Physics : asked on Lingz
 27.10.2020

The magnitude of vector λa is 5. Find the value of λ, if: a = (−6, 8)

. 0

Faq

Physics
Step-by-step answer
P Answered by Master

Given :

\:  \:

\color{pink}{\rm \: The \:magnitude \:of \:vector\: λa\: is \:  {\bold5\:}}

\:

\color{green}{\rm \: a = (−6, 8)}

\:

To Find :

\:  \:

\orange{ \rm\: value \:  of \:  \bold{ λ \: }}

\:  \:

\rm \: The \:  magnitude \:  of \:  the  \: vector  \: a  \: is  \:  ||a|| = \sqrt{(-6)^2+ 8^2)}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    \:  \:  \rm = \sqrt{( 36+64)} \\ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\:\:   \: \:\:= \rm\sqrt{100} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \: \:  \:  \:   \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:\\\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:\: \rm   \underline{\boxed{\red{ \:  = 10 \: }}} \green✓

\:  \:

\rm \: Therefore, \:  λ =   \cancel{\frac{5}{10} } \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \underline  {  \: \boxed{ \red{\: \rm = 0.5\:}}}{  \green ✓ }

Hope helps ~

\color{purple}\frak{SarcasticSmileeᥫ᭡}

`

Physics
Step-by-step answer
P Answered by Specialist

The question is missing the alternatives. Here is the complete question.

Two vectors of magnitude |A| = 8units and |B| = 5units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A+B CANNOT have the value of:

A. 2 units

B. 5 units

C. 8 units

D. 12 units

A. 2 units

Explanation: Vector is an entity that has characteristics as magnitude and direction. Resultant vector is the "sum" of 2 or more vectors.

In this question, the vectors have magnitude and angle varies from 0° to 180°.

When angle between vectors A and B is 0°, they are parallel and pointing to the same direction, so:

V_{R} = |A| + |B|

V_{R}=8+5

V_{R} = 13

When the angle is 180°, it means vectors are in opposing directions, so:

V_{R} = |A| - |B|

V_{R} = 8-5

V_{R} = 3

From the calculations, we can conclude the magnitude of resultant vector varies between 3 and 13.

The least value is 3, so it cannot have a value of 2 units.

Physics
Step-by-step answer
P Answered by Specialist

The question is missing the alternatives. Here is the complete question.

Two vectors of magnitude |A| = 8units and |B| = 5units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A+B CANNOT have the value of:

A. 2 units

B. 5 units

C. 8 units

D. 12 units

A. 2 units

Explanation: Vector is an entity that has characteristics as magnitude and direction. Resultant vector is the "sum" of 2 or more vectors.

In this question, the vectors have magnitude and angle varies from 0° to 180°.

When angle between vectors A and B is 0°, they are parallel and pointing to the same direction, so:

V_{R} = |A| + |B|

V_{R}=8+5

V_{R} = 13

When the angle is 180°, it means vectors are in opposing directions, so:

V_{R} = |A| - |B|

V_{R} = 8-5

V_{R} = 3

From the calculations, we can conclude the magnitude of resultant vector varies between 3 and 13.

The least value is 3, so it cannot have a value of 2 units.

Mathematics
Step-by-step answer
P Answered by Specialist

1. The given triangle ABC, has a right angle at C, BC=11, and B=30\degree

\tan 30\degree=\frac{AC}{11}

AC=11\tan 30\degree

AC=\frac{11\sqrt{3}}{3}

Ans: A

2. The reference angle is the angle the terminal side makes with x-axis.

-\frac{33\pi}{8}=-4\frac{\pi}{8}

This implies that, -\frac{33\pi}{8} has a reference angle of \frac{\pi}{8}.

Ans: C

3. Let x be the shortest distance the ramp can span.

From the diagram; \tan (4.76\degree)=\frac{2.5}{x}

\implies x=\frac{2.5}{\tan (4.76\degree)}

\implies x=30.0ft

Ans:B

4. Use the Pythagorean identity: 1+\tan ^2 \theta=\sec^2 \theta.

If \cot \theta=-\frac{1}{2},then  \tan \theta=-2

\implies 1+2^2=\sec^2 \theta

\implies \sec^2 \theta=5

\implies \sec \theta=-\sqrt{5}, In QII, the secant ratio is negative.

