1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andreyandreev [35.5K]
3 years ago
10

Given c=(2.4,0.45) and d = (7,-4) find the direction of 5c+4d

Mathematics
1 answer:
kakasveta [241]3 years ago
3 0

Answer:

The direction of 5c + 4d is approximately 19.0° clockwise with

the positive part of x-axis

Step-by-step explanation:

* Lets talk about the direction of a vector

- If the vector is (x , y), then  

# Its magnitude is √(x² + y²)

# Its direction is tan^-1 (y/x)

- The direction is the angle between the positive part of x-axis and  

  the vector

* Lets solve the problem

∵ c = (2.4 , 0.45) and d = (7 , -4)

- To find 5c + 4d , multiply the two coordinates of c by 5 and the two

  coordinates of d by 4

# Multiply c by 5

∴ 5c = [5(2.4) , 5(0.45)]

∴ 5c = (12 , 2.25)

# Multiply d by 4

∴ 4d = [4(7) , 4(-4)]

∴ 4d = (28 , -16)

- Lets add 5c and 4d

∴ 5c + 4d = (12 , 2.25) + (28 , -16)  

∴ 5c + 4d = [(12 + 28) , (2.25 + -16)]

∴ 5c + 4d = (40 , -13.75)

- The vector is in the 4th quadrant because the x-coordinate is

 positive and the y-coordinate is negative

* Find the direction of 5c + 4d

∵ The direction is tan^-1 (y/x)

∴ The direction is tan^-1 (-13.75/40) = -18.97°

* The direction of 5c + 4d is approximately 19.0° clockwise with

 the positive part of x-axis

You might be interested in
-ABC
White raven [17]

Answer A+B=C that is what I know.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
p is a polynomial of degree 5. p has roots of multiplicity 2 at t=4 and t=0, a root of multiplicity 1 at t=-4, and p(1)=2025. Fi
DENIUS [597]
P(x) = (x^2)(x - 4)^2(x + 4) + some constant(b)
2025 = (1^2)(1 - 4)^2(1 + 4) + b
2025 = 45 + b
b = 1980

Complete Equation:

p(x) = (x^2)(x - 4)^2(x +4) + 1980

or expanded form

p(x) = x^5 - 4x^4 - 16x^3 + 64x^2 + 1980
5 0
3 years ago
Which diagram best shows how fraction bars can be used to evaluate 1/2 divided by 1/4?
Helga [31]

Answer:

the second one

Step-by-step explanation:

2 halves make a whole. 1/2 + 1/2

4 fourths make a whole. 1/4 + 1/4 + 1/4 + 1/4

a half of a fourth is an eighth. 1/4 ÷ 1/2 = 1/8

3 0
3 years ago
Which expression can be used to solve 3/5 divide by 7/10
kramer

Answer:

\frac{3}{5} *\frac{10}{7}  

=  \frac{30}{35} =\frac{6}{7}

7 0
3 years ago
Why do you divide by 60 after calculating the area of the trapezoid (to calculate the distance)? I got 900 but I don’t know why
Free_Kalibri [48]

Answer:

Step-by-step explanation:

What you are trying to do is a nice way to solve this problem. Without knowing any physics, you are using what math you know to get the answer. You are actually very close to being correct, and you are right. You do have to divide by 60.

Here's why and it is the one bit of physics you have to know.

The speed is km/hour. That word hour is the culprit. Your time is in minutes and you have to get it into hours. In physics, the units have to be consistent.

So ...

b1 = 19 minutes which is 19 min [1 hour / 60 minutes] = 19/60 = 0.31667 hour

b2 = 26 minutes which is 26 min [ 1 hour/60 minutes] =  26/60 = 0.4333 hour

h = 40 km/hour

Area = (0.31667 hour + 0.4333 hour)*40 km/hour /2

Area = 0.75 hour * 40 km/hr //2

Area = 15 km

6 0
3 years ago
Other questions:
  • The sum of the digit of a certain two-digit number is 12. Reversing its digit increases the number by 36.find the number
    11·1 answer
  • Someone please help <br><br> What is the vertex of YVT <br><br> A) Q<br> B) V<br> C) Y<br> D) T
    5·2 answers
  • 2b for b = 9 evaluate the expression
    9·2 answers
  • Hi May I know how to solve this with step by step explanation please
    5·2 answers
  • If the lease factor is given as 0.0023, what interest rate is that equivalent to?
    13·1 answer
  • The value of which number lies between 14 and 15?
    5·1 answer
  • Please help meeeeeeeeeeeeeeeeeeeeeeee
    10·2 answers
  • PLEASEEE HELP MEEEEEEEEE !!!!!!!!!!!!!!!!!!!!!!
    8·1 answer
  • Find the surface area of this prism. Please help 20 points!!!!!
    11·2 answers
  • Can someone help me please ?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!