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8_murik_8 [283]
3 years ago
14

Sally has a discount card that reduces the price of her grocery bill in a certain grocery store by 5%. If c represents the cost

of Sally’s groceries, which expression represents Sally’s grocery bills
Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
5 0
Percentage discount = 5%
Percentage price of groceries after discount=100-5=95%
Given that the total price was c, sally's bill will be:
0.95×c
=0.95c
thus the expression is 0.95c
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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/∝

5 0
3 years ago
Six more than twice a number is 20
4vir4ik [10]

Answer:

7

Step-by-step explanation:

7x2=14

14+6=20

5 0
3 years ago
8+2=16106 what does 5+4 equal?
bazaltina [42]
Is this a riddle?? Or are you really doing this :-(
3 0
3 years ago
Given that T is the centroid of △DEF and FT=12
dlinn [17]

The centroid of a triangle divides the median of the triangle into 1 : 2

The measure of FQ is 18, while the measure of TQ is 6

Because point T is the centroid, then we have the following ratio

\mathbf{TQ : FT =1 : 2}

Where FT = 12.

Substitute 12 for FT in the above ratio

\mathbf{TQ : 12 =1 : 2}

Express as fraction

\mathbf{\frac{TQ }{ 12} =\frac{1 }{ 2}}

Multiply both sides by 12

\mathbf{TQ =\frac{1 }{ 2} \times 12}

This gives

\mathbf{TQ =\frac{1 2}{ 2}}

Divide 12 by 2

\mathbf{TQ =6}

The measure of FQ is calculated using:

\mathbf{FQ = FT + TQ}

Substitute 12 for FT, and 6 for TQ

\mathbf{FQ = 12 + 6}

Add 12 and 6

\mathbf{FQ = 18}

Hence, the measure of FQ is 18, while the measure of TQ is 6

Read more about centroids at:

brainly.com/question/11891965

6 0
2 years ago
How tall is the flag pole (please give explanation too)
Tpy6a [65]

Answer:

  22 3/4 ft

Step-by-step explanation:

The diagram seems to show a 6 1/2 ft person casting a 9 ft shadow at the same time a flagpole is casting a 31 1/2 ft shadow. You want the height of the flagpole.

<h3>Proportion</h3>

Shadow lengths are presumed proportional to the height of the object making them. This means ...

  h/(31 1/2) = (6 1/2)/9 . . . . . all lengths in feet

Multiplying by 31 1/2, we get ...

  h = (31 1/2)(6 1/2)/9 = (819/4)/9 = 91/4

  h = 22 3/4 . . . . ft

The flagpole is 22 3/4 feet tall.

3 0
1 year ago
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