Ans:C

5. We have \sin \frac{2\pi}{3}=\frac{\sqrt{3} }{2}

\cos \frac{\pi}{6}=\frac{\sqrt{3} }{2}

\cos \frac{\pi}{3}=\frac{1}{2}

\sin \frac{5\pi}{3}=-\frac{\sqrt{3} }{2}

\cos \frac{7\pi}{6}=-\frac{\sqrt{3} }{2}

\cos \frac{11\pi}{6}=\frac{\sqrt{3} }{2}

Ans:A and D

6.  The given function that is equivalent to f(x)=\sin x is f(x)=\cos (-x+\frac{\pi}{2}).

When we reflect the graph of  f(x)=\cos (x)  in the y-axis and shift it to the left by  \frac{\pi}{2} units, it coincides with graph of f(x)=\sin x.

Ans:C

7. The function y=\tan x is a one-to-one function on the interval [-\frac{\pi}{2},\frac{\pi}{2}]

When we restrict the domain of  y=\tan x on [-\frac{\pi}{2},\frac{\pi}{2}] it becomes an invertible function.

Ans: C

8. The given function is y=3\sin(4x-\pi)

The horizontal shift is given by \frac{C}{B}=\frac{\pi}{4}

The direction of the shift is to the right.

Ans:D

9.  \cos(-75\degree)=\cos(75\degree) by the symmetric property of even functions.

\cos(75\degree)=\cos(45\degree+30\degree)

\cos(75\degree)=\cos(45\degree) \cos30\degree-\sin(45\degree) \sin30\degree

\cos(75\degree)=\frac{\sqrt{2} }{2} \times \frac{\sqrt{3} }{2} -\frac{\sqrt{2} }{2} \times \frac{1}{2}

\cos(75\degree)=\frac{\sqrt{6}-\sqrt{2}}{4}

Ans: B

10. Recall the cosine rule: a^2=b^2+c^2-2bc\cos A

Let the angle measure opposite to the longest side be A, then a=19,b=17, and c=15.

\Rightarrow 19^2=17^2+15^2-2(17)(15)\cos A

\implies -153=-510\cos A

\implies \cos A=0.3

\implies A=\cos^{-1}(0.3)=73\degree

Ans:B

11.  We want to solve 2\sin(2x)\cos(x)-\sin(2x)=0 on the interval;

[-\frac{\pi}{2},\frac{\pi}{2}]

Factor:  \sin2(x)[2\cos(x)-1)=0

Either \sin(2x)=0 \implies x=0\frac{\pi}{2}

Or [2\cos x-1=0 This means that x=\frac{\pi}{3},-\frac{\pi}{3}

Therefore required solution is x=-\frac{\pi}{3},0,\frac{\pi}{3},\frac{\pi}{2}

Ans:D

12. Use the relation:r=\sqrt{x^2+y^2} and \theta=\tan^{-1}(\frac{y}{x})=

The given rectangular coordinate is (1,-2)

This implies that:r=\sqrt{1^2+(-2)^2}=\sqrt{5}

\theta=\tan^{-1}(\frac{-2}{1})= This means  \theta=116.6 or \theta=296.6

The polar forms are: -\sqrt{5},116.6 and \sqrt{5},296.6

Ans: B and C

13.  The polar equation that represents an ellipse is

r=\frac{2}{2-\sin \theta}.

When written in standard form; r=\frac{1}{1-0.5\sin \theta}.

The eccentricity is 0.5\:.

Therefore the r=\frac{2}{2-\sin \theta} is an ellipse.

Ans: B

14. The DeMoivre’s Theorem states that;

(\cos \theta+i\sin \theta)^n=\cos n\theta+i\sin n\theta

This implies that:

[2(\cos \frac{\pi}{9}+i\sin \frac{\pi}{9})]^3=2^3\cos 3\times \frac{\pi}{9}+i\sin 3\times \frac{\pi}{9})

[2(\cos \frac{\pi}{9}+i\sin \frac{\pi}{9})]^3=8(frac{2}{2})+i8(\frac{\sqrt{3}}{2})=4+4\sqrt{3}i

Ans: A

15. Let the initial point be (x,y), Then |v|=\sqrt{(-2-x)^2+(4-y)^2}.

If x=-8, and y=-4.

Then, |v|=\sqrt{(-2--8)^2+(4--4)^2}.

|v|=\sqrt{(-6)^2+(8)^2}=\sqrt{100}=10.

