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dimulka [17.4K]
3 years ago
9

A rectangular dog pen is constructed using a barn wall as one side and 60 meters of fencing for the other three sides. What is t

he maximum area of the dog pen?
Mathematics
1 answer:
Sever21 [200]3 years ago
3 0

Answer:

450 m^2

Step-by-step explanation:

let the length be y m (the single side)

let the width be x m

so according to the question

2x + y = 60

or, y = 60 - 2x

now, Area = xy

= x(60-2x)

= -2x^2 + 60x

d(Area)/dx = -4x + 60

= 0 for a max of area

-4x + 60 = 0

x = 15

then y = 30

the width has to be 15 m, and the length has to be 30 m for a maximum area of 15(30) or 450 m^2.

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Mamont248 [21]

Answer:

12

Step-by-step explanation:

4y - 2x

= 4(7) - 2(8)

= 28 - 16

= 12

4 0
2 years ago
A ferry will safely accommodate 82 tons of passenger cars. Assume that the meanweight of a passenger car is 2 tons with standard
Shalnov [3]

Answer:

The probability that the maximum safe-weight will be exceeded is <u>0.0455 or 4.55%</u>.

Step-by-step explanation:

Given:

Maximum safe-weight of 37 cars = 82 tons

∴ Maximum safe-weight of 1 car (x) = 82 ÷ 37 = 2.22 tons (Unitary method)

Mean weight of 1 car (μ) = 2 tons

Standard deviation of 37 cars = 0.8 tons

So, standard deviation of 1 car is given as:

\sigma=\frac{0.8}{\sqrt{37}}=0.13

Probability that maximum safe-weight is exceeded, P(x > 2.22) = ?

The sample is normally distributed (Assume)

Now, let us determine the z-score of the mean weight.

The z-score is given as:

z=\frac{x-\mu}{\sigma}\\\\z=\frac{2.22-2}{0.13}\\\\z=\frac{0.22}{0.13}=1.69

Now, finding P(x > 2.22) is same as finding P(z > 1.69).

From the z-score table of normal distribution curve, the value of area under the curve for z < 1.69 is 0.9545.

But we need the area under the curve for z > 1.69.

So, we subtract from the total area. Total area is 1 or 100%.

So, P(z > 1.69) = 1 - P(z < 1.69)

P(z>1.69)=1-0.9545=0.0455\ or\ 4.55\%

Therefore, the probability that the maximum safe-weight will be exceeded is 0.0455 or 4.55%.

8 0
3 years ago
A shopkeeper sold a dressing table for 7512.75 at a profit of 19*1/4% What was the cost price.​
Katarina [22]
Cp=7512.75×[100÷(100+77÷4)]
=7512.75×(100÷119.25)
=6300
c.p=6300
4 0
3 years ago
The population of a city increases by 5% each year. If the current population of the city is 125000, how much population will th
patriot [66]

Answer:

Step-by-step explanation:

125,000×1.05⁷ ≈ 175,888

7 0
3 years ago
Noon to 3:05 elapsed time
GrogVix [38]
Noon is 12, I'm guessing you mean both of these at am, or both at pm. 12-3 is 3 hours, but there's 5 extra, so the elapsed time would be 3:05.
6 0
2 years ago
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