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3 years ago

Alan had already read 12 books this year before joining a book club, and he plans to read 1

Mathematics

1 answer:

Verizon [17]3 years ago

5 0

Respuesta:

Step-by-step explanation:

7 libros

12 - 19 ⇒ 7

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A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the

creativ13 [48]

Answer:

$A(\theta)=\frac{162 \theta}{(\theta+2)^2}$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

$2r+s=18$

$s=r \theta$

$2r+r \theta=18$

solve for r

$r=\frac{18}{2+\theta}$

step 2

Find the value of s

$s=r \theta$

substitute the value of r

$s=\frac{18}{2+\theta}\theta$

step 3

we know that

The area of complete circle is equal to

$A=\pi r^{2}$

The complete circle subtends a central angle of 2π radians

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

$\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}$

substitute the value of r

$A=\frac{(\frac{18}{2+\theta})^2\theta}{2}$

$A=\frac{162 \theta}{(\theta+2)^2}$

Convert to function notation

$A(\theta)=\frac{162 \theta}{(\theta+2)^2}$

6 0

3 years ago

Solve for b: b² = 8b + 84

levacccp [35]

B² = 8b + 84
b² - 8b - 84 = 0
b = -(-8) +/- √((8)² - 4(1)(-84))
 2(1)
b = 8 +/- √(64 + 336)
 2
b = 8 +/- √(400)
 2
b = 8 +/- 20
 2
b = 4 + 10
b = 4 + 10 b = 4 - 10
b = 14 b = -6

4 0

3 years ago

The function A = 15x - x2, where x is the width in yards, gives the area A of a llama pen in square yards. Make a table using 1/

Mnenie [13.5K]

Answer:

The width which gives the greatest area is 7.5 yd

Step-by-step explanation:

This is an application of differential calculus. Given the area as a function of the width, we simply need to differentiate the function with respect to x and equate to zero which yields; 15-2x=0 since the slope of the graph is zero at the turning points. Solving for x yields, x=7.5 which indeed maximizes the area of the pen

6 0

3 years ago

Tim has twice as many marbles as Luke together they have 39 marbles how many marbles does time have

Travka [436]

Tim has 2 times as luke
t=2l
they have 29 goether
t+l=39
subsitute
2l+l=39
3l=39
divide by 3
l=13

subsitue
t=2l
t=2(13)
t=26

tim has 26 and luke has 13
I don't know how many marble Tim has but probably all of them since alll must die and then the marbles go to Time

3 0

3 years ago

Read 2 more answers

Evaluate the following expression: -2|9|. -18 -11 11 18

Blababa [14]

Answer:

-18 mat-way is good to use

6 0

3 years ago