(-11)+(-7)+(-3)0 -150-70 -21O 15

The equation provided offers a geometric representation of the cross product, which calculates a resulting vector perpendicular to two given vectors, based on their magnitudes, angle, and direction in three-dimensional space.

The provided equation represents the geometric representation of the cross product. The cross product of two vectors, \(\vec{A}\) and \(\vec{B}\), is denoted as \(\vec{C} = \vec{A} \times \vec{B}\). It is equal to the product of the magnitudes of the two vectors, \(|\vec{A}|\) and \(|\vec{B}|\), multiplied by the sine of the angle between them, \(\alpha\), and the unit vector \(\hat{C}\) perpendicular to the plane formed by \(\vec{A}\) and \(\vec{B}\).

To better understand the geometric representation of the cross product, let's break down the equation:

- \(\vec{C}\) represents the resulting vector obtained by taking the cross product of \(\vec{A}\) and \(\vec{B}\).

- \(|\vec{A}|\) and \(|\vec{B}|\) denote the magnitudes (or lengths) of vectors \(\vec{A}\) and \(\vec{B}\), respectively.

- \(\alpha\) represents the angle between vectors \(\vec{A}\) and \(\vec{B}\).

- \(\sin \alpha\) calculates the sine of the angle \(\alpha\).

- \(\hat{C}\) is a unit vector perpendicular to the plane formed by \(\vec{A}\) and \(\vec{B}\).

The magnitude of the resulting vector \(\vec{C}\) is given by the product of the magnitudes of \(\vec{A}\) and \(\vec{B}\) multiplied by the sine of the angle \(\alpha\) between them. The direction of \(\vec{C}\) is determined by the right-hand rule. If you align your right-hand fingers with \(\vec{A}\) and curl them towards \(\vec{B}\), your thumb points in the direction of \(\vec{C}\).

It's important to note that the cross product is only defined in three dimensions, and the resulting vector is always perpendicular to both \(\vec{A}\) and \(\vec{B}\). If the vectors are parallel or antiparallel, the cross product will be zero.

In summary, the equation provided offers a geometric representation of the cross product, which calculates a resulting vector perpendicular to two given vectors, based on their magnitudes, angle, and direction in three-dimensional space.

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Answer:

26.92 min

if I'm not wrong!

The transpose of the matrix is given by

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Given:

\(\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}\)

Express 16 as \(4^{2}\): \(x^2+y^2=16\)

\(x^2+y^2=4^2\\x^2+y^2=4^2 \times 1\)

Trignometry,

\(\cos ^2(t)+\sin ^2(t)=1\)

Now, substitute \(\cos ^2(t)+\sin ^2(t)\) for 1:

\(\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)\)

Law of indicates:
\(\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2\)

Taking positive square roots as follows:

\(x=4 \cos (t), y=4 \sin (t)\)

Recall that, z = xy.

Now, we have:

\(\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}\)

Now, substitute the values:
\(r(t)=x_t i+y_t j+z_t k\)

So, the vector r(t) is: \(r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i\)

Therefore, the vector function r(t) is written as: \(r(t)=x_t i+y_t j+z_t k\)

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The body displacement and average velocity for the given time interval is 65m and 13m/s respectively .

Given,

s = t³ - 12t² + 48t

0 ≤ t ≤ 5

Now,

Displacement = Δs

= s(5) - s(0)

Substitute the values of time in the displacement function:

Δs = s(5) - s(0)

Δs = [5³ - 12×5 + 48×5 ] - 0

Δs = 65 m

Thus displacement = 65m

Now the average velocity of the moving body,

V(average) = displacement / time

V (average) = 65/5

V(average)  = 13m/s

Thus the average velocity of the moving body is 13m/s .

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Complete question:

The function s = t³ - 12t² + 48t gives the position of a body moving on a coordinate line with s in meters and v in m/s .

a) Find the body's displacement and average velocity for the given time interval .

Answer for

14

=

2

x

^2

+

x

Step-by-step explanation:

Rewrite the equation as  2

x^

2

+

x=

14

.

2

x

^2

+

x

=

14

Move  14  to the left side of the equation by subtracting it from both sides.

2

x

^2

+

x

−

14

=

0

Use the quadratic formula to find the solutions.

−

b

±

√

b

^2

−

4

(

a

c

)

       2

a

Substitute the values  a

=

2

,  b

=

1

, and  c

=

−

14  into the quadratic formula and solve for  x

.

