You can compare irrational numbers using rational approximation.

This famous clock tower has a clock face with a diameter of 23 feet. What is the approximate area of this clock face

pashok25 [27]

Answer:

Therefore the approximate area of this clock face is 415.3 feet².

Step-by-step explanation:

Given:

Clock is of Circular Shape,

Diameter = 23 feet

$Radius =r =\dfrac{diameter}{2}=\dfrac{23}{2}=11.5\ feet$

To Find :

Area of Clock Face = ?

Solution:

Area of Circle having Radius 'r' is given as,

$\textrm{Area of Circle}=\pi r^{2}$

Substituting the values we get

$\textrm{Area of Clock Face}=3.14\times (11.5)^{2}=415.265=415.3\ feet^{2}$

Therefore the approximate area of this clock face is 415.3 feet².

7 0

2 years ago

A coin collector has $45 in just dimes and quarters in a piggy bank he counted all the coins and there are 240 total how many ea

Whitepunk [10]

Answer:

The number of <u>dimes are 100</u> and number of <u>quarters are 140.</u>

Step-by-step explanation:

Let the number of dimes be 'd' and quarters be 'q'.

Given:

The sum of amount is $45.

The total number of coins are 240.

1 dime = $0.10

∴ 'd' dimes = $\$0.10d$

1 quarter = $0.25

∴ 'q' quarters = $\$0.25q$

Now, as per question:

$d+m=240-----1\\0.1d+0.25q=45---2$

Multiplying equation (1) by -0.1 and adding the result to equation (2), we get:

$-0.1d-0.1q=240\times -0.1\\-0.1d-0.1q=-24\\0.1d+0.25q=45\\-----------\\0.15q=21\\q=\frac{21}{0.15}=140\\\\d=240-q=240-140=100$

Therefore, the number of dimes are 100 and number of quarters are 140.

7 0

2 years ago

Use the rewritten formula to find the width of a rectangle with an area of 42 square inches and a length of 16.8 inches.

Leviafan [203]

Length * Width = Area

Width = Area / Length

W = 42 / 16.8

W = 2.5 inches

4 0

2 years ago

Read 2 more answers

[30 POINTS] Please help!!!

Len [333]

Answer:

Part 1) $y=1.5x+5$

Part 2) $y=-(2/3)x-(11/3)$

Part 3) $y=0.25x+2.75$

Part 4) $y=-2x+5$

Part 5) $y=0.5x-1$

Part 6) The graph in the attached figure

Step-by-step explanation:

Part 1) we have

$m=3/2=1.5$

$point(-2,2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-2=1.5(x+2)$

$y=1.5x+3+2$

$y=1.5x+5$

Part 2) we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

so

$m1*m2=-1$

the slope of the line 1 is equal to

$m1=1.5$

Find the slope m2

$1.5*m2=-1$

$m2=-2/3$

Find the equation of the line 2

we have

$m2=-2/3$

$point(-7,1)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-1=(-2/3)(x+7)$

$y=-(2/3)x-(14/3)+1$

$y=-(2/3)x-(11/3)$

Part 3) we have

$m=1/4=0.25$

$point(1,3)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-3=0.25(x-1)$

$y=0.25x-0.25+3$

$y=0.25x+2.75$

Part 4) we have

$m=-2$

$b=5$ -----> y-intercept

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

substitute the values

$y=-2x+5$

Part 5) we have that

The slope of the line 4 is equal to $-2$

so

the slope of the line perpendicular to the line 4 is equal to

$-2*m=-1\\m=(1/2)=0.5$

therefore

in this problem we have

$m=0.5$

$point(-2,-2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y+2=0.5(x+2)$

$y=0.5x+1-2$

$y=0.5x-1$

Part 6)

using a graphing tool

see the attached figure

3 0

2 years ago

A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school coll

Mademuasel [1]

Amount of money collected in the 2-day fundraiser is represented by the following equations:

12x + 4y = 152 .................. (i)
32x + 12y = 420 .................. (ii)

where x is the cost of a chicken lunch and y is the cost of a vegetarian lunch

Multiplying (i) with 3 and subtracting it from (ii)

36x + 12y - (32x + 12y) = 456 - 420

⇒ 4x = 36

⇒ x = 9

Put value of x in (i)

⇒ 12 × 9 + 4y = 152

⇒ 108 + 4y = 152

⇒ 4y = 44

⇒ y = 11

Hence, cost of the vegetarian meal is 11.

7 0

2 years ago