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MAXImum [283]
2 years ago
13

Find the dimensions of a rectangle with an area of 100 square feet that has the minimum perimeter.

Mathematics
1 answer:
STatiana [176]2 years ago
8 0
The polygon with the shortest perimeter for a given area is a regular polygon. The regular 4-sided polygon is the square.

The side length of the square with an area of 100 ft² is √(100 ft²) = 10 ft.

The rectangle with the minimum perimeter for an area of 100 ft² is 10 ft by 10 ft.
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Which expression is equivalent to 27 + 45?
PilotLPTM [1.2K]
9(3+5)

if you go through each answer choice you will notice that none of the rest are right 

8(3+6) = 24 +48
8(19 +37) = 152 + 296
9(18 +36)= 162 +324
6 0
3 years ago
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Can somebody please help meee??
inysia [295]

Answer: d. He multiplied when he was supposed to divide

Step-by-step explanation:

He just multiplied across when he was supposed to divide (or cross multiply) to find the unit rate :)

8 0
3 years ago
What is the answer to -4/22t -5/22t
marta [7]

Answer:

<h2>-9/22t</h2>

Step-by-step explanation:

Just do -4/22-5/22 = 9/22 and just add a t, which is 9/22t.

6 0
2 years ago
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A punch glass is in the shape of a hemisphere with a radius of 5 cm. If the punch is being poured into the glass so that the cha
Galina-37 [17]

Answer:

28.27 cm/s

Step-by-step explanation:

Though Process:

  • The punch glass (call it bowl to have a shape in mind) is in the shape of a hemisphere
  • the radius r=5cm
  • Punch is being poured into the bowl
  • The height at which the punch is increasing in the bowl is \frac{dh}{dt} = 1.5
  • the exposed area is a circle, (since the bowl is a hemisphere)
  • the radius of this circle can be written as 'a'
  • what is being asked is the rate of change of the exposed area when the height h = 2 cm
  • the rate of change of exposed area can be written as \frac{dA}{dt}.
  • since the exposed area is changing with respect to the height of punch. We can use the chain rule: \frac{dA}{dt} = \frac{dA}{dh} . \frac{dh}{dt}
  • and since A = \pi a^2 the chain rule above can simplified to \frac{da}{dt} = \frac{da}{dh} . \frac{dh}{dt} -- we can call this Eq(1)

Solution:

the area of the exposed circle is

A =\pi a^2

the rate of change of this area can be, (using chain rule)

\frac{dA}{dt} = 2 \pi a \frac{da}{dt} we can call this Eq(2)

what we are really concerned about is how a changes as the punch is being poured into the bowl i.e \frac{da}{dh}

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

r = \frac{a^2 + h^2}{2h}

and rearrage the formula so that a is the subject:

a^2 = 2rh - h^2

now we can derivate a with respect to h to get \frac{da}{dh}

2a \frac{da}{dh} = 2r - 2h

simplify

\frac{da}{dh} = \frac{r-h}{a}

we can put this in Eq(1) in place of \frac{da}{dh}

\frac{da}{dt} = \frac{r-h}{a} . \frac{dh}{dt}

and since we know \frac{dh}{dt} = 1.5

\frac{da}{dt} = \frac{(r-h)(1.5)}{a}

and now we use substitute this \frac{da}{dt}. in Eq(2)

\frac{dA}{dt} = 2 \pi a \frac{(r-h)(1.5)}{a}

simplify,

\frac{dA}{dt} = 3 \pi (r-h)

This is the rate of change of area, this is being asked in the quesiton!

Finally, we can put our known values:

r = 5cm

h = 2cm from the question

\frac{dA}{dt} = 3 \pi (5-2)

\frac{dA}{dt} = 9 \pi cm/s// or//\frac{dA}{dt} = 28.27 cm/s

5 0
2 years ago
Explain how knowing that five divided by eight equals 0.625 helps you write the decimal for four and five eighth
NNADVOKAT [17]
5/8=0.625

4 and 5/8=4+5/8=4+0.625=4.625
you can just seperate the fractions and add
4 0
2 years ago
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