Fill in the blanks to find the quotient 5/8 divided by 3 3/4 . Give the quotient as a fraction in simplest form.

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

4 years ago

40 students at a particular school are randomly selected for a survey. 18 have blue eyes. If there are 400 students at this scho

podryga [215]

A reasonable estimate would be 180 students with blue eyes

7 0

3 years ago

Read 2 more answers

How to find median with even amount of numbers?

Paladinen [302]

Sort the numbers in ascending or descending order, then eliminate the greatest and least numbers until you're left with the middle two. The median is the average of the last two numbers.

For example, the median for the set $\{2,10,-1,4\}=\{-1,2,4,10\}$ is 3 because the middle two numbers are 2 and 4, and their average is $\dfrac{2+4}2=3$ .

8 0

3 years ago

A bookstore manager marks down the price of older hardcover books, which originally sell for b dollars, by 42%. Part 1 out of 4

BigorU [14]

Answer:

0.42

Step-by-step explanation:

The original price of the old hardcover books was sold for b dollars. But the manager markdown the hardcover books by 42%.

The expression of the markdown using a decimal can be represented below.

Recall the markdown is 42 %. If you want to convert from percentage to a decimal, you have to move the decimal point two places to the left . The percentage sign is removed at this stage and the value is represent in decimal. Or you can just divide the percentage value by 100.

In our case the percentage value can be solved as 42/100 = 0.42 in decimal or by just simply moving the decimal points two places to the left which is 0.42.

6 0

3 years ago

Use the arc length formula and the given information to find r.. s = 16 cm, θ = 48°; r = ?

saveliy_v [14]

Answer:

The value for r is 19.1 cm

Step-by-step explanation:

We have been given that s = 16 cm, θ = 48° and we have to find the radius r.

We know the relation

$\theta=\frac{s}{r}\\\\r=\frac{s}{\theta},\text{ where }\theta \text{ is in radian}$