3)= -12+5

f(-3)= -7

Hopes this helps please mark brainliest

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

The problem requires evaluating the integral of 8ln(x) with respect to x over the interval [7, 8ln(8)].Method of integration by parts to solve the given integral by choosing u = ln(x) and dv = 8 dx, du = (1/x) dx and v = 8x.

To evaluate the integral ∫8ln(x) dx over the given interval, we can use the properties of logarithmic functions and integration techniques. First, we rewrite the integral as ∫ln(x^8) dx.

Using the power rule of integration, we can bring the exponent down and integrate the function term by term. Therefore, the integral becomes 8∫ln(x) dx.

To integrate ln(x), we use integration by parts. Let u = ln(x) and dv = dx. Then, du = (1/x) dx and v = x. Applying the integration by parts formula, we have ∫ln(x) dx = xln(x) - ∫(1/x) x dx.

Simplifying further, the integral becomes ∫ln(x) dx = xln(x) - ∫dx = xln(x) - x + C, where C is the constant of integration.

Now, we can substitute the limits of integration into the antiderivative expression. Evaluating at the upper limit, we have 8ln(8)ln(8) - 8ln(8) + C. Evaluating at the lower limit, we have 7ln(7) - 7ln(7) + C.

Subtracting the lower limit result from the upper limit result, we get the value of the integral over the given interval: 8ln(8)ln(8) - 8ln(8) + C - (7ln(7) - 7ln(7) + C).

Simplifying further, we have 8ln(8)ln(8) - 8ln(8) - 7ln(7) + 7ln(7). In summary, the evaluation of the integral ∫8ln(x) dx over the interval [7, 8ln(8)] yields the result 8ln(8)ln(8) - 8ln(8) - 7ln(7) + 7ln(7).

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Answer:

1,500

Step-by-step explanation:

It's preetty fast but it cannot be the record holder of " Lockheed SR-71 Blackbird " Which it's top speed i 2,100 miles per hour !!

The rectangular coordinate for the polar coordinate (4, 210°) is  (-3.46, -2).

The rectangular coordinate for the polar coordinate (4, 210°) is calculated by applying the following formula as shown below;

x = r cos(θ)

y = r sin(θ)

where;

From the given  polar coordinate (4, 210°);

r = 4

θ = 210⁰

The rectangular coordinate is calculated as follows;

x = 4 x cos(210°)

y = 4 x sin(210°)

x = -3.46

y = -2

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Given:

y = 4/5x - 3

y = 4/5x + 1

Looking at the above equation, they both have the same coefficient of y and also the same slope but there intercepts are different.

If we are to subtract the second equation from the first equation, we will have

0 = -4.

The above statement is incorrect because 0 ≠ 4 .

Hence, we can now say the system of equations has no solutions from the above reasoning.

Answer:

(-9), (-2), 1, 3

Step-by-step explanation:

Answer:

|1|, |-2|, |3|, |-9|

Step-by-step explanation:

Find the absolute values

Order from least to greatest

Answer:

x=6

Step-by-step explanation:

3x+19=7x-5

First of all you have to group like terms

19+5=7x-3x

24 = 4x

4 4

6=x