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3 years ago

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The circumference of a circle varies directly with its radius. if the circumference of a circle with a radius of 1.5 inches is 9

.42 in, what is the circumference of a circle with a radius of 9 in? use π = 3.14. round your answer to the nearest inch.

2 answers:

zavuch27 [327]3 years ago

7 0

Answer: 57 in.

Step-by-step explanation:

When two quantities x and y are directly proportional , then the equation to show direct proportion is given y :-

$\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}$ (1)

Given : The circumference of a circle varies directly with its radius.

Let c be the circumference of a circle with a radius of 9 in.

If the circumference of a circle with a radius of 1.5 inches is 9.42 in, then from (1) we have

$\dfrac{c}{9}=\dfrac{9.42}{1.5}\\\\\Rightarrow\ c=\dfrac{9.42}{1.5}\times9=56.52\approx57\ in.$

Hence, the circumference of a circle with a radius of 9 in is approximately 57 in.

Vitek1552 [10]3 years ago

6 0

<span>1) Circumference = 2πr
C = 2 x π x 9
C = 18π = 56.548... = 57 inches (to the nearest inch)

2) 6h = $52.50
1h = $52.50/6 = 8.75
11h = 8.75 x 11 = $96.25 = $96 (to the nearest cent)</span>

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First group rate is x+10, Second is x
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3 years ago

Please help: Find the volume of the solid. Use 3.14 for π.

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Answer:

The volume of the solid is 420m³

Step-by-step explanation:

The area of any pyramid is "1/3 · B · h", where B is the area of the base, and h is the height.

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1/3 · B · 15

Second, we need to find the area of the base of the pyramid. That's done easily by finding the area of a triangle ( $\frac{base * height}{2}$ → $\frac{24*7}{2}$ → $\frac{168}{2}$ → $84$ ) giving us 84 units. This puts another number into our equation.

1/3 · 84 · 15

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4 years ago

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3 years ago

The DiMonte Corporation invented a new type of sunglass lens. Their variable expenses are $12.66 per unit, and their fixed expen

Sladkaya [172]

Answer:

a)one lens: 111,212.66

15000 lenses: 301,100

b)y=111,200+12.66x

slope: 12.66

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d) 20.07

e) 19.2

f)decreases

Step-by-step explanation:

a) Cost of producing one lens

fixed expenses+variable expenses=111,200+12.66=111,212.66

Cost of producing 15,000 lenses

fixed expenses+variable expenses=111,200+12.66(15,000)=301,100

b)Expense function:

let y be the expense cost

let x be the number of lenses produced

y=111,200+12.66x

Slope:

The function is a line equation: y=mx+b where m is the slope.

In this case b=111,200 and m=12.66. So the slope is 12.66

c) the cost increases 12.66 dollars per unit of lens produced

d) The cost of producing 15000 lenses is:

111,200+12.66(15,000)=301,100

If DiMonte produces 15000 lenses, the average cost per lens is:

301,100/15000=20.073≈20.07

e)The cost of producing 17000 lenses is:

111,200+12.66(17,000)=326,420

If DiMonte produces 17000 lenses, the average cost per lens is:

326,420/17,000=19.2

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4 years ago

The length of each side of a square is 3 inches more than the length of each side of a small square. The sum of the areas of the

NeX [460]

Answer:

$\text{Smaller square's 15 inches, Bigger square's 18 inches}$

Step-by-step explanation:

GIVEN: The length of each side of a square is $3$ inches more than the length of each side of a small square. The sum of the areas of the square is $549$ inches.

TO FIND: the lengths of the sides of the two squares.

SOLUTION:

let the length of side of small square be $\text{x}$

Area of small square $=(\text{side})^2=\text{x}^2$

As length of each side of bigger square is $3\text{ inches}$ more than the smaller square

length of side of bigger square $=\text{x}+3\text{ inches}$

Area of bigger square $=(\text{x+3})^2$

Also

Sum of areas of both square $=549\text{ inch}^2$

$(\text{x})^2+(\text{x+3})^2=549$

$2\text{x}^2+6\text{x}+9=549$

$\text{x}^2+3\text{x}-270=0$

$\text{x}=15,-18$

as the length of side can never be negative

$\text{x}=15$

length of side of smaller square $=15\text{ inches}$

length of side of bigger square $=\text{x}+3\text{ inches}$ $=18\text{ inches}$

Hence the length of smaller and bigger square are $15\text{ inches}$ and $18\text{ inches}$ respectively.

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3 years ago