I NEED HELP WITH THIS ASAP PLEASE!

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

The distance between two cities on a map is 10 in. The actual distance between the cities is 135. What is the scale on the map?

spayn [35]

The scale on the map is 1 in = 13.5 units

135/10 = 13.5

4 0

3 years ago

The angle Johnny holds his pen on paper creates a linear pair. The measure of one angle is 13x + 7. The

tresset_1 [31]

<h3>The value of x is 4.10</h3>

<em><u>Solution:</u></em>

Given that,

The angle Johnny holds his pen on paper creates a linear pair

Angles in a linear pair are supplementary angles

Two angles are supplementary, when they add up to 180 degrees

The measure of one angle is 13x + 7

The measure of the second angle is one less than twice the first angle

Therefore,

Measure of second angle = twice the first angle - 1

Measure of second angle = 2(13x + 7) - 1

Measure of second angle = 26x + 14 - 1

Measure of second angle = 26x + 13

Therefore,

Measure of first angle + measure of second angle = 180

13x + 7 + 26x + 13 = 180

39x + 20 = 180

39x = 180 - 20

39x = 160

x = 4.1

Thus value of x is 4.10

3 0

3 years ago

"Which ratio does not belong with the other three?" Explain your reasoning." Help me on 3. Please

SIZIF [17.4K]

12:15 does not belong, since that is a ratio of 4:5, whilst the others are all 3:4.

8 0

3 years ago

Read 2 more answers

What is the factored form of the expression. (2n^2 + 5n + 3) (4n - 5)

7nadin3 [17]

So firstly, <u>the factor (4n - 5) cannot be further factored, so we will be focusing on 2n² + 5n + 3.</u>

So for this, we will be factoring by grouping. Firstly, what two terms have a product of 6n² and a sum of 5n? That would be 2n and 3n. Replace 5n with 2n + 3n:

$(2n^2 + 2n + 3n + 3)(4n - 5)$

Next, factor 2n² + 2n and 3n + 3 separately. Make sure that they have the same quantity on the inside of the parentheses:

$(2n(n+1)+3(n+1))(4n-5)$

Now we can rewrite this expression as<u> $(2n+3)(n+1)(4n-5)$ , which is your final answer.</u>

7 0

3 years ago