(Chapter 12) For any vectors u and v in V3 and any scalar k,k(u à v)= (ku) à v

Answer:

\(3v^2\left(5v^6-7v^3\right)=15v^8-21v^5\)

Step-by-step explanation:

Given the expression

\(3v^2\left(5v^6-7v^3\right)\)

Apply the distributive law

\(a\left(b-c\right)=ab-ac\)

\(a=3v^2,\:b=5v^6,\:c=7v^3\)

\(=3v^2\cdot \:5v^6-3v^2\cdot \:7v^3\)

\(=3\cdot \:5v^6v^2-3\cdot \:7v^3v^2\)

\(=15v^8-21v^5\)

Thus, we conclude that

\(3v^2\left(5v^6-7v^3\right)=15v^8-21v^5\)

Answer:

it is a two-dimensional shape that can be modified to form a three-dimensional shape or a solid

Step-by-step explanation:

Bඞ වචනඞ වචනඞ වචනඞ වචනඞ වචනඞ වචන

Answer:

first question : solve for m: multiply both sides by n

m/n=p

m*(n)/n=p*n

m= p*n

Step-by-step explanation:

to solve for m in the first part, you have to get rid of the extras next to m. in this case because m is divided by n, if we multiply both sides by n, both n on the m side will cancel out n/n=1 . this will leave m*1= n*p

because we can ignore the coefficient 1, the solution of ot will give you m=n*p

this also answers the question that's asked in the first place. in the first question, you have to multiply both sides by n in order to get the answer.

The direction of D⃗ = A⃗ − B⃗ expressed in degrees above the negative x-axis is approximately 46.5 degrees.

To find the direction of D⃗ = A⃗ − B⃗, we need to calculate the angle it makes with the negative x-axis.

First, let's find the components of D⃗:

Dx = Ax - Bx = -3.89 - (-1.48) = -2.41

Dy = Ay - By = -2.4 - (-4.91) = 2.51

The angle θ that D⃗ makes with the negative x-axis can be found using the arctan function:

θ = arctan(Dy / Dx)

Substituting the values:

θ = arctan(2.51 / -2.41)

Using a calculator or trigonometric tables, we find:

θ ≈ -46.5 degrees

Since we want the angle above the negative x-axis, we take the absolute value of θ:

|θ| ≈ 46.5 degrees

As a result, the direction of D = A B is approximately 46.5 degrees above the negative x-axis.

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The outer diameter of the thin-walled pipe can be calculated by adding twice the thickness to the inner diameter. Therefore, the outer diameter is 0.5 in + 2(0.025 in) = 0.55 in.

A thin-walled pipe is a hollow cylinder with a relatively small thickness compared to its inner and outer diameters. In this case, the inner diameter of the pipe is given value as 0.5 in, and the thickness is 0.025 in.

To find the outer diameter, we add twice the thickness to the inner diameter. This is because the thickness is divided equally on both sides of the inner diameter. So, the outer diameter can be calculated as 0.5 in + 2(0.025 in) = 0.55 in.

The outer diameter is an important parameter in determining the overall size and structural integrity of the pipe. It affects the flow capacity, strength, and compatibility with other pipe fittings.

Knowing the outer diameter allows for proper sizing and fitting of the thin-walled pipe in various applications, such as plumbing, HVAC systems, or fluid transportation.

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Answer:

D

Step-by-step explanation:

To get from A to B you must divide by x on each side, therefore dividing by the same variable expression

The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

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Answer:

13/8 45/3/8  7 7/8

Step-by-step explanation:

Answer:

The dimensions of the rectangle are length = 22 meters and width = 13 meters.

Step-by-step explanation:

It is given that the length of a rectangle is 4 meters less than twice the width and if the area of the rectangle is 286 square meters we need to calculate the dimensions.

Firstly, let us look at the dimensions of the rectangle;

=> Let 'l' be the length and 'b' be the width of the rectangle.

Now, let us look at the area of a rectangle;

=> l × b

So, we get an equation from the above condition;

=> l = 2b - 4

Now, the area of the rectangle is given that is 286 square​ meters;

=> A = 286 sq. m.

Using the above-mentioned formula for the area of the rectangle we get;

=> A = l × b

=> 286 = (2b - 4) × b

=> 286 = 2b² - 4b

=> 2b² - 4b - 286 = 0

After solving it further we get;

=> 2b² - 4b - 286 = 0

=> b² - 2b - 143 = 0

=> b² - 13b + 11b - 143 = 0

=> (b - 13) + (b + 11) = 0

Now, after equating both the sides we get;

=> (b - 13) = 0

=> b = 13

and

=> (b + 11) = 0

=> b = -11

But, b = -11 is not possible so, the width of the rectangle is 13 meters.

And the length of the rectangle would be,

=> l = 2b - 4

=> l = 2 × 13 - 4

=> l = 22

Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters.

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The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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The given statement "The median of a quantitative data set is always one of the individual data values" is false.

When a given data set is arranged in ascending order the observation which at the between of the data is the median of that data set. It is a value in the set whose left and right both have the same number of observations.

The given statement is not true, this is because the median is the mid-value of any data set.

Hence, the given statement "The median of a quantitative data set is always one of the individual data values" is false.

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Answer:

y= -5x-2

Step-by-step explanation:

Parallel equations have the same slope, so we know our slope will be -5. To get our y-intercept, we need to plug in our slope. 1 times -5 is -5, so we need to figure out how to get from -5 to -7. We're going to subtract 2, so the y-intercept is -2.

The equation of the line parallel to y=12-5x and passes through the point (1,-7) will be y= -5x-2.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of a line that is parallel to y=12-5x and passes through the point (1,-7).

The slope of the parallel lines is always the same. The slope of the line will be -5.

The y-intercept of the line will be calculated as,

y = mx + c

-7 = -5(1) + c

c = -7 + 5

c = -2

The equation of the line will be written as,

y = mx + c

y = -5x - 2

Therefore, the equation of the line parallel to y=12-5x and passes through the point (1,-7) will be y= -5x-2.

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The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

The complete image is attached.

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This is because

This is found through trial and error.

This is for problem 1 only. Problems 2 through 6 will follow a similar structure.

The length of a truck is an example of a continuous data set, and 20 feet is just one possible value within that range.

The given value, "a truck with a length of 20 feet," is an example of a continuous data set.

Continuous data refers to values that can take on any numerical value within a range, with no gaps or interruptions. In this case, the length of a truck can take on any value between 0 and some maximum length, with no gaps or interruptions in between.

In contrast, discrete data refers to values that can only take on certain specific values, usually integers. For example, the number of tires on a truck is a discrete data set because it can only take on integer values (e.g. 4, 6, 8).

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\(\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{ns^2}{4}\cot\left( \frac{180}{n} \right) ~~ \begin{cases} n=\stackrel{sides'}{number}\\ s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ n=5\\ s=14 \end{cases}\implies A=\cfrac{(5)(14)^2}{4}\cot\left( \frac{180}{5} \right) \\\\\\ A=36\cot(20^o)\implies A\approx 98.91~m^2 \\\\\\ A=245\cot(36^o)\implies A\approx 337.21~in^2\)

Make sure your calculator is in Degree mode.

Answer:5

Step-by-step explanation:I divided 80.0 by 16.0

Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.

The cylindrical, which is frequently a lobed solid, comprises one of the most simple curvature geometric forms. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinders" is also used to refer to an infinitely curved surface in a number of modern domains of topology and geometries. A "cylinder" is a two half object made up of curved surfaces with circle tops and bases. A cylinder is a two half solid figure with two bases that are both similar circles connected at its height, which is controlled by the separation of the legs from the center. Cans of iced drinks and the wicks from toilet paper are example of cylinders.

given

r = d/2 = 40/2 = 20 cm

v = pi *r*r*h

100 = 3.14 * 20*20 *h

100 = 1256*h

h = 0.08 cm

strong box = surface area of cuboid = 45 * 90

= 4050 cm2

surface area of water heater = A=2πrh+2πr2=2·π·20·0.08+2·π·202

≈2523.3

Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.

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a) The expected number of people to die before their 71st birthday is given as follows: 128.

b) The probability that a 67 year old woman will live to her 68th birthday is given as follows: 0.8876 = 88.76%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

0.025679 of the 70 year old men die, hence the expected number out of 5000 is given as follows:

0.025679 x 5000 = 128.

The probability for item b is given as follows:

0.016798/0.018925 = 0.8876 = 88.76%.

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The most appropriate choice of percentage will be given by-

£47 after 24% decrease becomes £35.72

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Here,

Original Price = £47

Percentage decrease = 24 %

Decrease in Price = £(\(\frac{24}{100} \times 47\\\))

                              = £11.28

New Price = £(47 - 11.28)

                 = £35.72

So, £47 after 24% decrease becomes £35.72

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Answer:

y = f(x) = 7.

The output for the equation is 7 when x=2.

Step-by-step explanation:

First, let's transform y = 3x + 1 into a function (f(x)) form.

f(x) = 3x + 1

When the Input, or x, equals to 2, we have:

f(x) = 3x + 1

f(2) = 3(2) + 1

f(2) = 6 + 1

f(2) = 7.

Given that y = f(x),

The output for the equation is 7 when x=2.

Answer:

Step-by-step explanation:

Inverse variation satisfies the form yx=k, if y=2 while x=-6 then

2(-6)=k, k=-12, then

yx=-12, when y=-3

-3x=-12

x=4

Answer:

y = 4/5x +4

Step-by-step explanation:

Let me know if you need an explanation in the comments

Step-by-step explanation:

answer=-1

Since  \(l\) || \(m\) || \(n\) we can make the equation of

\(5x+1+8x+10=180\\13x=169\\x=13\)

Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

Answer:

it's the bottom right!! TRUST MR I PROMISE

Step-by-step explanation:

IT IS THE ONLY LINE GOING DOWN which proves it's negative!!!