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WARRIOR [948]
3 years ago
5

Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and

magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Mathematics
1 answer:
Anastaziya [24]3 years ago
3 0
The problem is modelled in the first picture shown below

To work out the resultant vector, we modelled the vectors 150N and 75N as triangle AOB is shown in the second picture with AB as the resultant vector. 

We use the cosine rule to work out the length AB
AB^{2}= 75^{2}+ 150^{2}-(2*75*150*cos(60))
AB^{2} =28125-11250
AB^{2}=16875
AB= \sqrt{16875} =130(nearest whole number)

The third picture shows the full diagram of the vectors

To work out the direction of the resultant vector, we use the sin rule to find the size of angle A and angle B

Angle A
\frac{130}{sin(60)}= \frac{75}{sin(A)}
130sin(A)=75sin(60)
sin(A)= \frac{75sin(60)}{130}
sin(A)=0.4996300406
A= sin^{-1}(0.4996300406)
A=30 (rounded to nearest whole number)

Angle B
B=180-60-30=90

Direction is 60° toward negative x-axis

Answer: Magnitude 130N and direction 60° toward negative x-axis

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3 years ago
Which real world image represents a negative slope?
salantis [7]

Answer:

The soccer goal

Step-by-step explanation:

A negative slope always points down.

4 0
3 years ago
Question 9
kiruha [24]

The slope of the linear equation is 20 and the y-intercept is 150

<h3>What is a Slope?</h3>

Slope measures how steep a straight line is. It is described as rise over run.

The slope of the linear equation can be found as follows;

He opens the account with $150 and he plans to save $20 each week. Therefore,

let

x = number of weeks

Therefore,

  • y = 20x + 150

where

y = amount in his account after x number of weeks.

Using the slope intercept equation,

<h3>Slope intercept equation:</h3>
  • y =mx + c

where

m = slope

c = y-intercept

Therefore, the slope of the linear equation is 20 and the y-intercept is 150

learn more on slope here: brainly.com/question/8057577

7 0
2 years ago
b) How many ways can you deal cards (from a deck of 52) to 4 people when each player gets 7 cards. 2 hidden and 5 visible. Assum
Mariana [72]

Answer:

{52 \choose 7}{45 \choose 7}{38 \choose 7}{31 \choose 7}{7 \choose 2}^4

Step-by-step explanation:

The dealing of the cards can be seen in the following way:

We first have to choose which 7 cards are going to be dealt to the 1st player. So we have to pick 7 cards out of the 52 available cards. This can be done in {52 \choose 7} ways. Now that we have chosen which 7 cards are going to be dealt to the 1st player, we have to choose which 2 of them are going to be the hidden ones. So we have to pick 2 cards out of the 7 cards to be the hidden ones. This can be done in {7 \choose 2} ways. At this point we now know which cards are being dealt to the 1st player, and which ones are hidden for him. Then we have to choose which 7 cards to deal to the 2nd player, out of the remaining ones. So we have to pick 7 out of 52-7=45. (since 7 have been already dealt to the 1st player). This can be done in {45 \choose 7}. Then again, we have to pick which 2 are going to be the hidden cards for this 2nd player. So we have to pick 2 out of the 7. This can be done in {7 \choose 2} ways. Then we continue with the 3rd player. We have to choose 7 cards out of the remaining ones, which at this point are 52-7-7=38. This can be done in {38 \choose 7}. And again, we have to choose which ones are the hidden ones, which can be chosen in {7 \choose 2} ways. Finally, for the last player, we choose 7 out of the remaining cards, which are 52-7-7-7=31. This can be done in {31 \choose 7} ways. And choosing which ones are the hidden ones for this player can be done in {7 \choose 2} ways. At the end, we should multiply all our available choices on each step, to get the total choices or total ways to deal the cards to our 4 players (since dealing the cards is a process of several steps with many choices on each step).

{52 \choose 7}{7 \choose 2}{45 \choose 7}{7 \choose 2}{38 \choose 7}{7 \choose 2}{31 \choose 7}{7 \choose 2}={52 \choose 7}{45 \choose 7}{38 \choose 7}{31 \choose 7}{7 \choose 2}^4

7 0
3 years ago
In a certain Algebra 2 class of 21 students, 14 of them play basketball and 9 of them play baseball. There are 3 students who pl
omeli [17]

Answer:

basketball= 66.66 infinite%

baseball=42.86%

Step-by-step explanation:

if you divide 14 by 21 you get .66 infinite which is 66.66 infinite%

divide 9 by 21 you get around .4286 which is 42.86%

7 0
3 years ago
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