A recipe that makes 7 servings calls for 1 1/6 cups of juice.

a 1ft long piece of wire needs to be divided into two pieces which will form the shape of a circle and a square. Determine the l

yan [13]

Answer:

Length of wire for circle is 0.44 ft

Length of wire for square is 0.56 ft

Step-by-step explanation:

Let x is circumference of the circle

then

(1-x) = perimeter of the square

Find the radius of the circle

r = (x/2.π)

Find the area of the circle

a = π(x/2π)^2

a = π(x^2/4π^2)

Cancel π

a = x^2/4π

Find the area of the square:

a = (1-x/4)^2

a = (1-2x+x^2)/16

Total area

A = (x^2/4π)+(1-2x+x^2/16)

A = 4x^2+3.142-6.284x+3.142x^2

A = 7.142x^2-6.284x+3.142

Find the axis of symmetry [x = -b/(2a)]

x = -(-6.284)/{2.(7.142)}

x = 6.284/14.284

x = 0.44 ft, the piece of wire creating a circle

and

1 - 0.44 = 0.56 ft, the piece of wire creating the square

These lengths should give minimum area of the circle and square together

7 0

2 years ago

Help due in 45 minutes!!

Nat2105 [25]

Answer:

(14,-1)

Step-by-step explanation:

okay so first you need to use the "x=4y+10" in the first equation.

Rewrite as

3(4y+10) +11y=7

Distribute the 3(4y+10)

Rewrite as

12y+30

You'll have the equation

12y +30 +11y= 7

Subtract the 7 from both sides

12y+30+11y-7= 0

Combine like terms

23y+23=0

the best thing to do here is divide the equation by 23.

23/23 = 1

you'll have

y + 1 = 0

this simplifies to

y= -1

use this y value to solve for x

the easiest way to do this is start with the equation

x = 4y +10

Substitute the y for -1

x = -4(-1) +10

x = 4 +10

x = 14

the solution point is

(14,-1)

3 0

3 years ago

If AB = 8 and BC = 24, then AC =<br><br> If AB = 17 and AC = 68, then BC =

Kryger [21]

Answer:

(i) The length of AC is 32 units, (ii) The length of BC is 51 units.

Step-by-step explanation:

(i) Let suppose that AB and BC are collinear to each other, that is, that both segments are contained in the same line. Algebraically, it can be translated into this identity:

$AC = AB + BC$

If we know that $AB = 8$ and $BC = 24$ , then:

$AC = 8 + 24$

$AC = 32$

The length of AC is 32 units.

(ii) Let suppose that AB and AC are collinear to each other, that is, that both segments are contained in the same line. Algebraically, it can be translated into this identity:

$AC = AB + BC$

$BC = AC - AB$

If we know that $AC = 68$ and $AB = 17$ , then:

$BC = 68-17$

$BC = 51$

The length of BC is 51 units.

6 0

3 years ago

there are 750 people at a football game. Out of this number, 320 are students. What percent of the people at the football game

Norma-Jean [14]

To do this problem you use is/of=percent/100
So:
320/750=x/100
cross multiply
32,000=750x
divide both sides by 750
x=42.66 repeating

ANSWER: X=42.66 REPEATING

3 0

3 years ago

Read 2 more answers

The expression 3xy+12y-5x+7w has how many terms in polynomial ??

bulgar [2K]

Answer:

4

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers