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jenyasd209 [6]
2 years ago
7

Estimate, then add. Write each sum in the simplest form.

Mathematics
1 answer:
Likurg_2 [28]2 years ago
5 0

Answer:

add the fractions and then divide

Step-by-step explanation:

so you add the top two and then the bottem two and then after you get those two anwsers divide them

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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
2 years ago
Help identify measure of arc UV
weqwewe [10]
M<UWV =180- 99 -36= 45
45 = 1/2(94+20- arcUV)
45=57 - arcUV/2
arcUV / 2 = 57-45
arcUV / 2 =12
arcUV = 12(2)
arcUV = 24

answer is B. 24

6 0
3 years ago
Two numbers are between 10 and 20. Their greatest common factor is 3. Which two numbers could they be?
alina1380 [7]

Answer:

12 and 15     or

12 and 18    or

15 or 18

Step-by-step explanation:

The two numbers have to both be divisible by 3, since their greatest common factor is 3.  This only leaves..

12, 15, or 18     (no other numbers between 10 and 20 are divisible by 3)

The factors of 12 are: 2, 3, 4, 6, and 12

The factors of 15 are: 3, 5, and 15

The factors of 18 are: 2, 3, 6, 9, and 18

All three numbers have 3 as a greatest common factor, so we have 3 pairs of numbers they could be...

12 and 15     or

12 and 18    or

15 or 18

4 0
2 years ago
Find the value of y.
lutik1710 [3]

Answer:

200 I think just kidding or you ca

5 0
2 years ago
Jeremy baked 9 cakes for the bake sale. he shifted 2 cups of powdered sugar evenly on the tops of the cakes. how much powdered s
Ira Lisetskai [31]
9 cakes of a 2 cups equals 18 cups
6 0
3 years ago
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