−

1

±

√

1

2

−

4

⋅

(

2

⋅

−

14

)

        2

⋅

2

Simplify the numerator.

x

=

−

1

±

√

113

    2

⋅

2

Multiply  2  by  2

.

x

=

−

1

±

√

113

      4

The final answer is the combination of both solutions.

x

=

−

1

−

√

113

 -  1

+

√

113  

       4               4

The result can be shown in multiple forms.

Exact Form:

x

=

−

1

−

√

113  

,  −

1

+

√

113

4

      4               4

Decimal Form:

x

=

2.40753645

…  ,  −

2.90753645

…

The parabola's vertex is located at (-2, 8). The parabola's graph is then depicted below.

Let a be the leading coefficient and the parabola's vertex be the point (h, k). The parabola's equation will therefore be stated as,

y = a(x - h)² + k

The parabola's equation is stated as,

y = -(x + 2)² + 8

The downward-pointing parabola is represented by the negative sign.

The vertex of the parabola is at (-2, 8), according to the equation above. The parabola's graph is then depicted below.

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Answer:

Quadrant 4

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

The name of the segment inside the large triangle is called the: 3. angle bisector.

The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.

The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.

A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.

Therefore, we can state that the name of the segment is: 3. angle bisector.

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Answer:

\( \huge 0 \)

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

From the question we have

\(m = \frac{ - 5 - - 5}{8 - 3} = \frac{ - 5 + 5}{5} = \frac{0}{5} = 0 \\ \)

We have the final answer as

Hope this helps you

The shortest distance between planet Q and planet R is 1.64 * 10⁷ km

An equation is an expression that shows the relationship between variables and numbers.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:

hypotenuse² = adjacent² + opposite²

From the diagram, QR is the shortest distance between planet Q and planet R. Hence using Pythagoras:

QR² = QP² + PR²

QR² = (3.6 * 10⁶)² + (1.6 * 10⁷)²

QR = 1.64 * 10⁷ km

The shortest distance is 1.64 * 10⁷ km

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Answer:

126 square feet

Step-by-step explanation:

Lateral Surface Area :

Perimeter :

Height : 4.5 ft

Solving :

Answer:

D i think

Step-by-step explanation:

Just because the lines are the same length doesn’t mean the angles are equal

High-tech processes rely on high technology, highly educated workers, and government financial support, while low-tech processes rely on low technology, less educated workers, and minimal government support.

High-tech processes are characterized by the utilization of advanced technology, sophisticated equipment, and specialized interest. These processes often require a highly skilled and educated workforce capable of operating and maintaining complex systems. Additionally, high-tech industries often receive substantial financial support from governments in the form of research funding, subsidies, and infrastructure development to foster innovation and competitiveness.

On the other hand, low-tech processes involve simpler technology and require less specialized knowledge. These processes typically rely on manual labor and may not require advanced education or training. Low-tech industries often operate with minimal government support, as they may not be considered strategic or high-priority sectors

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Answer:

(5x+40)+x+2(2x+20)=360

5x+40+x+4x+40=360

10x+80=360

10x=360-80

10x=280

x=28°

substitute x=28° into (5x+40)

=140+40= 180

therefore line Ac is the diameter of a he circle because a diameter divides a circle into 2 equal part and the angle on the line is 180° showing that the circle is on a straight line

The real part of the principal value of (1+i√√3)i is 1/2.

To find the real part of the principal value of (1+i√√3)i, we can first find the principal value of the complex number (1+i√√3).

To do this, we find the magnitude (or modulus) of the complex number by using the Pythagorean theorem:|

1+i√√3| = √(1² + (√√3)²) = 2

Then, we find the argument (or angle) of the complex number using the inverse tangent function:

arg(1+i√√3) = tan⁻¹(√√3/1) = π/3

Therefore, the principal value of (1+i√√3) is 2(cos(π/3) + i sin(π/3)) = 1/2 + i(√3/2).

Next, we multiply this principal value by i: i(1/2 + i(√3/2)) = -√3/2 + i/2

The real part of this complex number is -√3/2, but we want the real part of the principal value.

Since the imaginary part of the principal value is (√3/2)i, we know that the imaginary part of the product must be -(1/2)i. Therefore, the real part of the principal value is 1/2.

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Answer:

The triangle is not isosceles

Explanation:

The initial figure is:

Now, the angle with measure 55° and angle A are vertically opposite angles. It means that these angles have the same measure. So, angle A has a measure of 55°.

In the same way. Angle x and B are vertically opposite angles. So, angle B has a measure of x°

Then, the sum of the interior angles of a triangle is always 180°. It means that:

A + B + 60° = 180°

55° + x° + 60° = 180°

Solving for x, we get:

115° + x° = 180°

x° = 180° - 115°

x° = 65°

Finally, a triangle isosceles if two of its interior angles have the same measure. Since the measures of the interior angles of the triangle are 60°, 55°, and 65°, the triangle is not isosceles.

Answer:

the nwser is 8 please mark brainliest

Step-by-step explanation:

Answer:

4x²+17x-15

Use the FOIL method. Multiply the first term in each group, then the outer ones, then the inner ones, and finally the last term in each group together. The first terms in this case are 4x and x, the outer terms are 4x and 5, the inner terms are -3 and x, and the last terms are -3 and 5.

Hope this helps!

Step-by-step explanation:

4x^2+20x-3x+5

4x^2+17x-15

Answer:

Step-by-step explanation:

Replace x

x=-y+21

2(-y+21)-15=y

Then solve the rest

Answer:

15 is larger than -4

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

15 ÷ (-4) = -3.75

Hence,  when \(n=10\) the given inequality is true.

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.

So,

\(2(n + 2) < 5(n-1)\)

When

\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)

Hence,  when \(n=10\) the given inequality is true.

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To test for consistency in the given system of equations:

\(\[\begin{align*}x - 4y + 7z &= 14 \\3x + 8y - 2z &= 13 \\7x - 8y + 26z &= 5\end{align*}\]\)\(\[x - 4y + 7z &= 14 \\3x + 8y - 2z &= 13 \\7x - 8y + 26z &= 5\]\)

We can use the method of Gaussian elimination or matrix operations. However, to provide a short answer using LaTeX, I will use matrix notation to perform row reduction:

\(\[\begin{bmatrix}1 & -4 & 7 & 14 \\3 & 8 & -2 & 13 \\7 & -8 & 26 & 5\end{bmatrix}\]\)

Performing row reduction operations, we can obtain the row-echelon form:

\(\[\begin{bmatrix}1 & -4 & 7 & 14 \\0 & 20 & -23 & -29 \\0 & 0 & 1 & -3\end{bmatrix}\]\)

Since we do not have a row with the form [0 0 ... 0 | b], where b is a non-zero value, the system is consistent. Additionally, all the rows have at least one non-zero entry in the augmented column. Therefore, the system of equations is consistent.

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The probability that both digits in a New York State daily lottery game are different is 0.9, or 9 out of 10.

To find the probability that both digits in a New York State daily lottery game are different, we need to first calculate the total number of possible outcomes. Since there are 10 digits (0-9) that can be selected for each of the two digits in the sequence, there are a total of 10 x 10 = 100 possible outcomes.

Now, we need to determine the number of outcomes where both digits are different. There are 10 possible choices for the first digit and only 9 possible choices for the second digit, since we cannot choose the same digit as the first. Therefore, there are a total of 10 x 9 = 90 outcomes where both digits are different.

The probability of both digits being different is equal to the number of outcomes where both digits are different divided by the total number of possible outcomes. Thus, the probability is 90/100, which simplifies to 9/10, or 0.9.

In summary, the probability that both digits in a New York State daily lottery game are different is 0.9, or 9 out of 10. This means that there is a high likelihood that both digits selected will be different.

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The line of code needed below to complete the factorial recursion method is: return x * fact(x-1);

This will recursively call the fact method with x-1 as the parameter until x reaches 1, and then it will start multiplying all the values from x down to 1 to get the factorial value.

To complete the factorial recursion method using the terms you provided, you can add the following line of code:

```java
public int fact(int x) {
   if (x <= 1) {
       return 1;
   }
   return x * fact(x - 1);
}
```

This code checks if x is less than or equal to 1, and if so, returns 1. Otherwise, it returns x multiplied by the factorial of x-1, allowing for the proper recursive calculation of the factorial.

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From the given information, cholesterol level X follows the N(222, 37) distribution.

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:

z = (x - μ) / σ

For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595

For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as

P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406

In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:

z = (x - μ) / σ

Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.

So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.

By using the standard normal distribution table,

we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274

The cholesterol level of 90% of men in this population is at most 274 mg/dl.

The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.

The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.

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