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
kramer
3 years ago
7

Resolve the vector into components. 1. A vector starting at the point Q = (4, 6) and ending at the point P = (1, 2).

Mathematics
1 answer:
lesya692 [45]3 years ago
8 0

Answer:

1. Horizontal component = -3 units

  Vertical component = -4 units

2. Horizontal component = 3 units

  Vertical component = 4 units

Step-by-step explanation:

If a vector M, starting at point A = (a, b) and ending at point B = (c, d) is given, then the vector can be resolved into x and y components as follows;

M = AB

Where;

AB = B - A

AB = (a, b) - (c, d)

AB = (a-c, b-d)

AB = (a-c)i + (b-d)k

<em>Therefore, </em><em>a-c </em><em>and </em><em>b-d</em><em> are the x and y components of the vector M.</em>

<em />

(1) Let the vector be M:

Starting point of M = Q = (4, 6)

Ending point of M = P = (1, 2)

So,

M = PQ

Where;

PQ = Q - P

PQ = (1,2) - (4,6)

PQ = (1-4, 2-6)  

PQ = (-3, -4)

Therefore,

M = PQ = -3i - 4j

The x and y components of M are therefore, -3 and -4 respectively.

(2) Let the vector be M:

Starting point of M = P = (1, 2)

Ending point of M = Q = (4, 6)

So,

M = PQ

Where;

PQ = Q - P

PQ = (4,6) - (1,2)

PQ = (4-1, 6-2)  

PQ = (3, 4)

Therefore,

M = PQ = 3i + 4j

The x and y components of M are therefore, 3 and 4 respectively.

<em>Note: The x and y components are also called the horizontal and vertical components respectively.</em>

<em></em>

You might be interested in
Pork chops cost $3.30 a pound at the market. Mary buys 4.4 pounds. Find the cost. a. $7.70 b. $14.52 c. $18.92 d. $15.52
Fofino [41]

Answer:

B) $14.52

Step-by-step explanation:

1 lb of pork chop = $3.30

Mary is buying 4.4 pounds.

Multiply 4.4 with 3.30

4.4 x 3.30 = 14.52

$14.52, or B) is your answer

~

8 0
3 years ago
Read 2 more answers
The weight of Jane and Jessica was in the ratio of 8 : 9. Jane gained 2 kg while Jessica lost 4 kg. They then had the same weigh
postnew [5]

Answer:

  48 kg

Step-by-step explanation:

The given relations can be used to write a system of equations for the two weights. Those can be solved to find Jane's weight.

__

<h3>setup</h3>

Let x and y represent Jane's and Jessica's original weight, respectively. The ratio of weights was ...

  x/y = 8/9

After the changes in weight, they were equal:

  x+2 = y-4

__

<h3>solution</h3>

Adding 4 to the second equation, we have an expression for y that can be substituted into the first equation.

  y = x +6 . . . . . . . . . . solve the second equation for y

  x/(x+6) = 8/9 . . . . . . substitute for y in the first equation

  9x = 8(x +6) . . . . . . . multiply by 9(x+6)

  x = 48 . . . . . . . . . . . simplify and subtract 8x

Jane weighed 48 kg at first.

_____

<em>Alternate solution</em>

The original difference in "ratio units" was 9-8 = 1 ratio unit. We find that this corresponds to 6 kg after the weight changes make the weights equal. Then 8 ratio units will be 8(6 kg) = 48 kg—Jane's original weight.

(This mental solution is virtually the same as the solution using equations shown above.)

3 0
1 year ago
AB is a diameter of a circle, center O. C is a point on the circumference of the circle, such that
Solnce55 [7]

Given:

AB is the diameter of a circle.

m∠CAB = 26°

To find:

The measure of m∠CBA.

Solution:

Angle formed in the diameter of a circle is always 90°.

⇒ m∠ACB = 90°

In triangle ACB,

Sum of the angles in the triangle = 180°

m∠CAB + m∠ACB + m∠CBA = 180°

26° + 90° + m∠CBA = 180°

116° + m∠CBA = 180°

Subtract 116° from both sides.

116° + m∠CBA - 116° = 180° - 116°

m∠CBA = 64°

The measure of m∠CBA is 64°.

7 0
3 years ago
Solve x2+12x=-11 by completing the square . Which is the the solution set of the equation?
Dmitriy789 [7]

Answer:

{- 11, - 1 }

Step-by-step explanation:

Since the coefficient of the x² term is 1 , to complete the square

add (half the coefficient of the x-term )² to both sides

x² + 2(6)x + 36 = - 11 + 36 ← complete the square on the left side

(x + 6)² = 25 ( take the square root of both sides

\sqrt{(x+6)^2} = ± \sqrt{25}

x + 6 = ± 5 ( subtract 6 from both sides )

x = - 6 ± 5

x = - 6 + 5 = - 1 or x = - 6 - 5 = - 11




8 0
3 years ago
Read 2 more answers
Write the equation of each line in slope-intercept form and identify the slope. 4x=2+y
RideAnS [48]

Answer:

y = 4x - 2

Step-by-step explanation:

Given: 4x=2+y

First, subtract 2 on both sides to isolate out y. (Slope-intercept form is y=mx+b)

Once subtracted, you get: 4x-2=y

Rearrange it, and you get: y=4x-2

7 0
2 years ago
Other questions:
  • Which relationship describes angles 1 and 2?
    7·1 answer
  • Which of these are the smallest <br><br> A. asteroids <br> B. meteriods<br> C. comets<br> D. palnets
    10·2 answers
  • Ryan and Scott are each studying a square pyramid.
    12·2 answers
  • What will be the reason for the answer?
    12·1 answer
  • Simplify the expression
    15·1 answer
  • Divide 6x^6+5x^5+2x^4-9x^3+7x^2-10x+2 by 3x + 1 by using long division. Show all work and steps work. Then explain if 3x + 1 is
    12·1 answer
  • Your mom opens an account to save money for a family vacation. The account earns an annual interest rate of 4%. She earns $37 in
    15·1 answer
  • Deleted question.....
    10·1 answer
  • Answer this question please and thank you
    6·1 answer
  • A construction crew has just finished building a road. The crew worked for 4 4/9 days. If they built 2 1/5 kilometers of road ea
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!