Simplify the algebraic expression: 5x + 9 + 4 + 6x

Please answer the question below (ABOUT VECTORS AND MAGNITUDE)

coldgirl [10]

(a) v appears to have a fixed direction along the positive x-axis. If ||u|| = 150 N, ||v|| = 220 N, then when θ = 30°, you have

u = (150 N) (cos(30°) i + sin(30°) j ) ≈ (129.904 i + 75 j ) N

v = (220 N) (cos(0°) i + sin(0°) j ) = (220 i ) N

(i and j are the unit vectors in the positive x and y directions)

and their sum is

u + v ≈ (349.904 i + 75 j ) N

with magnitude

||u + v|| ≈ √((349.904)² + (75)²) N ≈ 357.851 N ≈ 357.9 N

and at angle φ made with the positive x-axis such that

tan(φ) ≈ (75 N) / (349.904 N) → φ ≈ 12.098° ≈ 12.1°

(b) Letting θ vary from 0° to 180° would make v a function of θ :

u = (150 N) (cos(θ) i + sin(θ) j ) = (150 cos(θ) i + 150 sin(θ) j ) N

Then

u + v = ((220 + 150 cos(θ)) i + (150 sin(θ)) j ) N

→ M = ||u + v|| = √((220 + 150 cos(θ))² + (150 sin(θ))²) N

M = √(48,400 + 66,000 cos(θ) + 22,500 cos²(θ) + 22,500 sin²(θ)) N

M = 10 √(709 + 660 cos(θ)) N

(c) As a function of θ, u + v makes an angle α with the positive x-axis such that

tan(α) = (150 sin(θ) / (220 + 150 cos(θ))

→ α = tan⁻¹((15 sin(θ) / (22 + 15 cos(θ)))

(d) Filling in the table is just a matter of evaluating M and α for each of the given angles θ. For example, when θ = 0°,

M = 10 √(709 + 660 cos(0°)) N = 370 N

α = tan⁻¹((15 sin(0°) / (22 + 15 cos(0°))) = 0°

When θ = 30°, you get the same result as in part (a).

When θ = 60°,

M = 10 √(709 + 660 cos(60°)) N ≈ 323.3 N

α = tan⁻¹((15 sin(60°) / (22 + 15 cos(60°))) = 23.8°

and so on.

4 0

3 years ago

The lcm of a set of numbers is equal to one of the numbers in the set.

Lana71 [14]

Then, the number must be greatest in the series.

4 0

3 years ago

Heeeeeeeeeeeeeeeeeeeeeeeeeeelp

aliina [53]

Answer:

28.9 miles per gallon

Step-by-step explanation:

divide 289 by 10 to get 28.9

4 0

3 years ago

Read 2 more answers

A random sample of 10 subjects have weights with a standard deviation of 11.9407 kg. What is the variance of their weights? Be

Brut [27]

Answer: $142.58\text{squared kg}[$

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given : A random sample of 10 subjects have weights with a standard deviation of 11.9407 kg

i.e. $\sigma = 11.9407$

Since we know that the value of variance is the square of standard deviation.

i.e. $\text{Variance}=\sigma^2$

Therefore, to find the value of variance, we need to find the square of the given standard deviation.

i.e. $\text{Variance}=(11.9407)^2=142.58031649\approx142.58\text{squared kg}$

Thus, the variance of their weights = $142.58\text{squared kg}[$

8 0

4 years ago

HomePride manufactures solid oak racks for displaying baseball equipment and karate belts. They usually sell six times as many b

kramer

Let the number of baseball racks sold be x.
Let the number of karate-belt racks sold be y. 

a) 

Since 6 times as many baseball racks is sold as karate-belt racks, we have: 
x = 6y, which is our first equation 

Net profit from baseball racks 
= $3x 

Net profit from karate-belt racks 
= $5y 

Total profit is $46000, so we have: 
3x + 5y = 46000, which is our second equation 

b) 

x = 6y --- (1) 
3x + 5y = 46000 --- (2) 

Substituting (1) into (2), we will get: 
3(6y) + 5y = 46000 
18y + 5y = 46000 
23y = 46000 
y = 46000 / 23 
y = 2000 

Substituting y = 2000 into (1), we will get: 
x = 6(2000) 
x = 12000 

c) 

They should sell 12000 baseball racks and 2000 karate-belt racks.

5 0

4 years ago