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2 years ago

Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If w = 10 find u and v.

Mathematics

1 answer:

tangare [24]2 years ago

8 0

a. The value of v is 9.2

b. The value of u is 9.9

<h3>What are vectors?</h3>

Vectors are physical quantities that have both magnitude and direction

<h3>How to find the value of vectors u and v?</h3>

Since we have vectors

u at 70° to the x-axis

v at 47° to the x-axis and
w = 10 at 15° to the x-axis,

We resolve them into component form

So, u = -(ucos70°)i - (usin70°)j

u = -(0.3420u)i - (0.9397u)j

v = -(vcos47°)i + (vsin47°)j

v = -(0.6820v)i - (0.7314v)j

w = (wcos15°)i + (wsin15°)j

w = (0.9659w)i + (0.2588w)j

w = (9.659)i + (2.588)j

Since the sum of the three vectors is zero, we have that

u + v + w = 0

u + v = -w

So,

-(0.3420u)i - (0.9397u)j + [-(0.6820v)i - (0.7314v)j] = -[(9.659)i + (2.588)j]

-(0.3420u)i - (0.9397u)j -(0.6820v)i - (0.7314v)j = -(9.659)i - (2.588)j]

-(0.3420u)i -(0.6820v)i - (0.9397u)j - (0.7314v)j = -(9.659)i - (2.588)j]

-[0.3420u + 0.6820v]i - [0.9397u + 0.7314v]j = -(9.659)i - (2.588)j

Equating i components, we have

-[0.3420u + 0.6820v]i = -9.659i

0.3420u + 0.6820v = 9.659

Dividing through by 0.3420. we have

u + 1.994v = 28.242 (1) and

Also, equating j components, we have

- [0.9397u + 0.7314v]j = -2.588j

0.9397u + 0.7314v = 2.588

Dividing through by 0.9397 we have

u + 0.778v = 2.754 (2)

<h3>a. The value of v</h3>

Subracring equation (2) from(1),we have

u + 1.994v = 28.242 (1)

u + 0.778v = 2.754 (2)

2.772v = 25.488

v = 25.488/2.772

v = 9.19

v ≅ 9.2

The value of v is 9.2

<h3>b. The value of u</h3>

Substituting v into (1), we have

u + 1.994v = 28.242 (1)

u + 1.994(9.19) = 28.242

u + 18.325 = 28.242

u = 28.242 - 18.325

u = 9.917

u ≅ 9.9

The value of u is 9.2

Learn more about vectors here:

brainly.com/question/25705666

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Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

$\Rightarrow y=\sqrt{x^2+100}$

Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

$=\frac{24\times (-13)}{\sqrt{676}}$

$=\frac{24\times (-13)}{26}$

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Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

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3 years ago

Brandon rode in a taxi that charges a flat fee of $2.25 and an additional $0.40 per mile of his trip. If he paid $6.80 for the c

r-ruslan [8.4K]

Answer:

11 $\frac{3}{8}$ miles.

Step-by-step explanation:

To find how many miles Brandon rode, we can create an equation in slope-intercept form: y = mx + b

$2.25 is the flat fee, or the unchanging variable. This is our y-intercept, or b.

$0.40 is the changing variable, as it changes value depending on the amount of miles ridden. This is our slope, or m.

We know Brandon spent $6.80 on the cab ride. So, this is our y.

We get the equation: 6.80 = 0.40x + 2.25.

To solve, first subtract 2.25 from both sides of the equation:

6.80 - 2.25 = 0.40x + 2.25 - 2.25

We get: 4.55 = 0.40x

Now, just divide by 0.40 on both sides:

4.55 ÷ 0.40 = 0.40x ÷ 0.40

We get: 11.375 = x

So, Brandon rode for 11.375 miles. When converted to a mixed number, we get 11 $\frac{3}{8}$ .

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