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
Damm [24]
2 years ago
12

U and v are position vectors with terminal points at (6, 14) and (3, 7), respectively. Find the terminal point of 2u - v.

Mathematics
1 answer:
e-lub [12.9K]2 years ago
6 0

Answer:

The terminal point of 2u - v is (9 , 21) ⇒ 3rd answer

Step-by-step explanation:

The position vector is the vector whose starting point is the origin (0 , 0)

You can find it from its terminal point on it (a, b), the vector is <a - 0 , b - 0> = <a , b>

∵ u is a position vector with terminal point (6 , 14)

∴ u = <6 - 0 , 14 - 0>

∴ u = <6 , 14>

∵ v is a position vector with terminal point (3 , 7)

∴ v = <3 - 0 , 7 - 0>

∴ v = <3 , 7>

∵ 2u - v = 2<6 , 14> - <3 , 7>

- Multiply 6 and 14 by 2

∴ 2u - v = <12 , 28> - <3 , 7>

- Add subtract 3 from 12 and 7 from 28

∴ 2u - v = <9 , 21>

∴ The terminal point of 2u - v = (9 , 21)

You might be interested in
Find the surface area of a sphere with a great circle that has an area of 49 π square miles.
Mademuasel [1]
The answer is <span>B. 196 π mi2
</span>
(1) Find radius r:
The area of the circle is:
A = r²π
A = 49π mi²

49π = r²π
49 = r²
r = √49 = 7 mi

(2) Find the surface area of the sphere.
The surface area of the sphere is: 
A = 4πr²
r = 7 mi
A = 4π * 7²
A = 4π * 49
A = 196π mi²
3 0
3 years ago
A boat takes 4 hours to go 20 miles upstream.It can go 32 miles downstream in same time.Find the rate of the current and the rat
Mandarinka [93]
Recall your d = rt, distance = rate * time.

now, if the boat has a speed of say "b", and the current has a speed of say "c", when the boat is going upstream, is not really going "b" fast, is going " b - c " fast, because the current is eroding speed from it, going upwards.

And when the boat is going downstream, is not going "b" fast either, because the current is now adding to speed to it, so is really going " b + c " fast.

The time it took one way, is the same time it took back, 4 hours each way.

thus

\bf \begin{array}{lccclll}&#10;&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{t}\\&#10;&------&------&------\\&#10;Upstream&20&b-c&4\\&#10;Downstream&32&b+c&4&#10;\end{array}&#10;\\\\\\&#10;\begin{cases}&#10;20=4(b-c)\implies \frac{20}{4}=b-c\implies 5+c=\boxed{b}\\&#10;32=4(b+c)\implies \frac{32}{4}=b+c\implies 8=b+c\\&#10;--------------------\\&#10;8=\left(\boxed{5+c}  \right)+c&#10;\end{cases}&#10;\\\\\\&#10;8=5+2c\implies 3=2c\implies \cfrac{3}{2}=c\implies 1\frac{1}{2}=c

what's the speed of the boat?  well, 5 + c = b.
6 0
3 years ago
What is the area of a rectangle floor that is 7’3” long and 4’2” wide
Svetllana [295]
<h3>✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽</h3>

➷ Area = length x width

Convert all the values into just inches:

7'3'' = 87 inches

4'2'' = 50 inches

Substitute these values in:

area = 87 x 50

Solve:

area = 4350 in^2

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

5 0
2 years ago
3) An existing track is perpendicular to y=1/2x + 2 and passes through B(7,5)
stira [4]

Answer:

2. y=\frac{1}{2}x +3

Step-by-step explanation:

2. The line will be parallel to the current track which means they have the same slope. To write the equation, use the slope m=1/2 and the point (2,4) in point slope form:

y-y_1=m(x-x_1)\\y-4=\frac{1}{2}(x-2)

This is the equation of the line. You can convert it to slope intercept form:

y-4=\frac{1}{2}(x-2)\\y-4 = \frac{1}{2}x -1 \y=\frac{1}{2}x +3

8 0
2 years ago
(Brainliest) Can someone please answer this
Lorico [155]
1. The perimeter is 20. How I got that is to add all of them together- 9+3+3+3+2=20. The area is the area is 15. How I got that was I did the little square with 3 and 2 first. 3 times 2 = 6, then I did the 3 and 3 which = 9 and added those together 9+6=15

2. The perimeter is 15. How I got that is I add them all together. 6+3+2+2+2=15. The area is 10. I did 3 times 2 = 6, 2 times 2 = 4, 6+4=10
5 0
3 years ago
Other questions:
  • Solve the following equation 4(x-3)+5=1
    7·2 answers
  • Why do flies always bring there stopwatches to parties
    12·2 answers
  • A carnival sold 135 bottles of juice in one day. They sold 1/3 of the bottles in the first hour and 2/5 of the bottles in the se
    11·1 answer
  • Percentages:
    5·1 answer
  • The entrance fee for Mountain World theme park is $15. Visitors purchase additional $2.25 tickets for rides, games, and food. Th
    6·1 answer
  • A certain car in Canada can travel 15 kilometers per 1 liter of gasoline.How many miles per gallon is this.Round to the nearest
    5·1 answer
  • If Susan is 4 feet 8 inches tall and Sharon is 5 feet 4 inches tall, what is the ratio of Sharon’s height to Susan’s height?
    10·1 answer
  • The coordinates of the vertices of quadrilateral ABCD are A(4,1) B(1,5) C(-3,2) and D(0,-2). Prove the quadrilateral is a square
    5·1 answer
  • Jack is selling holiday ornaments and boxes of candy. Each ornament is $1.50 and
    11·1 answer
  • What is the volume of the prism with the dimensions given below? <br><br> 2/3m 1 1/8m 3 3/4m
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!