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
polet [3.4K]
2 years ago
10

For the vectors u = ⟨2, 9⟩, v = ⟨4, –8⟩, and w = ⟨–12, 4⟩, what is u + v + w? ⟨6, 1⟩ ⟨6, 5⟩ ⟨-6, 5⟩ ⟨-6, 21⟩

Mathematics
2 answers:
kow [346]2 years ago
8 0

Answer:

(- 6, 5)

Edge 2020

Levart [38]2 years ago
6 0

Answer:

< - 6, 5 >

Step-by-step explanation:

Add the corresponding components of each vector, that is

u + v + w

= < 2, 9 > + < 4, - 8 > + < - 12, 4 >

= > 2 + 4 - 12, 9 - 8 + 4 >

= < - 6, 5 >

You might be interested in
Solve and find value of y 3x/5x+2=-4
vladimir2022 [97]

Answer:

-8/23

Step-by-step explanation:

3x/(5x+2) = - 4

3x = - 4(5x + 2)

3x = -20x - 8

23x = - 8

x = - 8/23

3 0
3 years ago
Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)
ELEN [110]

Question:

Find the point (,) on the curve y = \sqrt x that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})

Step-by-step explanation:

y = \sqrt x can be represented as: (x,y)

Substitute \sqrt x for y

(x,y) = (x,\sqrt x)

So, next:

Calculate the distance between (x,\sqrt x) and (3,0)

Distance is calculated as:

d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}

So:

d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}

d = \sqrt{(x-3)^2 + (\sqrt x)^2}

Evaluate all exponents

d = \sqrt{x^2 - 6x +9 + x}

Rewrite as:

d = \sqrt{x^2 + x- 6x +9 }

d = \sqrt{x^2 - 5x +9 }

Differentiate using chain rule:

Let

u = x^2 - 5x +9

\frac{du}{dx} = 2x - 5

So:

d = \sqrt u

d = u^\frac{1}{2}

\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}

Chain Rule:

d' = \frac{du}{dx} * \frac{dd}{du}

d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}

d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}

d' = \frac{2x - 5}{2\sqrt u}

Substitute: u = x^2 - 5x +9

d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}

Next, is to minimize (by equating d' to 0)

\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0

Cross Multiply

2x - 5 = 0

Solve for x

2x  =5

x = \frac{5}{2}

Substitute x = \frac{5}{2} in y = \sqrt x

y = \sqrt{\frac{5}{2}}

Split

y = \frac{\sqrt 5}{\sqrt 2}

Rationalize

y = \frac{\sqrt 5}{\sqrt 2} *  \frac{\sqrt 2}{\sqrt 2}

y = \frac{\sqrt {10}}{\sqrt 4}

y = \frac{\sqrt {10}}{2}

Hence:

(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})

3 0
3 years ago
what abiotic factor is changing the ecosystem of Lake Washington,and how has this factor changed over time.​
raketka [301]

Answer:

Step-by-step explanation:

Temperature is the abiotic factor that is changing the ecosystem. Both the top layer temperature and the overall temperature of the lake are increasing. The warmer temperatures have delayed the yearly springtime mixing of warm and cold water in the lake.

3 0
3 years ago
Can someone please help me and explain​
Fiesta28 [93]

Answer:

0.23

Step-by-step explanation:

3 0
3 years ago
1. City A has a population of 25,000. The population Increases at 3.5% every year. Find the population size in 10 years.​
iren [92.7K]
???????????????????????????
6 0
3 years ago
Other questions:
  • 40% of the kids at the picnic went swimming if there were 25 kids, how many went swimming
    14·1 answer
  • What is the solution of this compound inequality?<br>  <br>5 &lt; 2 - 3y &lt; 14
    9·1 answer
  • Sarah lost her science book. Her school charges a lost book fee equal to 75% of the cost of the book. Sarah received a notice st
    5·2 answers
  • 5 (r-10)= -51 what is r
    8·1 answer
  • Which table represents a linear function
    11·1 answer
  • the volume of a triangular pyramid is 300 cubic meters. what is the area of the pyramid's base of the pyramid height is 3 meters
    7·1 answer
  • Please help multiple-choice image below with question!
    9·2 answers
  • The population of a town increased from 5,600 to 6,300 people. What was the percent of increase?
    7·2 answers
  • Please I need help ASAP
    9·2 answers
  • Please help i cant figure it out will mark branliest​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!