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3 years ago

the length of a rectangle is four less than three times the width. if the perimeter is 36, find the width.

Mathematics

1 answer:

nika2105 [10]3 years ago

5 0

Answer:

w = 5.5

Step-by-step explanation

8w-8=36

+8 +8

8w=44

/8 /8

w= 5.5

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Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt.

Oliga [24]

Answer:

(a) 0.288 kg/liter

(b) 0.061408 kg/liter

Step-by-step explanation:

(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute

The mass of salt exiting the tank per minute = 5 × (5 + x)/500

The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;

Δ/dt = x - 5 × (5 + x)/500

The increase, in mass, Δ, after an increase in time, dt, is therefore;

Δ = (x - 5 × (5 + x)/500)·dt

Integrating with a graphing calculator, with limits 0, 10, gives;

Δ = (99·x - 5)/10

Substituting x = 1 gives

(99 × 1 - 5)/10 = 9.4 kg

The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)

∴ The concentration of the salt and water in the tank after 10 minutes = (5 + 9.4)/500 = (14.4)/500 = 0.288

The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter

(b) With the added leak, we now have;

Δ/dt = x - 6 × (14.4 + x)/500

Δ = x - 6 × (14.4 + x)/500·dt

Integrating with a graphing calculator, with limits 0, 20, gives;

Δ = 19.76·x -3.456 = 16.304

Where x = 1

The increase in mass after an increase in = 16.304 kg

The total mass = 16.304 + 14.4 = 30.704 kg

The concentration of the salt in the tank then becomes;

Concentration = 30.704/500 = 0.061408 kg/liter.

6 0

3 years ago

An item is regularly priced at $83. It is on sale for 95% off the regular price.

natita [175]

Answer:

Step-by-step explanation:

Regular price = $ 83

Discount = 95% of 83

= 0.95 * 83

= $ 78.85

Price after discount = 83 - 78.85

= $ 4.15

7 0

3 years ago

Read 2 more answers

A certain forest covers an area of 4800 km^2 . Suppose that each year this area decreases by 5.25% . What will the area be after

9966 [12]

Answer:

the area after 6 years is 3,473 km^2

Step-by-step explanation:

The computation of the area after 6 years is as follows:

= Area × (1 - decreased percentage)^number of years

= 4,800 km^2 × (1 - 5.25%)^6

= 4,800 km^2 × 0.9475^6

= 3,473 km^2

Hence, the area after 6 years is 3,473 km^2

5 0

3 years ago

Please help<br>step by step<br>Parentheses, Braces, and Brackets

AURORKA [14]

Answer:

sorry iuuytffsa at tfyui0

3 0

3 years ago

A study was done to determine the average number of homes that a homeowner owns in his or her lifetime. For the 60 homeowners su

const2013 [10]

Answer:

D) (3.67, 4.73)

Step-by-step explanation:

Confidence Interval for the true average number of homes that a person owns in his or her lifetimecan be calculated using M±ME where

M is the average number of home owned (4.2)

ME is the margin of error from the mean

And margin of error (ME) can be calculated as

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic in the given confidence level(1.96)

s is the standard deviation of the sample(2.1)

N is the sample size (60)

Putting the numbers we get ME= $\frac{1.96*2.1}{\sqrt{60} }$ ≈0.53

Then the 95% confidence interval is 4.2±0.53 or (3.67, 4.73)

6 0

3 years ago