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3 years ago

Pls helpppppppppppppppp

Mathematics

2 answers:

vredina [299]3 years ago

5 0

Answer: D

Each time a new row and a new column is added. The last pattern had 3 rows and 4 columns, so the next pattern will have 4 rows and 5 column.

7nadin3 [17]3 years ago

4 0

Answer:

yes the awnser is d I can approve of that

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You and your friend rent a canoe. The canoe costs 10 dollars per half hour plus 5 dollars per day for each life vest. Life vests

REY [17]

The greatest range....the range is ur y value, it will be the total cost...the x is gonna be the number of 1/2 hrs. And the 5 per life vest has to be multiplied by 2 because there is 2 people, making it 10
y = 10x + 10

the greatest range will be when u rent the canoe for the longest.
8 a.m to 6 p.m......thats 10 hrs....20 half hrs...so the greatest range is when u rent the canoe for 20 half hrs.

y = 10(20) + 10
y = 200 + 10
y = 210 <=== the greatest range

3 0

3 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

The length of a rectangle is 6 in longer than its width.if the perimeter of the rectangle is 68in find the length and width ?

wel

The length and the width of the rectangle are 20 and 14 inches respectively

<h3>How to find the length and width?</h3>

The given parameters are:

Length = 6 + Width

Perimeter = 68 inches

The perimeter of a rectangle is calculated as:

Perimeter = 2 * (Length + Width)

So, we have:

2 * (Length + Width) = 68

Divide both sides by 2

Length + Width = 34

Substitute Length = 6 + Width in Length + Width = 34

6 + Width + Width = 34

Evaluate the like terms

2 * Width = 28

Divide both sides by 2

Width = 14

Substitute Width = 14 in Length = 6 + Width

Length = 6 + 14

Evaluate

Length = 20

Hence, the length and the width of the rectangle are 20 and 14 inches respectively