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marishachu [46]
3 years ago
12

31)

Mathematics
2 answers:
kifflom [539]3 years ago
5 0
It is 70 I believe you could check with an online calculator
lilavasa [31]3 years ago
5 0

Answer:

IT IS NOT 70!!!

Step-by-step explanation:

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A piece of wire of length 6363 is​ cut, and the resulting two pieces are formed to make a circle and a square. Where should the
Lerok [7]

Answer:

a.

35.2792 cm from one end (The square)

And 27.7208 cm from the other end (The circle)

b. See (b) explanation below

Step-by-step explanation:

Given

Length of Wire ,= 63cm

Let L be the length of one side of the square

Circumference of a circle = 2πr

Perimeter of a square = 4L

a. To minimise

4L + 2πr = 63 ----- make r the subject of formula

2πr = 63 - 4L

r = (63 - 4L)/2π

r = (31.5 - 2L)/π

Let X = Area of the Square. + Area of the circle

X = L² + πr²

Substitute (31.5 - 2L)/π for r

So,

X² = L² + π((31.5 - 2L)/π)²

X² = L² + π(31.5 - 2L)²/π²

X² = L² + (31.5 - 2L)²/π

X² = L² + (992.25 - 126L + 4L²)/π

X² = L² + 992.25/π - 126L/π +4L²/π ------ Collect Like Terms

X² = 992.25/π - 126L/π + 4L²/π + L²

X² = 992.25/π - 126L/π (4/π + 1)L² ---- Arrange in descending order of power

X² = (4/π + 1)L² - 126L/π + 992.25/π

The coefficient of L² is positive so this represents a parabola that opens upward, so its vertex will be at a minimum

To find the x-cordinate of the vertex, we use the vertex formula

i.e

L = -b/2a

L = - (-126/π) / (2 * (4/π + 1)

L = (126/π) / ( 2 * (4 + π)/π)

L = (126/π) /( (8 + 2π)/π)

L = 126/π * π/(8 + 2π)

L = (126)/(8 + 2π)

L = 63/(4 + π)

So, for the minimum area, the side of a square will be 63/(4 + π)

= 8.8198 cm ---- Approximated

We will need to cut the wire at 4 times the side of the square. (i.e. the four sides of the square)

I.e.

4 * (63/(4 + π)) cm

Or

35.2792 cm from one end.

Subtract this result from 63, we'll get the other end.

i.e. 63 - 35.2792

= 27.7208 cm from the other end

b. To maximize

Now for the maximum area.

The problem is only defined for 0 ≤ L ≤ 63/4 which gives

0 ≤ L ≤ 15.75

When L=0, the square shrinks to 0 and the whole 63 cm wire is made into a circle.

Similarly, when L =15.75 cm, the whole 63 cm wire is made into a square, the circle shrinks to 0.

Since the parabola opens upward, the maximum value is at one endpoint of the interval, either when

L=0 or when L = 15.75.

It is well known that if a piece of wire is bent into a circle or a square, the circle will have more area, so we will assume that the maximum area would be when we "cut" the wire 0, or no, centimeters from the

end, and bend the whole wire into a circle. That is we don't cut the wire at

all.

7 0
3 years ago
Can a smart person help me out? I really need help with these three questions​
Illusion [34]

Answer:

1.= 2.4 Hours

2.= 8 miles per hour

3.= 150 miles per hour

Step-by-step explanation:

4 0
3 years ago
Find the length of the third side. If necessary, write in simplest radical form.
pychu [463]

Answer: 84 is your answer hope this helped

plz make brainly

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A clown bought 6 bags of round balloons with 24 balloons in each bag.The clown also bought 3 bags of long balloons with 36 ballo
Ierofanga [76]
6 bags × 24 balloons = the amount of round balloons
6× 24 = 144
3 bags × 36 balloons = the amount of long balloons
3 ×36=108

108 long balloons - 144 round balloons = number of more long balloons that round ones
108-144=-36
He has -36 more long balloons that round ones
Or 36 more round balloons that long ones
7 0
3 years ago
In the late nineteenth century, the scientist Marie Curie performed experiments that led to the discovery of radioactive substan
gtnhenbr [62]

Answer:

Step-by-step explanation:

Half life is the time taken by a radioactive substance to reduce of half of its original size

If the half life of radium is 1600, this means that the original radioactive substance N0 have reduced to N0/2 after 1600 years

if we are given N0 = 1000grams

The amount of the substance that will remain after 1600 years will be N0/2 i.e 1000/2 = 500g

<em>Hence 500 grams of radium will be left after 600years</em>

5 0
3 years ago
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