Ans: B

16. We find the dot product to see if it is zero.

u\bullet v=-6(7)+4(10)=-2

Since the dot product is not zero the vectors are not orthogonal

\theta=\cos ^{-1}(\frac{u\bullet v}{|u||v|})

\theta=\cos ^{-1}(-\frac{2}{2\sqrt{13}\times \sqrt{1149} }) =91.3\degree

Ans:B

17. Given v=5i+4j, w=2i-3j.

u=v+w

Add corresponding components

This implies u=(5i+4j)+(2i-3j)

u=(5i+2i+4j-3j)

u=7i+j

Ans:B

See attachment.


1. in abc, c is a right angle and bc= 11. if the measure of angle b= 30degrees, find ac. a) (11sqrt3
1. in abc, c is a right angle and bc= 11. if the measure of angle b= 30degrees, find ac. a) (11sqrt3
Computers and Technology
Step-by-step answer
P Answered by Master

Explanation:

The following code is written in Java and loops five times asking for the desired inputs from the user and saves that information in two Vectors named jerseyNumber and ratings. Then creates a while loop for the menu and a seperate method for each of the options...

import java.util.Scanner;

import java.util.Vector;

class {

   static Scanner in = new Scanner(System.in);

   static Vector<Integer> jerseyNumber = new Vector<>();

   static Vector<Integer> ratings = new Vector<>();

   public static void main(String[] args) {

       for (int x = 0; x < 5; x++) {

           System.out.println("Enter player " + (x+1) + "'s jersey number:");

           jerseyNumber.add(in.nextInt());

           System.out.println("Enter player " + (x+1) + "'s rating:");

           ratings.add(in.nextInt());

       }

       boolean reloop = true;

       while (reloop == true) {

           System.out.println("Menu");

           System.out.println("a - Add player");

           System.out.println("d - Remove player");

           System.out.println("u - Update player rating");

           System.out.println("r - Output players above a rating");

           System.out.println("o - Output roster");

           System.out.println("q - Quit");

           char answer = in.next().charAt(0);

           switch (answer) {

               case 'a': addPlayer();

                   break;

               case 'd': removePlayer();

                   break;

               case 'u': updatePlayer();

                   break;

               case 'r': outputRating();

                   break;

               case 'o': outputRoster();

                   break;

               case 'q': System.exit(0);

                   reloop = false;

                   break;

           }

       }

   }

   public static void addPlayer() {

       System.out.println("Enter player's jersey number:");

       jerseyNumber.add(in.nextInt());

       System.out.println("Enter player's rating:");

       ratings.add(in.nextInt());

   }

   public static void removePlayer() {

       System.out.println("Enter Jersey number:");

       int number = in.nextInt();

       for (int x = 0; x < jerseyNumber.size(); x++) {

           if (jerseyNumber.get(x) == number) {

               jerseyNumber.remove(x);

               ratings.remove(x);

           }

       }

   }

   public static void updatePlayer() {

       System.out.println("Enter Jersey number:");

       int number = in.nextInt();

       System.out.println("Enter new Rating:");

       int rating = in.nextInt();

       for (int x = 0; x < jerseyNumber.size(); x++) {

           if (jerseyNumber.get(x) == number) {

               ratings.set(x, rating);

           }

       }

   }

   public static void outputRating() {

       System.out.println("Enter Rating:");

       int rating = in.nextInt();

       for (int x = 0; x < ratings.size(); x++) {

           if (ratings.get(x) >= rating) {

               System.out.println(jerseyNumber.get(x));

           }

       }

   }

   public static void outputRoster() {

       for (int x = 0; x < jerseyNumber.size(); x++) {

           System.out.println("Player " + (x+1) + " -- Jersey number: " + jerseyNumber.get(x) + ", Rating: " + ratings.get(x));

       }

   }

}


5.27 LAB*: Program: Soccer team roster (Vectors)

This program will store roster and rating informat
5.27 LAB*: Program: Soccer team roster (Vectors)

This program will store roster and rating informat
Computers and Technology
Step-by-step answer
P Answered by Specialist

Explanation:

The following code is written in Java and loops five times asking for the desired inputs from the user and saves that information in two Vectors named jerseyNumber and ratings. Then creates a while loop for the menu and a seperate method for each of the options...

import java.util.Scanner;

import java.util.Vector;

class {

   static Scanner in = new Scanner(System.in);

   static Vector<Integer> jerseyNumber = new Vector<>();

   static Vector<Integer> ratings = new Vector<>();

   public static void main(String[] args) {

       for (int x = 0; x < 5; x++) {

           System.out.println("Enter player " + (x+1) + "'s jersey number:");

           jerseyNumber.add(in.nextInt());

