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bulgar [2K]
3 years ago
11

The price of a notebook was

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
5 0
3.35 - 3.10 = .25

.25/3.35 = .0746

.0746*100 = 7.46 or 7.5 rounded
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75 percent of the sutdents in a school went on a field trip. If 285 students went on the trip, how any students are in the schoo
natita [175]

Answer:

380

Step-by-step explanation:

285 / x = 75 / 100

Cross multiply 28500 = 75x

Divide by 75  380

8 0
2 years ago
A sled is being held at rest on a slope that makes an angle theta with the horizontal. After the sled is released, it slides a d
Alenkasestr [34]

Answer:

μ =  Sin θ * d₁ / (d₂ - Cos θ*d₁)

d₂ = (d₁*Sin θ) / μ

Step-by-step explanation:

a) We apply The work-energy theorem

W = ΔE

W = - Ff*d

Ff = μ*N = μ*m*g

<em>Distance 1:</em>

- Ff*d₁ = Ef - Ei

⇒  - (μ*m*g*Cos θ)*d₁ = (Kf+Uf) - (Ki+Ui) = (Kf+0) - (0+Ui) = Kf - Ui

Kf = 0.5*m*vf² = 0.5*m*v²

Ui = m*g*h = m*g*d₁*Sin θ

then

- (μ*m*g*Cos θ)*d₁ = 0.5*m*v² - m*g*d₁*Sin θ  

⇒   - μ*g*Cos θ*d₁ = 0.5*v² - g*d₁*Sin θ   <em>(I)</em>

 

<em>Distance 2:</em>

<em />

- Ff*d₂ = Ef - Ei

⇒  - (μ*m*g)*d₂ = (0+0) - (Ki+0) = - Ki

Ki = 0.5*m*vi² = 0.5*m*v²

then

- (μ*m*g)*d₂ = - 0.5*m*v²

⇒   μ*g*d₂ = 0.5*v²     <em>(II)</em>

<em />

<em>If we apply (I) + (II)</em>

- μ*g*Cos θ*d₁ = 0.5*v² - g*d₁*Sin θ

μ*g*d₂ = 0.5*v²

 ⇒ μ*g (d₂ - Cos θ*d₁) = v² - g*d₁*Sin θ   <em>  (III)</em>

Applying the equation (for the distance 1) we get v:

vf² = vi² + 2*a*d = 0² + 2*(g*Sin θ)*d₁   ⇒   vf² = 2*g*Sin θ*d₁ = v²

then (from the equation <em>III</em>) we get

μ*g (d₂ - Cos θ*d₁) = 2*g*Sin θ*d₁ - g*d₁*Sin θ

⇒  μ (d₂ - Cos θ*d₁) = Sin θ * d₁

⇒   μ =  Sin θ * d₁ / (d₂ - Cos θ*d₁)

b)

If μ is a known value

d₂ = ?

We apply The work-energy theorem again

W = ΔK   ⇒   - Ff*d₂ = Kf - Ki

Ff = μ*m*g

Kf = 0

Ki = 0.5*m*v² = 0.5*m*2*g*Sin θ*d₁ = m*g*Sin θ*d₁

Finally

- μ*m*g*d₂ = 0 - m*g*Sin θ*d₁   ⇒   d₂ = Sin θ*d₁ / μ

3 0
3 years ago
Simplify <br><br> (1/2)^2 -6(2-2/3)
Kruka [31]

Answer:

= −31/4

(Decimal: -7.75)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Find the mean of the following: 158, 213, 107, 213, and 213. If needed, round your answer to the nearest tenth
Shalnov [3]

Answer:

180.8

Step-by-step explanation:

1. Add all the numbers

2. Divide the sum by 5

3. you get the answer

4 0
3 years ago
Read 2 more answers
Tawny has 2 1/2 pints of juice. She has glasses that can hold 5 fluid ounces. How any glasses can she fill with juice?
Oduvanchick [21]
1 pint = 20 fl. oz
20/5 = 4 cups can be filler per pint
4*2.5 = 10 cups can be filled overall
6 0
3 years ago
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