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2 years ago

What does geometric progression mean?

Mathematics

1 answer:

damaskus [11]2 years ago

7 0

Step-by-step explanation:

$\large\tt\underline\blue{a} \underline\pink{n} \underline\green{s} \underline\red{w}\underline \purple{e} \underline\orange{r}$

A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.

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Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into

Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = $(\frac{60\pi }{\pi+4}) in$

b)the length of the wire for the square = $(\frac{240}{\pi+4}) in$

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

b= $\frac{y}{4}$

Area of the square which is L² can now be said to be;

$A_S=(\frac{y}{4})^2 = \frac{y^2}{16}$

On the otherhand; let the radius (r) of the circle be;

2πr = 60-y

$r = \frac{60-y}{2\pi }$

Area of the circle which is πr² can now be;

$A_C= \pi (\frac{60-y}{2\pi } )^2$

$=( \frac{60-y}{4\pi } )^2$

Total Area (A);

A = $A_S+A_C$

= $\frac{y^2}{16} +(\frac{60-y}{4\pi } )^2$

For the smallest possible area; $\frac{dA}{dy}=0$

∴ $\frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0$

If we divide through with (2) and each entity move to the opposite side; we have:

$\frac{y}{18}=\frac{(60-y)}{2\pi}$

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

$y= \frac{240}{\pi+4}$

∴ since $y= \frac{240}{\pi+4}$ , we can determine for the length of the circle ;

60-y can now be;

= $60-\frac{240}{\pi+4}$

= $\frac{(\pi+4)*60-240}{\pi+40}$

= $\frac{60\pi+240-240}{\pi+4}$

= $(\frac{60\pi}{\pi+4})in$

also, the length of wire for the square (y) ; $y= (\frac{240}{\pi+4})in$

The smallest possible area (A) = $\frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})$

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0

3 years ago

Square A has an area of 18a2 + 862 – 24ab.

alina1380 [7]

I don’t know but you can go download Conects. :)

7 0

3 years ago

What’s the area and perimeter for this problem?

notka56 [123]

Answer:

the area of the triangle is 41

the perimiter of the triangle is 33.25

Step-by-step explanation:

4 0

2 years ago

Which equation can be used to find the two numbers whose ratio is 3 to 2 and that have a sum of 35

dusya [7]

Idk like 3+2 _=5
35
--- = 7
5
3:2
21:14

4 0

3 years ago

Read 2 more answers

Solve -6 (4-x) <-4 (x + 1).<br> O A. x ≤2<br> B. x > 3<br> OC. x <3<br> OD. 2

emmainna [20.7K]

Answer:

Step-by-step explanation:

-6(4 - x) <= -4(x + 1)

-24 + 6x <= -4x - 4

-24 + 10x <= -4

10x <= 20

x <= 2

5 0

2 years ago