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Sphinxa [80]
3 years ago
13

-2w - 5w simplify the expression and combine like terms

Mathematics
2 answers:
mafiozo [28]3 years ago
8 0

Answer:

Step-by-step explanation:

-w(2+5)

W is like term

ElenaW [278]3 years ago
5 0
It’s already simplified just add the like terms and the answer would be -7w
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Read 2 more answers
A pond forms as water collects in a conical depression of radius a and depth h. Suppose that water flows in at a constant rate k
Scrat [10]

Answer:

a. dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. πa² ≥ k/∝

Step-by-step explanation:

a.

The rate of volume of water in the pond is calculated by

The rate of water entering - The rate of water leaving the pond.

Given

k = Rate of Water flows in

The surface of the pond and that's where evaporation occurs.

The area of a circle is πr² with ∝ as the coefficient of evaporation.

Rate of volume of water in pond with time = k - ∝πr²

dV/dt = k - ∝πr² ----- equation 1

The volume of the conical pond is calculated by πr²L/3

Where L = height of the cone

L = hr/a where h is the height of water in the pond

So, V = πr²(hr/a)/3

V = πr³h/3a ------ Make r the subject of formula

3aV = πr³h

r³ = 3aV/πh

r = ∛(3aV/πh)

Substitute ∛(3aV/πh) for r in equation 1

dV/dt = k - ∝π(∛(3aV/πh))²

dV/dt = k - ∝π((3aV/πh)^⅓)²

dV/dt = K - ∝π(3aV/πh)^⅔

dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. Equilibrium depth of water

The equilibrium depth of water is when the differential equation is 0

i.e. dV/dt = K - ∝π(3a/πh)^⅔V^⅔ = 0

k - ∝π(3a/πh)^⅔V^⅔ = 0

∝π(3a/πh)^⅔V^⅔ = k ------ make V the subject of formula

V^⅔ = k/∝π(3a/πh)^⅔ -------- find the 3/2th root of both sides

V^(⅔ * 3/2) = k^3/2 / [∝π(3a/πh)^⅔]^3/2

V = (k^3/2)/[(∝π.π^-⅔(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝π^⅓(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝^3/2.π^½.(3a/h))]

V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. Condition that must be satisfied

If we continue adding water to the pond after the rate of water flow becomes 0, the pond will overflow.

i.e. dV/dt = k - ∝πr² but r = a and the rate is now ≤ 0.

So, we have

k - ∝πa² ≤ 0 ---- subtract k from both w

- ∝πa² ≤ -k divide both sides by - ∝

πa² ≥ k/∝

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Heron Island is a coral cay in the Great Barrier Reef. Around Heron Island (and elsewhere in Australia) there are 2 color morphs
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In case A, as the error would be a difference of 1, the assumption could be mantained, but in case B the difference will be bigger, showing that the ratio is not 3:1 but 4:1.

<h3><u>Ratios</u></h3>

Given that a preliminary study was carried out to test the hypothesis that the ratio of white to dark herons on the island was 3:1, but A) a small census found 16 white morphs and 4 dark, to determine if the assumption of a 3 :1 ratio could be rejected, and B) to determine the same question if the census were larger with 160 white morphs and 40 dark, the following calculations must be made:

A)

  • 3 + 1 = 4
  • 16 + 4 = 20
  • 4 = 20
  • 3 = X
  • 60 / 4 = X
  • 15 = X
  • Therefore, as the error would be a difference of 1, the assumption could be mantained.

B)

  • 3 + 1 = 4
  • 160 + 40 = 200
  • 150 = 3:1
  • In this case, the difference will be bigger, showing that the ratio is not 3:1 but 4:1.

Learn more about ratios in brainly.com/question/1504221

3 0
2 years ago
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