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2 years ago

A walkway is 4 feet wide and is paved with square stones that are eight inches wide. How many stones wide is the path?

Mathematics

1 answer:

alukav5142 [94]2 years ago

7 0

Answer:

6 Stones

Step-by-step explanation:

It is given that a walkaway is 4 feet wide.

It is paved with square stones that are eight inches wide.

So let us convert 8 inches into feet.

We know that 1 inch = 0.0833 foot

So 8 inches = $8\times 0.0833 = 0.667$ foot.

Now, to cover the width of 4 feet we need,

$\frac{4}{0.6667} = 6$ stones.

So to cover the width of 4 feet we need 6 stones.

We can also say that walkway is 6 stones wide.

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A chef bought some green and red peppers. She bought 18 green peppers, which was 3/4 the total number.

Nezavi [6.7K]

A: Their would be 24 red peppers because I did 18 divided by 3/4 and got 24 and 24 times 3/4 is 18
B:She bought 42 peppers all together because 18 plus 24 is 42

4 0

2 years ago

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:

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/∝

5 0

2 years ago

A publishing company prints newspapers and magazines. Let NNN represent the number of newspapers and MMM represent the number of

adelina 88 [10]

Answer:

At most 800 magazines the company can print daily with the remaining number of ink cartridges.

Step-by-step explanation:

We are given the following in the question:

$0.5N+2.5M \leq 6000$

The above inequality gives the relation for daily supply of ink cartridges where N is the number of newspaper and M is the number of magazines.

Number of newspaper to be printed daily,N = 8000

We have to find the number of magazines at most can the company print daily with the remaining number of ink cartridges.

Puting the value in the given inequality,

$0.5(8000)+2.5M \leq 6000\\\Rightarrow 4000+2.5M \leq 6000\\\Rightarrow 2.5M \leq 2000\\\\\Rightarrow M \leq \dfrac{2000}{2.5}\\\\\Rightarrow M \leq 800$