           System.out.println("Enter player " + (x+1) + "'s rating:");

           ratings.add(in.nextInt());

       }

       boolean reloop = true;

       while (reloop == true) {

           System.out.println("Menu");

           System.out.println("a - Add player");

           System.out.println("d - Remove player");

           System.out.println("u - Update player rating");

           System.out.println("r - Output players above a rating");

           System.out.println("o - Output roster");

           System.out.println("q - Quit");

           char answer = in.next().charAt(0);

           switch (answer) {

               case 'a': addPlayer();

                   break;

               case 'd': removePlayer();

                   break;

               case 'u': updatePlayer();

                   break;

               case 'r': outputRating();

                   break;

               case 'o': outputRoster();

                   break;

               case 'q': System.exit(0);

                   reloop = false;

                   break;

           }

       }

   }

   public static void addPlayer() {

       System.out.println("Enter player's jersey number:");

       jerseyNumber.add(in.nextInt());

       System.out.println("Enter player's rating:");

       ratings.add(in.nextInt());

   }

   public static void removePlayer() {

       System.out.println("Enter Jersey number:");

       int number = in.nextInt();

       for (int x = 0; x < jerseyNumber.size(); x++) {

           if (jerseyNumber.get(x) == number) {

               jerseyNumber.remove(x);

               ratings.remove(x);

           }

       }

   }

   public static void updatePlayer() {

       System.out.println("Enter Jersey number:");

       int number = in.nextInt();

       System.out.println("Enter new Rating:");

       int rating = in.nextInt();

       for (int x = 0; x < jerseyNumber.size(); x++) {

           if (jerseyNumber.get(x) == number) {

               ratings.set(x, rating);

           }

       }

   }

   public static void outputRating() {

       System.out.println("Enter Rating:");

       int rating = in.nextInt();

       for (int x = 0; x < ratings.size(); x++) {

           if (ratings.get(x) >= rating) {

               System.out.println(jerseyNumber.get(x));

           }

       }

   }

   public static void outputRoster() {

       for (int x = 0; x < jerseyNumber.size(); x++) {

           System.out.println("Player " + (x+1) + " -- Jersey number: " + jerseyNumber.get(x) + ", Rating: " + ratings.get(x));

       }

   }

}


5.27 LAB*: Program: Soccer team roster (Vectors)

This program will store roster and rating informat
5.27 LAB*: Program: Soccer team roster (Vectors)

This program will store roster and rating informat
Mathematics
Step-by-step answer
P Answered by Specialist

ANSWER

See attachment for questions 6 to 25

y= - 11x   - 16

QUESTION 26

The given function is:

f(x) = 4 {x}^{2}  + 5x

The slope function is obtained by taking the first derivative of the function with respect to x.

f'(x) = 8x + 5

At (-2,6), x= -2

We plug in the x-value to find the slope of the function.

f'( - 2) = 8( - 2)+ 5

f'( - 2) =  - 16+ 5

f'( - 2) =  - 11

The equation is given by:

y-y_1=m(x-x_1)

We substitute the point and slope into the formula to get;

y-6= - 11(x- - 2)

y= - 11x  - 22 + 6

y= - 11x   - 16

The correct answer is D


6.which trigonometric function is equivalent to f(x)=sin x?  a) f(x)=cos(-x+(3pi/2)) b) f(x)=cos(x+(
Mathematics
Step-by-step answer
P Answered by Master

ANSWER

See attachment for questions 6 to 25

y= - 11x   - 16

QUESTION 26

The given function is:

f(x) = 4 {x}^{2}  + 5x

The slope function is obtained by taking the first derivative of the function with respect to x.

f'(x) = 8x + 5

At (-2,6), x= -2

We plug in the x-value to find the slope of the function.

f'( - 2) = 8( - 2)+ 5

f'( - 2) =  - 16+ 5

f'( - 2) =  - 11

The equation is given by:

y-y_1=m(x-x_1)

We substitute the point and slope into the formula to get;

y-6= - 11(x- - 2)

y= - 11x  - 22 + 6

y= - 11x   - 16

The correct answer is D


6.which trigonometric function is equivalent to f(x)=sin x?  a) f(x)=cos(-x+(3pi/2)) b) f(x)=cos(x+(

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